Prompt:
<|im_start|>user
To increase its corrosion resistance, chromium $(\mathrm{Cr})$ is diffused into steel at $980^{\circ} \mathrm{C}$. If during diffusion the surface concentration of chromium remains constant at $100 \%$, how long will it take (in days) to achieve a $\mathrm{Cr}$ concentration of $1.8 \%$ at a depth of $0.002 \mathrm{~cm}$ below the steel surface? Round your answer to 1 decimal place. $\left(D_{o}=0.54 \mathrm{~cm}^{2} / \mathrm{s} ; E_{A}=286 \mathrm{~kJ} / \mathrm{mol}\right.$ )
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
To increase its corrosion resistance, chromium $(\mathrm{Cr})$ is diffused into steel at $980^{\circ} \mathrm{C}$. If during diffusion the surface concentration of chromium remains constant at $100 \%$, how long will it take (in days) to achieve a $\mathrm{Cr}$ concentration of $1.8 \%$ at a depth of $0.002 \mathrm{~cm}$ below the steel surface? Round your answer to 1 decimal place. $\left(D_{o}=0.54 \mathrm{~cm}^{2} / \mathrm{s} ; E_{A}=286 \mathrm{~kJ} / \mathrm{mol}\right.$ )
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
To increase its corrosion resistance, chromium $(\mathrm{Cr})$ is diffused into steel at $980^{\circ} \mathrm{C}$. If during diffusion the surface concentration of chromium remains constant at $100 \%$, how long will it take (in days) to achieve a $\mathrm{Cr}$ concentration of $1.8 \%$ at a depth of $0.002 \mathrm{~cm}$ below the steel surface? Round your answer to 1 decimal place. $\left(D_{o}=0.54 \mathrm{~cm}^{2} / \mathrm{s} ; E_{A}=286 \mathrm{~kJ} / \mathrm{mol}\right.$ )
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Subproblem 0: What is the working temperature for silica glass in Celsius?

Solution: \boxed{1950}.

Final answer: The final answer is 1950. I hope it is correct.

Subproblem 1: What is the softening temperature for silica glass in Celsius?

Solution: \boxed{1700}.

Final answer: The final answer is 1700. I hope it is correct.

Subproblem 2: What is the working temperature for Pyrex in Celsius?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Subproblem 0: What is the working temperature for silica glass in Celsius?

Solution: \boxed{1950}.

Final answer: The final answer is 1950. I hope it is correct.

Subproblem 1: What is the softening temperature for silica glass in Celsius?

Solution: \boxed{1700}.

Final answer: The final answer is 1700. I hope it is correct.

Subproblem 2: What is the working temperature for Pyrex in Celsius?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Subproblem 0: What is the working temperature for silica glass in Celsius?

Solution: \boxed{1950}.

Final answer: The final answer is 1950. I hope it is correct.

Subproblem 1: What is the softening temperature for silica glass in Celsius?

Solution: \boxed{1700}.

Final answer: The final answer is 1700. I hope it is correct.

Subproblem 2: What is the working temperature for Pyrex in Celsius?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Subproblem 0: What is the working temperature for silica glass in Celsius?

Solution: \boxed{1950}.

Final answer: The final answer is 1950. I hope it is correct.

Subproblem 1: What is the softening temperature for silica glass in Celsius?

Solution: \boxed{1700}.

Final answer: The final answer is 1700. I hope it is correct.

Subproblem 2: What is the working temperature for Pyrex in Celsius?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Calculate the vacancy fraction in copper (Cu) in $\mathrm{~cm}^{-3}$ at the following temperatures. Measurements have determined the values of the enthalpy of vacancy formation, $\Delta \mathrm{H}_{\mathrm{V}}$, to be $1.03 \mathrm{eV}$ and the entropic prefactor, A, to be 1.1. Please format your answers as $n \times 10^x$ where $n$ is to 2 decimal places.

$20^{\circ} \mathrm{C}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Calculate the vacancy fraction in copper (Cu) in $\mathrm{~cm}^{-3}$ at the following temperatures. Measurements have determined the values of the enthalpy of vacancy formation, $\Delta \mathrm{H}_{\mathrm{V}}$, to be $1.03 \mathrm{eV}$ and the entropic prefactor, A, to be 1.1. Please format your answers as $n \times 10^x$ where $n$ is to 2 decimal places.

$20^{\circ} \mathrm{C}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Calculate the vacancy fraction in copper (Cu) in $\mathrm{~cm}^{-3}$ at the following temperatures. Measurements have determined the values of the enthalpy of vacancy formation, $\Delta \mathrm{H}_{\mathrm{V}}$, to be $1.03 \mathrm{eV}$ and the entropic prefactor, A, to be 1.1. Please format your answers as $n \times 10^x$ where $n$ is to 2 decimal places.

$20^{\circ} \mathrm{C}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Calculate the vacancy fraction in copper (Cu) in $\mathrm{~cm}^{-3}$ at the following temperatures. Measurements have determined the values of the enthalpy of vacancy formation, $\Delta \mathrm{H}_{\mathrm{V}}$, to be $1.03 \mathrm{eV}$ and the entropic prefactor, A, to be 1.1. Please format your answers as $n \times 10^x$ where $n$ is to 2 decimal places.

$20^{\circ} \mathrm{C}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: For aluminum at $300 \mathrm{~K}$,

Calculate the planar packing fraction (fractional area occupied by atoms) of the ( 110 ) plane. Please round your answer to 3 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: For aluminum at $300 \mathrm{~K}$,

Calculate the planar packing fraction (fractional area occupied by atoms) of the ( 110 ) plane. Please round your answer to 3 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: For aluminum at $300 \mathrm{~K}$,

Calculate the planar packing fraction (fractional area occupied by atoms) of the ( 110 ) plane. Please round your answer to 3 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: For aluminum at $300 \mathrm{~K}$,

Calculate the planar packing fraction (fractional area occupied by atoms) of the ( 110 ) plane. Please round your answer to 3 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the inter-ionic equilibrium distance in meters between the sodium and chlorine ions in a sodium chloride molecule knowing that the bond energy is $3.84 \mathrm{eV}$ and that the repulsive exponent is 8. Please format your answer as $n \times 10^x$ where $n$ is to 1 decimal place.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the inter-ionic equilibrium distance in meters between the sodium and chlorine ions in a sodium chloride molecule knowing that the bond energy is $3.84 \mathrm{eV}$ and that the repulsive exponent is 8. Please format your answer as $n \times 10^x$ where $n$ is to 1 decimal place.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the inter-ionic equilibrium distance in meters between the sodium and chlorine ions in a sodium chloride molecule knowing that the bond energy is $3.84 \mathrm{eV}$ and that the repulsive exponent is 8. Please format your answer as $n \times 10^x$ where $n$ is to 1 decimal place.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the inter-ionic equilibrium distance in meters between the sodium and chlorine ions in a sodium chloride molecule knowing that the bond energy is $3.84 \mathrm{eV}$ and that the repulsive exponent is 8. Please format your answer as $n \times 10^x$ where $n$ is to 1 decimal place.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: A formation energy of $2.0 \mathrm{eV}$ is required to create a vacancy in a particular metal. At $800^{\circ} \mathrm{C}$ there is one vacancy for every 10,000 atoms.

At what temperature (in Celsius) will there be one vacancy for every 1,000 atoms? Format your answer as an integer.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: A formation energy of $2.0 \mathrm{eV}$ is required to create a vacancy in a particular metal. At $800^{\circ} \mathrm{C}$ there is one vacancy for every 10,000 atoms.

At what temperature (in Celsius) will there be one vacancy for every 1,000 atoms? Format your answer as an integer.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: A formation energy of $2.0 \mathrm{eV}$ is required to create a vacancy in a particular metal. At $800^{\circ} \mathrm{C}$ there is one vacancy for every 10,000 atoms.

At what temperature (in Celsius) will there be one vacancy for every 1,000 atoms? Format your answer as an integer.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: A formation energy of $2.0 \mathrm{eV}$ is required to create a vacancy in a particular metal. At $800^{\circ} \mathrm{C}$ there is one vacancy for every 10,000 atoms.

At what temperature (in Celsius) will there be one vacancy for every 1,000 atoms? Format your answer as an integer.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
For $\mathrm{NaF}$ the repulsive (Born) exponent, $\mathrm{n}$, is 8.7. Making use of data given in your Periodic Table, calculate the crystal energy ( $\left.\Delta \mathrm{E}_{\text {cryst }}\right)$ in kJ/mole, to 1 decimal place.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
For $\mathrm{NaF}$ the repulsive (Born) exponent, $\mathrm{n}$, is 8.7. Making use of data given in your Periodic Table, calculate the crystal energy ( $\left.\Delta \mathrm{E}_{\text {cryst }}\right)$ in kJ/mole, to 1 decimal place.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
For $\mathrm{NaF}$ the repulsive (Born) exponent, $\mathrm{n}$, is 8.7. Making use of data given in your Periodic Table, calculate the crystal energy ( $\left.\Delta \mathrm{E}_{\text {cryst }}\right)$ in kJ/mole, to 1 decimal place.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
For $\mathrm{NaF}$ the repulsive (Born) exponent, $\mathrm{n}$, is 8.7. Making use of data given in your Periodic Table, calculate the crystal energy ( $\left.\Delta \mathrm{E}_{\text {cryst }}\right)$ in kJ/mole, to 1 decimal place.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Calculate the molecular weight in g/mole (to 2 decimal places) of each of the substances listed below.

Subproblem 0: $\mathrm{NH}_{4} \mathrm{OH}$

Solution: $\mathrm{NH}_{4} \mathrm{OH}$ :
$5 \times 1.01=5.05(\mathrm{H})$
$1 \times 14.01=14.01(\mathrm{~N})$
$1 \times 16.00=16.00(\mathrm{O})$
$\mathrm{NH}_{4} \mathrm{OH}= \boxed{35.06}$ g/mole

Final answer: The final answer is 35.06. I hope it is correct.

Subproblem 1: $\mathrm{NaHCO}_{3}$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Calculate the molecular weight in g/mole (to 2 decimal places) of each of the substances listed below.

Subproblem 0: $\mathrm{NH}_{4} \mathrm{OH}$

Solution: $\mathrm{NH}_{4} \mathrm{OH}$ :
$5 \times 1.01=5.05(\mathrm{H})$
$1 \times 14.01=14.01(\mathrm{~N})$
$1 \times 16.00=16.00(\mathrm{O})$
$\mathrm{NH}_{4} \mathrm{OH}= \boxed{35.06}$ g/mole

Final answer: The final answer is 35.06. I hope it is correct.

Subproblem 1: $\mathrm{NaHCO}_{3}$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Calculate the molecular weight in g/mole (to 2 decimal places) of each of the substances listed below.

Subproblem 0: $\mathrm{NH}_{4} \mathrm{OH}$

Solution: $\mathrm{NH}_{4} \mathrm{OH}$ :
$5 \times 1.01=5.05(\mathrm{H})$
$1 \times 14.01=14.01(\mathrm{~N})$
$1 \times 16.00=16.00(\mathrm{O})$
$\mathrm{NH}_{4} \mathrm{OH}= \boxed{35.06}$ g/mole

Final answer: The final answer is 35.06. I hope it is correct.

Subproblem 1: $\mathrm{NaHCO}_{3}$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Calculate the molecular weight in g/mole (to 2 decimal places) of each of the substances listed below.

Subproblem 0: $\mathrm{NH}_{4} \mathrm{OH}$

Solution: $\mathrm{NH}_{4} \mathrm{OH}$ :
$5 \times 1.01=5.05(\mathrm{H})$
$1 \times 14.01=14.01(\mathrm{~N})$
$1 \times 16.00=16.00(\mathrm{O})$
$\mathrm{NH}_{4} \mathrm{OH}= \boxed{35.06}$ g/mole

Final answer: The final answer is 35.06. I hope it is correct.

Subproblem 1: $\mathrm{NaHCO}_{3}$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
In iridium (Ir), the vacancy fraction, $n_{v} / \mathrm{N}$, is $3.091 \times 10^{-5}$ at $12340^{\circ} \mathrm{C}$ and $5.26 \times 10^{-3}$ at the melting point. Calculate the enthalpy of vacancy formation, $\Delta \mathrm{H}_{\mathrm{v}}$. Round your answer to 1 decimal place.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
In iridium (Ir), the vacancy fraction, $n_{v} / \mathrm{N}$, is $3.091 \times 10^{-5}$ at $12340^{\circ} \mathrm{C}$ and $5.26 \times 10^{-3}$ at the melting point. Calculate the enthalpy of vacancy formation, $\Delta \mathrm{H}_{\mathrm{v}}$. Round your answer to 1 decimal place.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
In iridium (Ir), the vacancy fraction, $n_{v} / \mathrm{N}$, is $3.091 \times 10^{-5}$ at $12340^{\circ} \mathrm{C}$ and $5.26 \times 10^{-3}$ at the melting point. Calculate the enthalpy of vacancy formation, $\Delta \mathrm{H}_{\mathrm{v}}$. Round your answer to 1 decimal place.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
In iridium (Ir), the vacancy fraction, $n_{v} / \mathrm{N}$, is $3.091 \times 10^{-5}$ at $12340^{\circ} \mathrm{C}$ and $5.26 \times 10^{-3}$ at the melting point. Calculate the enthalpy of vacancy formation, $\Delta \mathrm{H}_{\mathrm{v}}$. Round your answer to 1 decimal place.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
If no electron-hole pairs were produced in germanium (Ge) until the temperature reached the value corresponding to the energy gap, at what temperature (Celsius)  would Ge become conductive? Please format your answer as $n \times 10^x$ where n is to 1 decimal place. $\left(\mathrm{E}_{\mathrm{th}}=3 / 2 \mathrm{kT}\right)$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
If no electron-hole pairs were produced in germanium (Ge) until the temperature reached the value corresponding to the energy gap, at what temperature (Celsius)  would Ge become conductive? Please format your answer as $n \times 10^x$ where n is to 1 decimal place. $\left(\mathrm{E}_{\mathrm{th}}=3 / 2 \mathrm{kT}\right)$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
If no electron-hole pairs were produced in germanium (Ge) until the temperature reached the value corresponding to the energy gap, at what temperature (Celsius)  would Ge become conductive? Please format your answer as $n \times 10^x$ where n is to 1 decimal place. $\left(\mathrm{E}_{\mathrm{th}}=3 / 2 \mathrm{kT}\right)$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
If no electron-hole pairs were produced in germanium (Ge) until the temperature reached the value corresponding to the energy gap, at what temperature (Celsius)  would Ge become conductive? Please format your answer as $n \times 10^x$ where n is to 1 decimal place. $\left(\mathrm{E}_{\mathrm{th}}=3 / 2 \mathrm{kT}\right)$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: A first-order chemical reaction is found to have an activation energy $\left(E_{A}\right)$ of 250 $\mathrm{kJ} /$ mole and a pre-exponential (A) of $1.7 \times 10^{14} \mathrm{~s}^{-1}$.

Determine the rate constant at $\mathrm{T}=750^{\circ} \mathrm{C}$. Round your answer to 1 decimal place, in units of $\mathrm{s}^{-1}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: A first-order chemical reaction is found to have an activation energy $\left(E_{A}\right)$ of 250 $\mathrm{kJ} /$ mole and a pre-exponential (A) of $1.7 \times 10^{14} \mathrm{~s}^{-1}$.

Determine the rate constant at $\mathrm{T}=750^{\circ} \mathrm{C}$. Round your answer to 1 decimal place, in units of $\mathrm{s}^{-1}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: A first-order chemical reaction is found to have an activation energy $\left(E_{A}\right)$ of 250 $\mathrm{kJ} /$ mole and a pre-exponential (A) of $1.7 \times 10^{14} \mathrm{~s}^{-1}$.

Determine the rate constant at $\mathrm{T}=750^{\circ} \mathrm{C}$. Round your answer to 1 decimal place, in units of $\mathrm{s}^{-1}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: A first-order chemical reaction is found to have an activation energy $\left(E_{A}\right)$ of 250 $\mathrm{kJ} /$ mole and a pre-exponential (A) of $1.7 \times 10^{14} \mathrm{~s}^{-1}$.

Determine the rate constant at $\mathrm{T}=750^{\circ} \mathrm{C}$. Round your answer to 1 decimal place, in units of $\mathrm{s}^{-1}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
A cubic metal $(r=0.77 \AA$ ) exhibits plastic deformation by slip along $<111>$ directions. Determine its planar packing density (atoms $/ \mathrm{m}^{2}$) for its densest family of planes. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
A cubic metal $(r=0.77 \AA$ ) exhibits plastic deformation by slip along $<111>$ directions. Determine its planar packing density (atoms $/ \mathrm{m}^{2}$) for its densest family of planes. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
A cubic metal $(r=0.77 \AA$ ) exhibits plastic deformation by slip along $<111>$ directions. Determine its planar packing density (atoms $/ \mathrm{m}^{2}$) for its densest family of planes. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
A cubic metal $(r=0.77 \AA$ ) exhibits plastic deformation by slip along $<111>$ directions. Determine its planar packing density (atoms $/ \mathrm{m}^{2}$) for its densest family of planes. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the total void volume $(\mathrm{cm}^{3} / mole)$ for gold (Au) at $27^{\circ} \mathrm{C}$; make the hard-sphere approximation in your calculation. Note that the molar volume of gold (Au) is $10.3 \mathrm{~cm}^{3} / \mathrm{mole}$. Please round your answer to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the total void volume $(\mathrm{cm}^{3} / mole)$ for gold (Au) at $27^{\circ} \mathrm{C}$; make the hard-sphere approximation in your calculation. Note that the molar volume of gold (Au) is $10.3 \mathrm{~cm}^{3} / \mathrm{mole}$. Please round your answer to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the total void volume $(\mathrm{cm}^{3} / mole)$ for gold (Au) at $27^{\circ} \mathrm{C}$; make the hard-sphere approximation in your calculation. Note that the molar volume of gold (Au) is $10.3 \mathrm{~cm}^{3} / \mathrm{mole}$. Please round your answer to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the total void volume $(\mathrm{cm}^{3} / mole)$ for gold (Au) at $27^{\circ} \mathrm{C}$; make the hard-sphere approximation in your calculation. Note that the molar volume of gold (Au) is $10.3 \mathrm{~cm}^{3} / \mathrm{mole}$. Please round your answer to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Subproblem 0: What is the working temperature for silica glass in Celsius?

Solution: \boxed{1950}.

Final answer: The final answer is 1950. I hope it is correct.

Subproblem 1: What is the softening temperature for silica glass in Celsius?

Solution: \boxed{1700}.

Final answer: The final answer is 1700. I hope it is correct.

Subproblem 2: What is the working temperature for Pyrex in Celsius?

Solution: \boxed{1200}.

Final answer: The final answer is 1200. I hope it is correct.

Subproblem 3: What is the softening temperature for Pyrex in Celsius?

Solution: \boxed{800}.

Final answer: The final answer is 800. I hope it is correct.

Subproblem 4: What is the working temperature for soda-lime glass in Celsius?

Solution: \boxed{900}.

Final answer: The final answer is 900. I hope it is correct.

Subproblem 5: What is the softening temperature for soda-lime glass in Celsius?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Subproblem 0: What is the working temperature for silica glass in Celsius?

Solution: \boxed{1950}.

Final answer: The final answer is 1950. I hope it is correct.

Subproblem 1: What is the softening temperature for silica glass in Celsius?

Solution: \boxed{1700}.

Final answer: The final answer is 1700. I hope it is correct.

Subproblem 2: What is the working temperature for Pyrex in Celsius?

Solution: \boxed{1200}.

Final answer: The final answer is 1200. I hope it is correct.

Subproblem 3: What is the softening temperature for Pyrex in Celsius?

Solution: \boxed{800}.

Final answer: The final answer is 800. I hope it is correct.

Subproblem 4: What is the working temperature for soda-lime glass in Celsius?

Solution: \boxed{900}.

Final answer: The final answer is 900. I hope it is correct.

Subproblem 5: What is the softening temperature for soda-lime glass in Celsius?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Subproblem 0: What is the working temperature for silica glass in Celsius?

Solution: \boxed{1950}.

Final answer: The final answer is 1950. I hope it is correct.

Subproblem 1: What is the softening temperature for silica glass in Celsius?

Solution: \boxed{1700}.

Final answer: The final answer is 1700. I hope it is correct.

Subproblem 2: What is the working temperature for Pyrex in Celsius?

Solution: \boxed{1200}.

Final answer: The final answer is 1200. I hope it is correct.

Subproblem 3: What is the softening temperature for Pyrex in Celsius?

Solution: \boxed{800}.

Final answer: The final answer is 800. I hope it is correct.

Subproblem 4: What is the working temperature for soda-lime glass in Celsius?

Solution: \boxed{900}.

Final answer: The final answer is 900. I hope it is correct.

Subproblem 5: What is the softening temperature for soda-lime glass in Celsius?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Subproblem 0: What is the working temperature for silica glass in Celsius?

Solution: \boxed{1950}.

Final answer: The final answer is 1950. I hope it is correct.

Subproblem 1: What is the softening temperature for silica glass in Celsius?

Solution: \boxed{1700}.

Final answer: The final answer is 1700. I hope it is correct.

Subproblem 2: What is the working temperature for Pyrex in Celsius?

Solution: \boxed{1200}.

Final answer: The final answer is 1200. I hope it is correct.

Subproblem 3: What is the softening temperature for Pyrex in Celsius?

Solution: \boxed{800}.

Final answer: The final answer is 800. I hope it is correct.

Subproblem 4: What is the working temperature for soda-lime glass in Celsius?

Solution: \boxed{900}.

Final answer: The final answer is 900. I hope it is correct.

Subproblem 5: What is the softening temperature for soda-lime glass in Celsius?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
What is the maximum wavelength $(\lambda)$ (in meters) of radiation capable of second order diffraction in platinum (Pt)? Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
What is the maximum wavelength $(\lambda)$ (in meters) of radiation capable of second order diffraction in platinum (Pt)? Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
What is the maximum wavelength $(\lambda)$ (in meters) of radiation capable of second order diffraction in platinum (Pt)? Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
What is the maximum wavelength $(\lambda)$ (in meters) of radiation capable of second order diffraction in platinum (Pt)? Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
What is the activation energy of a process which is observed to increase by a factor of three when the temperature is increased from room temperature $\left(20^{\circ} \mathrm{C}\right)$ to $40^{\circ} \mathrm{C}$ ? Round your answer to 1 decimal place, and express it in $\mathrm{~kJ} / \mathrm{mole}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
What is the activation energy of a process which is observed to increase by a factor of three when the temperature is increased from room temperature $\left(20^{\circ} \mathrm{C}\right)$ to $40^{\circ} \mathrm{C}$ ? Round your answer to 1 decimal place, and express it in $\mathrm{~kJ} / \mathrm{mole}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
What is the activation energy of a process which is observed to increase by a factor of three when the temperature is increased from room temperature $\left(20^{\circ} \mathrm{C}\right)$ to $40^{\circ} \mathrm{C}$ ? Round your answer to 1 decimal place, and express it in $\mathrm{~kJ} / \mathrm{mole}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
What is the activation energy of a process which is observed to increase by a factor of three when the temperature is increased from room temperature $\left(20^{\circ} \mathrm{C}\right)$ to $40^{\circ} \mathrm{C}$ ? Round your answer to 1 decimal place, and express it in $\mathrm{~kJ} / \mathrm{mole}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
How much oxygen (in kg, to 3 decimal places) is required to completely convert 1 mole of $\mathrm{C}_{2} \mathrm{H}_{6}$ into $\mathrm{CO}_{2}$ and $\mathrm{H}_{2} \mathrm{O}$ ?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
How much oxygen (in kg, to 3 decimal places) is required to completely convert 1 mole of $\mathrm{C}_{2} \mathrm{H}_{6}$ into $\mathrm{CO}_{2}$ and $\mathrm{H}_{2} \mathrm{O}$ ?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
How much oxygen (in kg, to 3 decimal places) is required to completely convert 1 mole of $\mathrm{C}_{2} \mathrm{H}_{6}$ into $\mathrm{CO}_{2}$ and $\mathrm{H}_{2} \mathrm{O}$ ?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
How much oxygen (in kg, to 3 decimal places) is required to completely convert 1 mole of $\mathrm{C}_{2} \mathrm{H}_{6}$ into $\mathrm{CO}_{2}$ and $\mathrm{H}_{2} \mathrm{O}$ ?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the differences in relative electronegativity $(\Delta x$ in $e V)$ for the systems ${H}-{F}$ and ${C}-{F}$ given the following data:
$\begin{array}{cl}\text { Bond Energy } & {kJ} / \text { mole } \\ {H}_{2} & 436 \\ {~F}_{2} & 172 \\ {C}-{C} & 335 \\ {H}-{F} & 565 \\ {C}-{H} & 410\end{array}$
\\
Please format your answer to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the differences in relative electronegativity $(\Delta x$ in $e V)$ for the systems ${H}-{F}$ and ${C}-{F}$ given the following data:
$\begin{array}{cl}\text { Bond Energy } & {kJ} / \text { mole } \\ {H}_{2} & 436 \\ {~F}_{2} & 172 \\ {C}-{C} & 335 \\ {H}-{F} & 565 \\ {C}-{H} & 410\end{array}$
\\
Please format your answer to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the differences in relative electronegativity $(\Delta x$ in $e V)$ for the systems ${H}-{F}$ and ${C}-{F}$ given the following data:
$\begin{array}{cl}\text { Bond Energy } & {kJ} / \text { mole } \\ {H}_{2} & 436 \\ {~F}_{2} & 172 \\ {C}-{C} & 335 \\ {H}-{F} & 565 \\ {C}-{H} & 410\end{array}$
\\
Please format your answer to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the differences in relative electronegativity $(\Delta x$ in $e V)$ for the systems ${H}-{F}$ and ${C}-{F}$ given the following data:
$\begin{array}{cl}\text { Bond Energy } & {kJ} / \text { mole } \\ {H}_{2} & 436 \\ {~F}_{2} & 172 \\ {C}-{C} & 335 \\ {H}-{F} & 565 \\ {C}-{H} & 410\end{array}$
\\
Please format your answer to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: The number of electron-hole pairs in intrinsic germanium (Ge) is given by:
\[
n_{i}=9.7 \times 10^{15} \mathrm{~T}^{3 / 2} \mathrm{e}^{-\mathrm{E}_{g} / 2 \mathrm{KT}}\left[\mathrm{cm}^{3}\right] \quad\left(\mathrm{E}_{\mathrm{g}}=0.72 \mathrm{eV}\right)
\]

What is the density of pairs at $\mathrm{T}=20^{\circ} \mathrm{C}$, in inverse $\mathrm{cm}^3$? Please format your answer as $n \times 10^x$ where n is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: The number of electron-hole pairs in intrinsic germanium (Ge) is given by:
\[
n_{i}=9.7 \times 10^{15} \mathrm{~T}^{3 / 2} \mathrm{e}^{-\mathrm{E}_{g} / 2 \mathrm{KT}}\left[\mathrm{cm}^{3}\right] \quad\left(\mathrm{E}_{\mathrm{g}}=0.72 \mathrm{eV}\right)
\]

What is the density of pairs at $\mathrm{T}=20^{\circ} \mathrm{C}$, in inverse $\mathrm{cm}^3$? Please format your answer as $n \times 10^x$ where n is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: The number of electron-hole pairs in intrinsic germanium (Ge) is given by:
\[
n_{i}=9.7 \times 10^{15} \mathrm{~T}^{3 / 2} \mathrm{e}^{-\mathrm{E}_{g} / 2 \mathrm{KT}}\left[\mathrm{cm}^{3}\right] \quad\left(\mathrm{E}_{\mathrm{g}}=0.72 \mathrm{eV}\right)
\]

What is the density of pairs at $\mathrm{T}=20^{\circ} \mathrm{C}$, in inverse $\mathrm{cm}^3$? Please format your answer as $n \times 10^x$ where n is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: The number of electron-hole pairs in intrinsic germanium (Ge) is given by:
\[
n_{i}=9.7 \times 10^{15} \mathrm{~T}^{3 / 2} \mathrm{e}^{-\mathrm{E}_{g} / 2 \mathrm{KT}}\left[\mathrm{cm}^{3}\right] \quad\left(\mathrm{E}_{\mathrm{g}}=0.72 \mathrm{eV}\right)
\]

What is the density of pairs at $\mathrm{T}=20^{\circ} \mathrm{C}$, in inverse $\mathrm{cm}^3$? Please format your answer as $n \times 10^x$ where n is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: For light with a wavelength $(\lambda)$ of $408 \mathrm{~nm}$ determine:

Subproblem 0: the frequency in $s^{-1}$. Please format your answer as $n \times 10^x$, where $n$ is to 3 decimal places.

Solution: To solve this problem we must know the following relationships:
\[
\begin{aligned}
v \lambda &=c
\end{aligned}
\]
$v$ (frequency) $=\frac{c}{\lambda}=\frac{3 \times 10^{8} m / s}{408 \times 10^{-9} m}= \boxed{7.353e14} s^{-1}$

Final answer: The final answer is 7.353e14. I hope it is correct.

Subproblem 1: the wave number in $m^{-1}$. Please format your answer as $n \times 10^x$, where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: For light with a wavelength $(\lambda)$ of $408 \mathrm{~nm}$ determine:

Subproblem 0: the frequency in $s^{-1}$. Please format your answer as $n \times 10^x$, where $n$ is to 3 decimal places.

Solution: To solve this problem we must know the following relationships:
\[
\begin{aligned}
v \lambda &=c
\end{aligned}
\]
$v$ (frequency) $=\frac{c}{\lambda}=\frac{3 \times 10^{8} m / s}{408 \times 10^{-9} m}= \boxed{7.353e14} s^{-1}$

Final answer: The final answer is 7.353e14. I hope it is correct.

Subproblem 1: the wave number in $m^{-1}$. Please format your answer as $n \times 10^x$, where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: For light with a wavelength $(\lambda)$ of $408 \mathrm{~nm}$ determine:

Subproblem 0: the frequency in $s^{-1}$. Please format your answer as $n \times 10^x$, where $n$ is to 3 decimal places.

Solution: To solve this problem we must know the following relationships:
\[
\begin{aligned}
v \lambda &=c
\end{aligned}
\]
$v$ (frequency) $=\frac{c}{\lambda}=\frac{3 \times 10^{8} m / s}{408 \times 10^{-9} m}= \boxed{7.353e14} s^{-1}$

Final answer: The final answer is 7.353e14. I hope it is correct.

Subproblem 1: the wave number in $m^{-1}$. Please format your answer as $n \times 10^x$, where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: For light with a wavelength $(\lambda)$ of $408 \mathrm{~nm}$ determine:

Subproblem 0: the frequency in $s^{-1}$. Please format your answer as $n \times 10^x$, where $n$ is to 3 decimal places.

Solution: To solve this problem we must know the following relationships:
\[
\begin{aligned}
v \lambda &=c
\end{aligned}
\]
$v$ (frequency) $=\frac{c}{\lambda}=\frac{3 \times 10^{8} m / s}{408 \times 10^{-9} m}= \boxed{7.353e14} s^{-1}$

Final answer: The final answer is 7.353e14. I hope it is correct.

Subproblem 1: the wave number in $m^{-1}$. Please format your answer as $n \times 10^x$, where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Calculate the volume in mL of $0.25 \mathrm{M} \mathrm{NaI}$ that would be needed to precipitate all the $\mathrm{g}^{2+}$ ion from $45 \mathrm{~mL}$ of a $0.10 \mathrm{M} \mathrm{Hg}\left(\mathrm{NO}_{3}\right)_{2}$ solution according to the following reaction:
\[
2 \mathrm{NaI}(\mathrm{aq})+\mathrm{Hg}\left(\mathrm{NO}_{3}\right)_{2}(\mathrm{aq}) \rightarrow \mathrm{HgI}_{2}(\mathrm{~s})+2 \mathrm{NaNO}_{3}(\mathrm{aq})
\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Calculate the volume in mL of $0.25 \mathrm{M} \mathrm{NaI}$ that would be needed to precipitate all the $\mathrm{g}^{2+}$ ion from $45 \mathrm{~mL}$ of a $0.10 \mathrm{M} \mathrm{Hg}\left(\mathrm{NO}_{3}\right)_{2}$ solution according to the following reaction:
\[
2 \mathrm{NaI}(\mathrm{aq})+\mathrm{Hg}\left(\mathrm{NO}_{3}\right)_{2}(\mathrm{aq}) \rightarrow \mathrm{HgI}_{2}(\mathrm{~s})+2 \mathrm{NaNO}_{3}(\mathrm{aq})
\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Calculate the volume in mL of $0.25 \mathrm{M} \mathrm{NaI}$ that would be needed to precipitate all the $\mathrm{g}^{2+}$ ion from $45 \mathrm{~mL}$ of a $0.10 \mathrm{M} \mathrm{Hg}\left(\mathrm{NO}_{3}\right)_{2}$ solution according to the following reaction:
\[
2 \mathrm{NaI}(\mathrm{aq})+\mathrm{Hg}\left(\mathrm{NO}_{3}\right)_{2}(\mathrm{aq}) \rightarrow \mathrm{HgI}_{2}(\mathrm{~s})+2 \mathrm{NaNO}_{3}(\mathrm{aq})
\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Calculate the volume in mL of $0.25 \mathrm{M} \mathrm{NaI}$ that would be needed to precipitate all the $\mathrm{g}^{2+}$ ion from $45 \mathrm{~mL}$ of a $0.10 \mathrm{M} \mathrm{Hg}\left(\mathrm{NO}_{3}\right)_{2}$ solution according to the following reaction:
\[
2 \mathrm{NaI}(\mathrm{aq})+\mathrm{Hg}\left(\mathrm{NO}_{3}\right)_{2}(\mathrm{aq}) \rightarrow \mathrm{HgI}_{2}(\mathrm{~s})+2 \mathrm{NaNO}_{3}(\mathrm{aq})
\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
A slab of plate glass containing dissolved helium (He) is placed in a vacuum furnace at a temperature of $400^{\circ} \mathrm{C}$ to remove the helium from the glass. Before vacuum treatment, the concentration of helium is constant throughout the glass. After 10 minutes in vacuum at $400^{\circ} \mathrm{C}$, at what depth (in $\mu \mathrm{m}$) from the surface of the glass has the concentration of helium decreased to $1 / 3$ of its initial value? The diffusion coefficient of helium in the plate glass at the processing temperature has a value of $3.091 \times 10^{-6} \mathrm{~cm}^{2} / \mathrm{s}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
A slab of plate glass containing dissolved helium (He) is placed in a vacuum furnace at a temperature of $400^{\circ} \mathrm{C}$ to remove the helium from the glass. Before vacuum treatment, the concentration of helium is constant throughout the glass. After 10 minutes in vacuum at $400^{\circ} \mathrm{C}$, at what depth (in $\mu \mathrm{m}$) from the surface of the glass has the concentration of helium decreased to $1 / 3$ of its initial value? The diffusion coefficient of helium in the plate glass at the processing temperature has a value of $3.091 \times 10^{-6} \mathrm{~cm}^{2} / \mathrm{s}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
A slab of plate glass containing dissolved helium (He) is placed in a vacuum furnace at a temperature of $400^{\circ} \mathrm{C}$ to remove the helium from the glass. Before vacuum treatment, the concentration of helium is constant throughout the glass. After 10 minutes in vacuum at $400^{\circ} \mathrm{C}$, at what depth (in $\mu \mathrm{m}$) from the surface of the glass has the concentration of helium decreased to $1 / 3$ of its initial value? The diffusion coefficient of helium in the plate glass at the processing temperature has a value of $3.091 \times 10^{-6} \mathrm{~cm}^{2} / \mathrm{s}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
A slab of plate glass containing dissolved helium (He) is placed in a vacuum furnace at a temperature of $400^{\circ} \mathrm{C}$ to remove the helium from the glass. Before vacuum treatment, the concentration of helium is constant throughout the glass. After 10 minutes in vacuum at $400^{\circ} \mathrm{C}$, at what depth (in $\mu \mathrm{m}$) from the surface of the glass has the concentration of helium decreased to $1 / 3$ of its initial value? The diffusion coefficient of helium in the plate glass at the processing temperature has a value of $3.091 \times 10^{-6} \mathrm{~cm}^{2} / \mathrm{s}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Subproblem 0: What is the working temperature for silica glass in Celsius?

Solution: \boxed{1950}.

Final answer: The final answer is 1950. I hope it is correct.

Subproblem 1: What is the softening temperature for silica glass in Celsius?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Subproblem 0: What is the working temperature for silica glass in Celsius?

Solution: \boxed{1950}.

Final answer: The final answer is 1950. I hope it is correct.

Subproblem 1: What is the softening temperature for silica glass in Celsius?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Subproblem 0: What is the working temperature for silica glass in Celsius?

Solution: \boxed{1950}.

Final answer: The final answer is 1950. I hope it is correct.

Subproblem 1: What is the softening temperature for silica glass in Celsius?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Subproblem 0: What is the working temperature for silica glass in Celsius?

Solution: \boxed{1950}.

Final answer: The final answer is 1950. I hope it is correct.

Subproblem 1: What is the softening temperature for silica glass in Celsius?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Two lasers generate radiation of (1) $9.5 \mu {m}$ and (2) $0.1 \mu {m}$ respectively.

Subproblem 0: Determine the photon energy (in eV, to two decimal places) of the laser generating radiation of $9.5 \mu {m}$.

Solution: \[
\begin{aligned}
{E} &={h} v=\frac{{hc}}{\lambda} {J} \times \frac{1 {eV}}{1.6 \times 10^{-19} {~J}} \\
{E}_{1} &=\frac{{hc}}{9.5 \times 10^{-6}} \times \frac{1}{1.6 \times 10^{-19}} {eV}= \boxed{0.13} {eV}
\end{aligned}
\]

Final answer: The final answer is 0.13. I hope it is correct.

Subproblem 1: Determine the photon energy (in eV, to one decimal place) of the laser generating radiation of $0.1 \mu {m}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Two lasers generate radiation of (1) $9.5 \mu {m}$ and (2) $0.1 \mu {m}$ respectively.

Subproblem 0: Determine the photon energy (in eV, to two decimal places) of the laser generating radiation of $9.5 \mu {m}$.

Solution: \[
\begin{aligned}
{E} &={h} v=\frac{{hc}}{\lambda} {J} \times \frac{1 {eV}}{1.6 \times 10^{-19} {~J}} \\
{E}_{1} &=\frac{{hc}}{9.5 \times 10^{-6}} \times \frac{1}{1.6 \times 10^{-19}} {eV}= \boxed{0.13} {eV}
\end{aligned}
\]

Final answer: The final answer is 0.13. I hope it is correct.

Subproblem 1: Determine the photon energy (in eV, to one decimal place) of the laser generating radiation of $0.1 \mu {m}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Two lasers generate radiation of (1) $9.5 \mu {m}$ and (2) $0.1 \mu {m}$ respectively.

Subproblem 0: Determine the photon energy (in eV, to two decimal places) of the laser generating radiation of $9.5 \mu {m}$.

Solution: \[
\begin{aligned}
{E} &={h} v=\frac{{hc}}{\lambda} {J} \times \frac{1 {eV}}{1.6 \times 10^{-19} {~J}} \\
{E}_{1} &=\frac{{hc}}{9.5 \times 10^{-6}} \times \frac{1}{1.6 \times 10^{-19}} {eV}= \boxed{0.13} {eV}
\end{aligned}
\]

Final answer: The final answer is 0.13. I hope it is correct.

Subproblem 1: Determine the photon energy (in eV, to one decimal place) of the laser generating radiation of $0.1 \mu {m}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Two lasers generate radiation of (1) $9.5 \mu {m}$ and (2) $0.1 \mu {m}$ respectively.

Subproblem 0: Determine the photon energy (in eV, to two decimal places) of the laser generating radiation of $9.5 \mu {m}$.

Solution: \[
\begin{aligned}
{E} &={h} v=\frac{{hc}}{\lambda} {J} \times \frac{1 {eV}}{1.6 \times 10^{-19} {~J}} \\
{E}_{1} &=\frac{{hc}}{9.5 \times 10^{-6}} \times \frac{1}{1.6 \times 10^{-19}} {eV}= \boxed{0.13} {eV}
\end{aligned}
\]

Final answer: The final answer is 0.13. I hope it is correct.

Subproblem 1: Determine the photon energy (in eV, to one decimal place) of the laser generating radiation of $0.1 \mu {m}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: $\mathrm{Bi}_{2} \mathrm{~S}_{3}$ dissolves in water according to the following reaction:
\[
\mathrm{Bi}_{2} \mathrm{~S}_{3}(\mathrm{~s}) \Leftrightarrow 2 \mathrm{Bi}^{3+}(\mathrm{aq})+3 \mathrm{~s}^{2-}(\mathrm{aq})
\]
for which the solubility product, $\mathrm{K}_{\mathrm{sp}}$, has the value of $1.6 \times 10^{-72}$ at room temperature.

At room temperature how many moles of $\mathrm{Bi}_{2} \mathrm{~S}_{3}$ will dissolve in $3.091 \times 10^{6}$ liters of water? Please format your answer as $n \times 10^x$ where $n$ is to 1 decimal place.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: $\mathrm{Bi}_{2} \mathrm{~S}_{3}$ dissolves in water according to the following reaction:
\[
\mathrm{Bi}_{2} \mathrm{~S}_{3}(\mathrm{~s}) \Leftrightarrow 2 \mathrm{Bi}^{3+}(\mathrm{aq})+3 \mathrm{~s}^{2-}(\mathrm{aq})
\]
for which the solubility product, $\mathrm{K}_{\mathrm{sp}}$, has the value of $1.6 \times 10^{-72}$ at room temperature.

At room temperature how many moles of $\mathrm{Bi}_{2} \mathrm{~S}_{3}$ will dissolve in $3.091 \times 10^{6}$ liters of water? Please format your answer as $n \times 10^x$ where $n$ is to 1 decimal place.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: $\mathrm{Bi}_{2} \mathrm{~S}_{3}$ dissolves in water according to the following reaction:
\[
\mathrm{Bi}_{2} \mathrm{~S}_{3}(\mathrm{~s}) \Leftrightarrow 2 \mathrm{Bi}^{3+}(\mathrm{aq})+3 \mathrm{~s}^{2-}(\mathrm{aq})
\]
for which the solubility product, $\mathrm{K}_{\mathrm{sp}}$, has the value of $1.6 \times 10^{-72}$ at room temperature.

At room temperature how many moles of $\mathrm{Bi}_{2} \mathrm{~S}_{3}$ will dissolve in $3.091 \times 10^{6}$ liters of water? Please format your answer as $n \times 10^x$ where $n$ is to 1 decimal place.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: $\mathrm{Bi}_{2} \mathrm{~S}_{3}$ dissolves in water according to the following reaction:
\[
\mathrm{Bi}_{2} \mathrm{~S}_{3}(\mathrm{~s}) \Leftrightarrow 2 \mathrm{Bi}^{3+}(\mathrm{aq})+3 \mathrm{~s}^{2-}(\mathrm{aq})
\]
for which the solubility product, $\mathrm{K}_{\mathrm{sp}}$, has the value of $1.6 \times 10^{-72}$ at room temperature.

At room temperature how many moles of $\mathrm{Bi}_{2} \mathrm{~S}_{3}$ will dissolve in $3.091 \times 10^{6}$ liters of water? Please format your answer as $n \times 10^x$ where $n$ is to 1 decimal place.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Whiskey, suspected to be of the "moonshine" variety, is analyzed for its age by determining its amount of naturally occurring tritium (T) which is a radioactive hydrogen isotope $\left({ }^{3} \mathrm{H}\right)$ with a half-life of $12.5$ years. In this "shine" the activity is found to be $6 \%$ of that encountered in fresh bourbon. What is the age (in years) of the whiskey in question?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Whiskey, suspected to be of the "moonshine" variety, is analyzed for its age by determining its amount of naturally occurring tritium (T) which is a radioactive hydrogen isotope $\left({ }^{3} \mathrm{H}\right)$ with a half-life of $12.5$ years. In this "shine" the activity is found to be $6 \%$ of that encountered in fresh bourbon. What is the age (in years) of the whiskey in question?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Whiskey, suspected to be of the "moonshine" variety, is analyzed for its age by determining its amount of naturally occurring tritium (T) which is a radioactive hydrogen isotope $\left({ }^{3} \mathrm{H}\right)$ with a half-life of $12.5$ years. In this "shine" the activity is found to be $6 \%$ of that encountered in fresh bourbon. What is the age (in years) of the whiskey in question?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Whiskey, suspected to be of the "moonshine" variety, is analyzed for its age by determining its amount of naturally occurring tritium (T) which is a radioactive hydrogen isotope $\left({ }^{3} \mathrm{H}\right)$ with a half-life of $12.5$ years. In this "shine" the activity is found to be $6 \%$ of that encountered in fresh bourbon. What is the age (in years) of the whiskey in question?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Subproblem 0: What is the working temperature for silica glass in Celsius?

Solution: \boxed{1950}.

Final answer: The final answer is 1950. I hope it is correct.

Subproblem 1: What is the softening temperature for silica glass in Celsius?

Solution: \boxed{1700}.

Final answer: The final answer is 1700. I hope it is correct.

Subproblem 2: What is the working temperature for Pyrex in Celsius?

Solution: \boxed{1200}.

Final answer: The final answer is 1200. I hope it is correct.

Subproblem 3: What is the softening temperature for Pyrex in Celsius?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Subproblem 0: What is the working temperature for silica glass in Celsius?

Solution: \boxed{1950}.

Final answer: The final answer is 1950. I hope it is correct.

Subproblem 1: What is the softening temperature for silica glass in Celsius?

Solution: \boxed{1700}.

Final answer: The final answer is 1700. I hope it is correct.

Subproblem 2: What is the working temperature for Pyrex in Celsius?

Solution: \boxed{1200}.

Final answer: The final answer is 1200. I hope it is correct.

Subproblem 3: What is the softening temperature for Pyrex in Celsius?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Subproblem 0: What is the working temperature for silica glass in Celsius?

Solution: \boxed{1950}.

Final answer: The final answer is 1950. I hope it is correct.

Subproblem 1: What is the softening temperature for silica glass in Celsius?

Solution: \boxed{1700}.

Final answer: The final answer is 1700. I hope it is correct.

Subproblem 2: What is the working temperature for Pyrex in Celsius?

Solution: \boxed{1200}.

Final answer: The final answer is 1200. I hope it is correct.

Subproblem 3: What is the softening temperature for Pyrex in Celsius?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Subproblem 0: What is the working temperature for silica glass in Celsius?

Solution: \boxed{1950}.

Final answer: The final answer is 1950. I hope it is correct.

Subproblem 1: What is the softening temperature for silica glass in Celsius?

Solution: \boxed{1700}.

Final answer: The final answer is 1700. I hope it is correct.

Subproblem 2: What is the working temperature for Pyrex in Celsius?

Solution: \boxed{1200}.

Final answer: The final answer is 1200. I hope it is correct.

Subproblem 3: What is the softening temperature for Pyrex in Celsius?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: A first-order chemical reaction is found to have an activation energy $\left(E_{A}\right)$ of 250 $\mathrm{kJ} /$ mole and a pre-exponential (A) of $1.7 \times 10^{14} \mathrm{~s}^{-1}$.

Subproblem 0: Determine the rate constant at $\mathrm{T}=750^{\circ} \mathrm{C}$. Round your answer to 1 decimal place, in units of $\mathrm{s}^{-1}$.

Solution: $\mathrm{k}=\mathrm{Ae} \mathrm{e}^{-\frac{\mathrm{E}_{\mathrm{A}}}{\mathrm{RT}}}=1.7 \times 10^{14} \times \mathrm{e}^{-\frac{2.5 \times 10^{5}}{8.31 \times 10^{23}}}= \boxed{28.8} \mathrm{~s}^{-1}$

Final answer: The final answer is 28.8. I hope it is correct.

Subproblem 1: What percent of the reaction will be completed at $600^{\circ} \mathrm{C}$ in a period of 10 minutes?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: A first-order chemical reaction is found to have an activation energy $\left(E_{A}\right)$ of 250 $\mathrm{kJ} /$ mole and a pre-exponential (A) of $1.7 \times 10^{14} \mathrm{~s}^{-1}$.

Subproblem 0: Determine the rate constant at $\mathrm{T}=750^{\circ} \mathrm{C}$. Round your answer to 1 decimal place, in units of $\mathrm{s}^{-1}$.

Solution: $\mathrm{k}=\mathrm{Ae} \mathrm{e}^{-\frac{\mathrm{E}_{\mathrm{A}}}{\mathrm{RT}}}=1.7 \times 10^{14} \times \mathrm{e}^{-\frac{2.5 \times 10^{5}}{8.31 \times 10^{23}}}= \boxed{28.8} \mathrm{~s}^{-1}$

Final answer: The final answer is 28.8. I hope it is correct.

Subproblem 1: What percent of the reaction will be completed at $600^{\circ} \mathrm{C}$ in a period of 10 minutes?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: A first-order chemical reaction is found to have an activation energy $\left(E_{A}\right)$ of 250 $\mathrm{kJ} /$ mole and a pre-exponential (A) of $1.7 \times 10^{14} \mathrm{~s}^{-1}$.

Subproblem 0: Determine the rate constant at $\mathrm{T}=750^{\circ} \mathrm{C}$. Round your answer to 1 decimal place, in units of $\mathrm{s}^{-1}$.

Solution: $\mathrm{k}=\mathrm{Ae} \mathrm{e}^{-\frac{\mathrm{E}_{\mathrm{A}}}{\mathrm{RT}}}=1.7 \times 10^{14} \times \mathrm{e}^{-\frac{2.5 \times 10^{5}}{8.31 \times 10^{23}}}= \boxed{28.8} \mathrm{~s}^{-1}$

Final answer: The final answer is 28.8. I hope it is correct.

Subproblem 1: What percent of the reaction will be completed at $600^{\circ} \mathrm{C}$ in a period of 10 minutes?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: A first-order chemical reaction is found to have an activation energy $\left(E_{A}\right)$ of 250 $\mathrm{kJ} /$ mole and a pre-exponential (A) of $1.7 \times 10^{14} \mathrm{~s}^{-1}$.

Subproblem 0: Determine the rate constant at $\mathrm{T}=750^{\circ} \mathrm{C}$. Round your answer to 1 decimal place, in units of $\mathrm{s}^{-1}$.

Solution: $\mathrm{k}=\mathrm{Ae} \mathrm{e}^{-\frac{\mathrm{E}_{\mathrm{A}}}{\mathrm{RT}}}=1.7 \times 10^{14} \times \mathrm{e}^{-\frac{2.5 \times 10^{5}}{8.31 \times 10^{23}}}= \boxed{28.8} \mathrm{~s}^{-1}$

Final answer: The final answer is 28.8. I hope it is correct.

Subproblem 1: What percent of the reaction will be completed at $600^{\circ} \mathrm{C}$ in a period of 10 minutes?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the energy gap (in eV) between the electronic states $n=7$ and $n=8$ in hydrogen. Please format your answer as $n \times 10^x$ where $n$ is to 1 decimal place.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the energy gap (in eV) between the electronic states $n=7$ and $n=8$ in hydrogen. Please format your answer as $n \times 10^x$ where $n$ is to 1 decimal place.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the energy gap (in eV) between the electronic states $n=7$ and $n=8$ in hydrogen. Please format your answer as $n \times 10^x$ where $n$ is to 1 decimal place.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the energy gap (in eV) between the electronic states $n=7$ and $n=8$ in hydrogen. Please format your answer as $n \times 10^x$ where $n$ is to 1 decimal place.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: The decay rate of ${ }^{14} \mathrm{C}$ in living tissue is $15.3$ disintegrations per minute per gram of carbon. Experimentally, the decay rate can be measured to $\pm 0.1$ disintegrations per minute per gram of carbon. The half-life of ${ }^{14} \mathrm{C}$ is 5730 years.

What is the maximum age of a sample that can be dated, in years?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: The decay rate of ${ }^{14} \mathrm{C}$ in living tissue is $15.3$ disintegrations per minute per gram of carbon. Experimentally, the decay rate can be measured to $\pm 0.1$ disintegrations per minute per gram of carbon. The half-life of ${ }^{14} \mathrm{C}$ is 5730 years.

What is the maximum age of a sample that can be dated, in years?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: The decay rate of ${ }^{14} \mathrm{C}$ in living tissue is $15.3$ disintegrations per minute per gram of carbon. Experimentally, the decay rate can be measured to $\pm 0.1$ disintegrations per minute per gram of carbon. The half-life of ${ }^{14} \mathrm{C}$ is 5730 years.

What is the maximum age of a sample that can be dated, in years?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: The decay rate of ${ }^{14} \mathrm{C}$ in living tissue is $15.3$ disintegrations per minute per gram of carbon. Experimentally, the decay rate can be measured to $\pm 0.1$ disintegrations per minute per gram of carbon. The half-life of ${ }^{14} \mathrm{C}$ is 5730 years.

What is the maximum age of a sample that can be dated, in years?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Estimate the ionic radius of ${Cs}^{+}$ in Angstroms to 2 decimal places. The lattice energy of $\mathrm{CsCl}$ is $633 \mathrm{~kJ} / \mathrm{mol}$. For $\mathrm{CsCl}$ the Madelung constant, $\mathrm{M}$, is $1.763$, and the Born exponent, $\mathrm{n}$, is 10.7. The ionic radius of $\mathrm{Cl}^{-}$is known to be $1.81 \AA$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Estimate the ionic radius of ${Cs}^{+}$ in Angstroms to 2 decimal places. The lattice energy of $\mathrm{CsCl}$ is $633 \mathrm{~kJ} / \mathrm{mol}$. For $\mathrm{CsCl}$ the Madelung constant, $\mathrm{M}$, is $1.763$, and the Born exponent, $\mathrm{n}$, is 10.7. The ionic radius of $\mathrm{Cl}^{-}$is known to be $1.81 \AA$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Estimate the ionic radius of ${Cs}^{+}$ in Angstroms to 2 decimal places. The lattice energy of $\mathrm{CsCl}$ is $633 \mathrm{~kJ} / \mathrm{mol}$. For $\mathrm{CsCl}$ the Madelung constant, $\mathrm{M}$, is $1.763$, and the Born exponent, $\mathrm{n}$, is 10.7. The ionic radius of $\mathrm{Cl}^{-}$is known to be $1.81 \AA$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Estimate the ionic radius of ${Cs}^{+}$ in Angstroms to 2 decimal places. The lattice energy of $\mathrm{CsCl}$ is $633 \mathrm{~kJ} / \mathrm{mol}$. For $\mathrm{CsCl}$ the Madelung constant, $\mathrm{M}$, is $1.763$, and the Born exponent, $\mathrm{n}$, is 10.7. The ionic radius of $\mathrm{Cl}^{-}$is known to be $1.81 \AA$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Given the ionic radii, $\mathrm{Cs}^{+}=1.67 \AA, \mathrm{Cl}^{-}=1.81 \AA$, and the Madelung constant $\mathrm{M}(\mathrm{CsCl})=1.763$, determine to the best of your ability the molar Crystal energy ( $\Delta \mathrm{E}_{\text {cryst }}$ ) for $\mathrm{CsCl}$. Please format your answer as $n \times 10^x$ where n is to 2 decimal places; answer in $\mathrm{J} / \text{mole}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Given the ionic radii, $\mathrm{Cs}^{+}=1.67 \AA, \mathrm{Cl}^{-}=1.81 \AA$, and the Madelung constant $\mathrm{M}(\mathrm{CsCl})=1.763$, determine to the best of your ability the molar Crystal energy ( $\Delta \mathrm{E}_{\text {cryst }}$ ) for $\mathrm{CsCl}$. Please format your answer as $n \times 10^x$ where n is to 2 decimal places; answer in $\mathrm{J} / \text{mole}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Given the ionic radii, $\mathrm{Cs}^{+}=1.67 \AA, \mathrm{Cl}^{-}=1.81 \AA$, and the Madelung constant $\mathrm{M}(\mathrm{CsCl})=1.763$, determine to the best of your ability the molar Crystal energy ( $\Delta \mathrm{E}_{\text {cryst }}$ ) for $\mathrm{CsCl}$. Please format your answer as $n \times 10^x$ where n is to 2 decimal places; answer in $\mathrm{J} / \text{mole}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Given the ionic radii, $\mathrm{Cs}^{+}=1.67 \AA, \mathrm{Cl}^{-}=1.81 \AA$, and the Madelung constant $\mathrm{M}(\mathrm{CsCl})=1.763$, determine to the best of your ability the molar Crystal energy ( $\Delta \mathrm{E}_{\text {cryst }}$ ) for $\mathrm{CsCl}$. Please format your answer as $n \times 10^x$ where n is to 2 decimal places; answer in $\mathrm{J} / \text{mole}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the amount (in grams) of boron (B) that, substitutionally incorporated into $1 \mathrm{~kg}$ of germanium (Ge), will establish a charge carrier density of $3.091 \mathrm{x}$ $10^{17} / \mathrm{cm}^{3}$. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the amount (in grams) of boron (B) that, substitutionally incorporated into $1 \mathrm{~kg}$ of germanium (Ge), will establish a charge carrier density of $3.091 \mathrm{x}$ $10^{17} / \mathrm{cm}^{3}$. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the amount (in grams) of boron (B) that, substitutionally incorporated into $1 \mathrm{~kg}$ of germanium (Ge), will establish a charge carrier density of $3.091 \mathrm{x}$ $10^{17} / \mathrm{cm}^{3}$. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the amount (in grams) of boron (B) that, substitutionally incorporated into $1 \mathrm{~kg}$ of germanium (Ge), will establish a charge carrier density of $3.091 \mathrm{x}$ $10^{17} / \mathrm{cm}^{3}$. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Subproblem 0: Is an energy level of $-1.362 \times 10^{-19} {~J}$ an allowed electron energy state in atomic hydrogen?

Solution: $E_{e l} =-\frac{1}{n^{2}} {~K}$ \\
$-1.362 \times 10^{-19} {~J}=-\frac{1}{{n}^{2}} \times 2.18 \times 10^{-18} {~J}$\\
${n} &=\sqrt{\frac{2.18 \times 10^{-18}}{1.362 \times 10^{-19}}}=4.00$\\
The answer is \boxed{Yes}.

Final answer: The final answer is Yes. I hope it is correct.

Subproblem 1: If your answer is yes, determine its principal quantum number $(n)$. If your answer is no, determine ${n}$ for the "nearest allowed state".
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Subproblem 0: Is an energy level of $-1.362 \times 10^{-19} {~J}$ an allowed electron energy state in atomic hydrogen?

Solution: $E_{e l} =-\frac{1}{n^{2}} {~K}$ \\
$-1.362 \times 10^{-19} {~J}=-\frac{1}{{n}^{2}} \times 2.18 \times 10^{-18} {~J}$\\
${n} &=\sqrt{\frac{2.18 \times 10^{-18}}{1.362 \times 10^{-19}}}=4.00$\\
The answer is \boxed{Yes}.

Final answer: The final answer is Yes. I hope it is correct.

Subproblem 1: If your answer is yes, determine its principal quantum number $(n)$. If your answer is no, determine ${n}$ for the "nearest allowed state".
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Subproblem 0: Is an energy level of $-1.362 \times 10^{-19} {~J}$ an allowed electron energy state in atomic hydrogen?

Solution: $E_{e l} =-\frac{1}{n^{2}} {~K}$ \\
$-1.362 \times 10^{-19} {~J}=-\frac{1}{{n}^{2}} \times 2.18 \times 10^{-18} {~J}$\\
${n} &=\sqrt{\frac{2.18 \times 10^{-18}}{1.362 \times 10^{-19}}}=4.00$\\
The answer is \boxed{Yes}.

Final answer: The final answer is Yes. I hope it is correct.

Subproblem 1: If your answer is yes, determine its principal quantum number $(n)$. If your answer is no, determine ${n}$ for the "nearest allowed state".
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Subproblem 0: Is an energy level of $-1.362 \times 10^{-19} {~J}$ an allowed electron energy state in atomic hydrogen?

Solution: $E_{e l} =-\frac{1}{n^{2}} {~K}$ \\
$-1.362 \times 10^{-19} {~J}=-\frac{1}{{n}^{2}} \times 2.18 \times 10^{-18} {~J}$\\
${n} &=\sqrt{\frac{2.18 \times 10^{-18}}{1.362 \times 10^{-19}}}=4.00$\\
The answer is \boxed{Yes}.

Final answer: The final answer is Yes. I hope it is correct.

Subproblem 1: If your answer is yes, determine its principal quantum number $(n)$. If your answer is no, determine ${n}$ for the "nearest allowed state".
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the highest linear density of atoms (atoms/m) encountered in vanadium (V). Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the highest linear density of atoms (atoms/m) encountered in vanadium (V). Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the highest linear density of atoms (atoms/m) encountered in vanadium (V). Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the highest linear density of atoms (atoms/m) encountered in vanadium (V). Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Strontium fluoride, $\mathrm{SrF}_{2}$, has a $\mathrm{K}_{\mathrm{sp}}$ value in water of $2.45 \times 10^{-9}$ at room temperature.
Calculate the solubility of $\mathrm{SrF}_{2}$ in water. Express your answer in units of molarity. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Strontium fluoride, $\mathrm{SrF}_{2}$, has a $\mathrm{K}_{\mathrm{sp}}$ value in water of $2.45 \times 10^{-9}$ at room temperature.
Calculate the solubility of $\mathrm{SrF}_{2}$ in water. Express your answer in units of molarity. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Strontium fluoride, $\mathrm{SrF}_{2}$, has a $\mathrm{K}_{\mathrm{sp}}$ value in water of $2.45 \times 10^{-9}$ at room temperature.
Calculate the solubility of $\mathrm{SrF}_{2}$ in water. Express your answer in units of molarity. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Strontium fluoride, $\mathrm{SrF}_{2}$, has a $\mathrm{K}_{\mathrm{sp}}$ value in water of $2.45 \times 10^{-9}$ at room temperature.
Calculate the solubility of $\mathrm{SrF}_{2}$ in water. Express your answer in units of molarity. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
You wish to dope a single crystal of silicon (Si) with boron (B). The specification reads $5 \times 10^{16}$ boron atoms/ $\mathrm{cm}^{3}$ at a depth of $25 \mu \mathrm{m}$ from the surface of the silicon. What must be the effective concentration of boron in units of atoms/ $\mathrm{cm}^{3}$ if you are to meet this specification within a time of 90 minutes? Round your answer to 4 decimal places. Assume that initially the concentration of boron in the silicon crystal is zero. The diffusion coefficient of boron in silicon has a value of $7.23 \times 10^{-9} \mathrm{~cm}^{2} / \mathrm{s}$ at the processing temperature.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
You wish to dope a single crystal of silicon (Si) with boron (B). The specification reads $5 \times 10^{16}$ boron atoms/ $\mathrm{cm}^{3}$ at a depth of $25 \mu \mathrm{m}$ from the surface of the silicon. What must be the effective concentration of boron in units of atoms/ $\mathrm{cm}^{3}$ if you are to meet this specification within a time of 90 minutes? Round your answer to 4 decimal places. Assume that initially the concentration of boron in the silicon crystal is zero. The diffusion coefficient of boron in silicon has a value of $7.23 \times 10^{-9} \mathrm{~cm}^{2} / \mathrm{s}$ at the processing temperature.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
You wish to dope a single crystal of silicon (Si) with boron (B). The specification reads $5 \times 10^{16}$ boron atoms/ $\mathrm{cm}^{3}$ at a depth of $25 \mu \mathrm{m}$ from the surface of the silicon. What must be the effective concentration of boron in units of atoms/ $\mathrm{cm}^{3}$ if you are to meet this specification within a time of 90 minutes? Round your answer to 4 decimal places. Assume that initially the concentration of boron in the silicon crystal is zero. The diffusion coefficient of boron in silicon has a value of $7.23 \times 10^{-9} \mathrm{~cm}^{2} / \mathrm{s}$ at the processing temperature.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
You wish to dope a single crystal of silicon (Si) with boron (B). The specification reads $5 \times 10^{16}$ boron atoms/ $\mathrm{cm}^{3}$ at a depth of $25 \mu \mathrm{m}$ from the surface of the silicon. What must be the effective concentration of boron in units of atoms/ $\mathrm{cm}^{3}$ if you are to meet this specification within a time of 90 minutes? Round your answer to 4 decimal places. Assume that initially the concentration of boron in the silicon crystal is zero. The diffusion coefficient of boron in silicon has a value of $7.23 \times 10^{-9} \mathrm{~cm}^{2} / \mathrm{s}$ at the processing temperature.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
An electron beam strikes a crystal of cadmium sulfide (CdS). Electrons scattered by the crystal move at a velocity of $4.4 \times 10^{5} \mathrm{~m} / \mathrm{s}$. Calculate the energy of the incident beam. Express your result in eV, and as an integer. CdS is a semiconductor with a band gap, $E_{g}$, of $2.45$ eV.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
An electron beam strikes a crystal of cadmium sulfide (CdS). Electrons scattered by the crystal move at a velocity of $4.4 \times 10^{5} \mathrm{~m} / \mathrm{s}$. Calculate the energy of the incident beam. Express your result in eV, and as an integer. CdS is a semiconductor with a band gap, $E_{g}$, of $2.45$ eV.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
An electron beam strikes a crystal of cadmium sulfide (CdS). Electrons scattered by the crystal move at a velocity of $4.4 \times 10^{5} \mathrm{~m} / \mathrm{s}$. Calculate the energy of the incident beam. Express your result in eV, and as an integer. CdS is a semiconductor with a band gap, $E_{g}$, of $2.45$ eV.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
An electron beam strikes a crystal of cadmium sulfide (CdS). Electrons scattered by the crystal move at a velocity of $4.4 \times 10^{5} \mathrm{~m} / \mathrm{s}$. Calculate the energy of the incident beam. Express your result in eV, and as an integer. CdS is a semiconductor with a band gap, $E_{g}$, of $2.45$ eV.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Subproblem 0: Determine the inter-ionic equilibrium distance in meters between the sodium and chlorine ions in a sodium chloride molecule knowing that the bond energy is $3.84 \mathrm{eV}$ and that the repulsive exponent is 8. Please format your answer as $n \times 10^x$ where $n$ is to 1 decimal place.

Solution: $\mathrm{E}_{\mathrm{equ}}=-3.84 \mathrm{eV}=-3.84 \times 1.6 \times 10^{-19} \mathrm{~J}=-\frac{\mathrm{e}^{2}}{4 \pi \varepsilon_{0} r_{0}}\left(1-\frac{1}{\mathrm{n}}\right)$
\\
$r_{0}=\frac{\left(1.6 \times 10^{-19}\right)^{2}}{4 \pi 8.85 \times 10^{-12} \times 6.14 \times 10^{-19}}\left(1-\frac{1}{8}\right)=
\boxed{3.3e-10} \mathrm{~m}$

Final answer: The final answer is 3.3e-10. I hope it is correct.

Subproblem 1: At the equilibrium distance, how much (in percent) is the contribution to the attractive bond energy by electron shell repulsion?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Subproblem 0: Determine the inter-ionic equilibrium distance in meters between the sodium and chlorine ions in a sodium chloride molecule knowing that the bond energy is $3.84 \mathrm{eV}$ and that the repulsive exponent is 8. Please format your answer as $n \times 10^x$ where $n$ is to 1 decimal place.

Solution: $\mathrm{E}_{\mathrm{equ}}=-3.84 \mathrm{eV}=-3.84 \times 1.6 \times 10^{-19} \mathrm{~J}=-\frac{\mathrm{e}^{2}}{4 \pi \varepsilon_{0} r_{0}}\left(1-\frac{1}{\mathrm{n}}\right)$
\\
$r_{0}=\frac{\left(1.6 \times 10^{-19}\right)^{2}}{4 \pi 8.85 \times 10^{-12} \times 6.14 \times 10^{-19}}\left(1-\frac{1}{8}\right)=
\boxed{3.3e-10} \mathrm{~m}$

Final answer: The final answer is 3.3e-10. I hope it is correct.

Subproblem 1: At the equilibrium distance, how much (in percent) is the contribution to the attractive bond energy by electron shell repulsion?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Subproblem 0: Determine the inter-ionic equilibrium distance in meters between the sodium and chlorine ions in a sodium chloride molecule knowing that the bond energy is $3.84 \mathrm{eV}$ and that the repulsive exponent is 8. Please format your answer as $n \times 10^x$ where $n$ is to 1 decimal place.

Solution: $\mathrm{E}_{\mathrm{equ}}=-3.84 \mathrm{eV}=-3.84 \times 1.6 \times 10^{-19} \mathrm{~J}=-\frac{\mathrm{e}^{2}}{4 \pi \varepsilon_{0} r_{0}}\left(1-\frac{1}{\mathrm{n}}\right)$
\\
$r_{0}=\frac{\left(1.6 \times 10^{-19}\right)^{2}}{4 \pi 8.85 \times 10^{-12} \times 6.14 \times 10^{-19}}\left(1-\frac{1}{8}\right)=
\boxed{3.3e-10} \mathrm{~m}$

Final answer: The final answer is 3.3e-10. I hope it is correct.

Subproblem 1: At the equilibrium distance, how much (in percent) is the contribution to the attractive bond energy by electron shell repulsion?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Subproblem 0: Determine the inter-ionic equilibrium distance in meters between the sodium and chlorine ions in a sodium chloride molecule knowing that the bond energy is $3.84 \mathrm{eV}$ and that the repulsive exponent is 8. Please format your answer as $n \times 10^x$ where $n$ is to 1 decimal place.

Solution: $\mathrm{E}_{\mathrm{equ}}=-3.84 \mathrm{eV}=-3.84 \times 1.6 \times 10^{-19} \mathrm{~J}=-\frac{\mathrm{e}^{2}}{4 \pi \varepsilon_{0} r_{0}}\left(1-\frac{1}{\mathrm{n}}\right)$
\\
$r_{0}=\frac{\left(1.6 \times 10^{-19}\right)^{2}}{4 \pi 8.85 \times 10^{-12} \times 6.14 \times 10^{-19}}\left(1-\frac{1}{8}\right)=
\boxed{3.3e-10} \mathrm{~m}$

Final answer: The final answer is 3.3e-10. I hope it is correct.

Subproblem 1: At the equilibrium distance, how much (in percent) is the contribution to the attractive bond energy by electron shell repulsion?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: A consumer's preferences are representable by the following utility function:
\[
  u(x, y)=x^{\frac{1}{2}}+y
\]

Obtain the marginal rate of substitution of the consumer at an arbitrary point $(X,Y)$, where $X>0$ and $Y>0$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: A consumer's preferences are representable by the following utility function:
\[
  u(x, y)=x^{\frac{1}{2}}+y
\]

Obtain the marginal rate of substitution of the consumer at an arbitrary point $(X,Y)$, where $X>0$ and $Y>0$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: A consumer's preferences are representable by the following utility function:
\[
  u(x, y)=x^{\frac{1}{2}}+y
\]

Obtain the marginal rate of substitution of the consumer at an arbitrary point $(X,Y)$, where $X>0$ and $Y>0$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: A consumer's preferences are representable by the following utility function:
\[
  u(x, y)=x^{\frac{1}{2}}+y
\]

Obtain the marginal rate of substitution of the consumer at an arbitrary point $(X,Y)$, where $X>0$ and $Y>0$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Xiaoyu spends all her income on statistical software $(S)$ and clothes (C). Her preferences can be represented by the utility function: $U(S, C)=4 \ln (S)+6 \ln (C)$.

Compute the marginal rate of substitution of software for clothes.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Xiaoyu spends all her income on statistical software $(S)$ and clothes (C). Her preferences can be represented by the utility function: $U(S, C)=4 \ln (S)+6 \ln (C)$.

Compute the marginal rate of substitution of software for clothes.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Xiaoyu spends all her income on statistical software $(S)$ and clothes (C). Her preferences can be represented by the utility function: $U(S, C)=4 \ln (S)+6 \ln (C)$.

Compute the marginal rate of substitution of software for clothes.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Xiaoyu spends all her income on statistical software $(S)$ and clothes (C). Her preferences can be represented by the utility function: $U(S, C)=4 \ln (S)+6 \ln (C)$.

Compute the marginal rate of substitution of software for clothes.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
What algebraic condition describes a firm that is at an output level that maximizes its profits, given its capital in the short-term?  Use standard acronyms in your condition.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
What algebraic condition describes a firm that is at an output level that maximizes its profits, given its capital in the short-term?  Use standard acronyms in your condition.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
What algebraic condition describes a firm that is at an output level that maximizes its profits, given its capital in the short-term?  Use standard acronyms in your condition.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
What algebraic condition describes a firm that is at an output level that maximizes its profits, given its capital in the short-term?  Use standard acronyms in your condition.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Moldavia is a small country that currently trades freely in the world barley market. Demand and supply for barley in Moldavia is governed by the following schedules:
Demand: $Q^{D}=4-P$
Supply: $Q^{S}=P$
The world price of barley is $\$ 1 /$ bushel.

Subproblem 0: Calculate the free trade equilibrium price of barley in Moldavia, in dollars per bushel.

Solution: In free trade, Moldavia will import barley because the world price of $\$ 1 /$ bushel is lower than the autarkic price of $\$ 2$ /bushel. Free trade equilibrium price will be \boxed{1} dollar per bushel.

Final answer: The final answer is 1. I hope it is correct.

Subproblem 1: Calculate the free trade equilibrium quantity of barley in Moldavia (in bushels).
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Moldavia is a small country that currently trades freely in the world barley market. Demand and supply for barley in Moldavia is governed by the following schedules:
Demand: $Q^{D}=4-P$
Supply: $Q^{S}=P$
The world price of barley is $\$ 1 /$ bushel.

Subproblem 0: Calculate the free trade equilibrium price of barley in Moldavia, in dollars per bushel.

Solution: In free trade, Moldavia will import barley because the world price of $\$ 1 /$ bushel is lower than the autarkic price of $\$ 2$ /bushel. Free trade equilibrium price will be \boxed{1} dollar per bushel.

Final answer: The final answer is 1. I hope it is correct.

Subproblem 1: Calculate the free trade equilibrium quantity of barley in Moldavia (in bushels).
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Moldavia is a small country that currently trades freely in the world barley market. Demand and supply for barley in Moldavia is governed by the following schedules:
Demand: $Q^{D}=4-P$
Supply: $Q^{S}=P$
The world price of barley is $\$ 1 /$ bushel.

Subproblem 0: Calculate the free trade equilibrium price of barley in Moldavia, in dollars per bushel.

Solution: In free trade, Moldavia will import barley because the world price of $\$ 1 /$ bushel is lower than the autarkic price of $\$ 2$ /bushel. Free trade equilibrium price will be \boxed{1} dollar per bushel.

Final answer: The final answer is 1. I hope it is correct.

Subproblem 1: Calculate the free trade equilibrium quantity of barley in Moldavia (in bushels).
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Moldavia is a small country that currently trades freely in the world barley market. Demand and supply for barley in Moldavia is governed by the following schedules:
Demand: $Q^{D}=4-P$
Supply: $Q^{S}=P$
The world price of barley is $\$ 1 /$ bushel.

Subproblem 0: Calculate the free trade equilibrium price of barley in Moldavia, in dollars per bushel.

Solution: In free trade, Moldavia will import barley because the world price of $\$ 1 /$ bushel is lower than the autarkic price of $\$ 2$ /bushel. Free trade equilibrium price will be \boxed{1} dollar per bushel.

Final answer: The final answer is 1. I hope it is correct.

Subproblem 1: Calculate the free trade equilibrium quantity of barley in Moldavia (in bushels).
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Consider the market for apple juice. In this market, the supply curve is given by $Q_{S}=$ $10 P_{J}-5 P_{A}$ and the demand curve is given by $Q_{D}=100-15 P_{J}+10 P_{T}$, where $J$ denotes apple juice, $A$ denotes apples, and $T$ denotes tea.

Subproblem 0: Assume that $P_{A}$ is fixed at $\$ 1$ and $P_{T}=5$. Calculate the equilibrium price in the apple juice market.

Solution: We have the system of equations $Q=10 P_{J}-5 \cdot 1$ and $Q=100-15 P_{J}+10 \cdot 5$. Solving for $P_{J}$ we get that $P_{J}=\boxed{6.2}$.

Final answer: The final answer is 6.2. I hope it is correct.

Subproblem 1: Assume that $P_{A}$ is fixed at $\$ 1$ and $P_{T}=5$. Calculate the equilibrium quantity in the apple juice market.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Consider the market for apple juice. In this market, the supply curve is given by $Q_{S}=$ $10 P_{J}-5 P_{A}$ and the demand curve is given by $Q_{D}=100-15 P_{J}+10 P_{T}$, where $J$ denotes apple juice, $A$ denotes apples, and $T$ denotes tea.

Subproblem 0: Assume that $P_{A}$ is fixed at $\$ 1$ and $P_{T}=5$. Calculate the equilibrium price in the apple juice market.

Solution: We have the system of equations $Q=10 P_{J}-5 \cdot 1$ and $Q=100-15 P_{J}+10 \cdot 5$. Solving for $P_{J}$ we get that $P_{J}=\boxed{6.2}$.

Final answer: The final answer is 6.2. I hope it is correct.

Subproblem 1: Assume that $P_{A}$ is fixed at $\$ 1$ and $P_{T}=5$. Calculate the equilibrium quantity in the apple juice market.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Consider the market for apple juice. In this market, the supply curve is given by $Q_{S}=$ $10 P_{J}-5 P_{A}$ and the demand curve is given by $Q_{D}=100-15 P_{J}+10 P_{T}$, where $J$ denotes apple juice, $A$ denotes apples, and $T$ denotes tea.

Subproblem 0: Assume that $P_{A}$ is fixed at $\$ 1$ and $P_{T}=5$. Calculate the equilibrium price in the apple juice market.

Solution: We have the system of equations $Q=10 P_{J}-5 \cdot 1$ and $Q=100-15 P_{J}+10 \cdot 5$. Solving for $P_{J}$ we get that $P_{J}=\boxed{6.2}$.

Final answer: The final answer is 6.2. I hope it is correct.

Subproblem 1: Assume that $P_{A}$ is fixed at $\$ 1$ and $P_{T}=5$. Calculate the equilibrium quantity in the apple juice market.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Consider the market for apple juice. In this market, the supply curve is given by $Q_{S}=$ $10 P_{J}-5 P_{A}$ and the demand curve is given by $Q_{D}=100-15 P_{J}+10 P_{T}$, where $J$ denotes apple juice, $A$ denotes apples, and $T$ denotes tea.

Subproblem 0: Assume that $P_{A}$ is fixed at $\$ 1$ and $P_{T}=5$. Calculate the equilibrium price in the apple juice market.

Solution: We have the system of equations $Q=10 P_{J}-5 \cdot 1$ and $Q=100-15 P_{J}+10 \cdot 5$. Solving for $P_{J}$ we get that $P_{J}=\boxed{6.2}$.

Final answer: The final answer is 6.2. I hope it is correct.

Subproblem 1: Assume that $P_{A}$ is fixed at $\$ 1$ and $P_{T}=5$. Calculate the equilibrium quantity in the apple juice market.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Suppose, in the short run, the output of widgets is supplied by 100 identical competitive firms, each having a cost function:
\[
c_{s}(y)=\frac{1}{3} y^{3}+2
\]
The demand for widgets is given by:
\[
y^{d}(p)=6400 / p^{\frac{1}{2}}
\]

Subproblem 0: Obtain the short run industry supply function for widgets.

Solution: Since $P=M C=y^{2}$, the supply function of each firm is given by $y_{i}^{s}=p^{\frac{1}{2}}$.
The industry supply function is $y^{s}(p)=100 y_{i}^{s}(p)=\boxed{100 p^{\frac{1}{2}}}$.

Final answer: The final answer is 100 p^{\frac{1}{2}}. I hope it is correct.

Subproblem 1: Obtain the short run equilibrium price of widgets.

Solution: $y^{s}=y^{d} \longrightarrow 100 p^{\frac{1}{2}}=\frac{6400}{p^{\frac{1}{2}}} \longrightarrow p=\boxed{64}$.

Final answer: The final answer is 64. I hope it is correct.

Subproblem 2: Obtain the the output of widgets supplied by each firm.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Suppose, in the short run, the output of widgets is supplied by 100 identical competitive firms, each having a cost function:
\[
c_{s}(y)=\frac{1}{3} y^{3}+2
\]
The demand for widgets is given by:
\[
y^{d}(p)=6400 / p^{\frac{1}{2}}
\]

Subproblem 0: Obtain the short run industry supply function for widgets.

Solution: Since $P=M C=y^{2}$, the supply function of each firm is given by $y_{i}^{s}=p^{\frac{1}{2}}$.
The industry supply function is $y^{s}(p)=100 y_{i}^{s}(p)=\boxed{100 p^{\frac{1}{2}}}$.

Final answer: The final answer is 100 p^{\frac{1}{2}}. I hope it is correct.

Subproblem 1: Obtain the short run equilibrium price of widgets.

Solution: $y^{s}=y^{d} \longrightarrow 100 p^{\frac{1}{2}}=\frac{6400}{p^{\frac{1}{2}}} \longrightarrow p=\boxed{64}$.

Final answer: The final answer is 64. I hope it is correct.

Subproblem 2: Obtain the the output of widgets supplied by each firm.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Suppose, in the short run, the output of widgets is supplied by 100 identical competitive firms, each having a cost function:
\[
c_{s}(y)=\frac{1}{3} y^{3}+2
\]
The demand for widgets is given by:
\[
y^{d}(p)=6400 / p^{\frac{1}{2}}
\]

Subproblem 0: Obtain the short run industry supply function for widgets.

Solution: Since $P=M C=y^{2}$, the supply function of each firm is given by $y_{i}^{s}=p^{\frac{1}{2}}$.
The industry supply function is $y^{s}(p)=100 y_{i}^{s}(p)=\boxed{100 p^{\frac{1}{2}}}$.

Final answer: The final answer is 100 p^{\frac{1}{2}}. I hope it is correct.

Subproblem 1: Obtain the short run equilibrium price of widgets.

Solution: $y^{s}=y^{d} \longrightarrow 100 p^{\frac{1}{2}}=\frac{6400}{p^{\frac{1}{2}}} \longrightarrow p=\boxed{64}$.

Final answer: The final answer is 64. I hope it is correct.

Subproblem 2: Obtain the the output of widgets supplied by each firm.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Suppose, in the short run, the output of widgets is supplied by 100 identical competitive firms, each having a cost function:
\[
c_{s}(y)=\frac{1}{3} y^{3}+2
\]
The demand for widgets is given by:
\[
y^{d}(p)=6400 / p^{\frac{1}{2}}
\]

Subproblem 0: Obtain the short run industry supply function for widgets.

Solution: Since $P=M C=y^{2}$, the supply function of each firm is given by $y_{i}^{s}=p^{\frac{1}{2}}$.
The industry supply function is $y^{s}(p)=100 y_{i}^{s}(p)=\boxed{100 p^{\frac{1}{2}}}$.

Final answer: The final answer is 100 p^{\frac{1}{2}}. I hope it is correct.

Subproblem 1: Obtain the short run equilibrium price of widgets.

Solution: $y^{s}=y^{d} \longrightarrow 100 p^{\frac{1}{2}}=\frac{6400}{p^{\frac{1}{2}}} \longrightarrow p=\boxed{64}$.

Final answer: The final answer is 64. I hope it is correct.

Subproblem 2: Obtain the the output of widgets supplied by each firm.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Sebastian owns a coffee factory in Argentina. His production function is:
\[
F(K, L)=(K-1)^{\frac{1}{4}} L^{\frac{1}{4}}
\]
Consider the cost of capital to be $r$ and the wage to be $w$. Both inputs are variable, and Sebastian faces no fixed costs.

What is the marginal rate of technical substitution of labor for capital?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Sebastian owns a coffee factory in Argentina. His production function is:
\[
F(K, L)=(K-1)^{\frac{1}{4}} L^{\frac{1}{4}}
\]
Consider the cost of capital to be $r$ and the wage to be $w$. Both inputs are variable, and Sebastian faces no fixed costs.

What is the marginal rate of technical substitution of labor for capital?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Sebastian owns a coffee factory in Argentina. His production function is:
\[
F(K, L)=(K-1)^{\frac{1}{4}} L^{\frac{1}{4}}
\]
Consider the cost of capital to be $r$ and the wage to be $w$. Both inputs are variable, and Sebastian faces no fixed costs.

What is the marginal rate of technical substitution of labor for capital?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant