Chapter 5, Problem 55E

A certain quantity of hydrogen occupies a volume of 1000 cm³ at 0°C (273 K) and ordinary atmospheric pressure. (a) If the pressure is tripled but the temperature is held constant, what will the volume of the hydrogen be? (b) If the temperature is increased to 273°C but the pressure is held constant, what will the volume of the hydrogen be?

To determine

The volume of hydrogen when the pressure is tripled but temperature is kept constant.

Answer to Problem 55E

The volume of hydrogen when the pressure is tripled but temperature is kept constant is $333.33{\text{cm}}^{\text{3}}$.

Explanation of Solution

Given info: The initial volume of hydrogen is $1000{\text{cm}}^{\text{3}}$ and the temperature is $0\text{°C}$.

Write the expression of Boyle’s law for a gas.

$\frac{p_1}{p_2}=\frac{V_2}{V_1}\left(\text{at constant temperature}\right)$

Here,

$p_1$ is the initial pressure

$p_2$ is the final pressure

$V_1$ is the initial volume

$V_2$ is the final volume

Solve for $V_2$.

$V_2=\frac{p_1{V}_1}{p_2}$

Given the initial pressure $p_1$ is ordinary atmospheric temperature, and the final pressure is triple of the initial pressure.

$p_2=3p_1$

Thus, the expression for $V_2$ can be modified as,

$\begin{array}{c}{V}_2=\frac{p_1{V}_1}{3p_1}\\ =\frac{V_1}{3}\end{array}$

Substitute $1000{\text{cm}}^{\text{3}}$ for $V_1$ to find the final volume of hydrogen $V_2$.

$\begin{array}{c}{V}_2=\frac{1000{\text{cm}}^{\text{3}}}{3}\\ =333.33{\text{cm}}^{\text{3}}\end{array}$

Conclusion:

Therefore, the volume of hydrogen when the pressure is tripled but temperature is kept constant is $333.33{\text{cm}}^{\text{3}}$.

To determine

The volume of hydrogen when the temperature is $273\text{°C}$ but pressure is kept constant.

Answer to Problem 55E

The volume of hydrogen when the temperature is $273\text{°C}$ but pressure is kept constant is $2000{\text{cm}}^{\text{3}}$.

Explanation of Solution

Given info: The initial volume of hydrogen is $1000{\text{cm}}^{\text{3}}$, the initial temperature is $0\text{°C}$ and the final temperature is $273\text{°C}$

Write the expression of Charles’s law for gases.

$\frac{V_1}{V_2}=\frac{T_1}{T_2}\left(\text{at constant pressure}\right)$

Here,

$V_1$ is the initial volume

$V_2$ is the final volume

$T_1$ is the initial temperature in Kelvin scale

$T_2$ is the final temperature in Kelvin scale

The initial and final temperatures can be converted to Kelvin scale as, $T\left(\text{K}\right)=T\left(\text{°C}\right)+273$.

$\begin{array}{c}{T}_1\left(\text{K}\right)=0\text{°C}+273\\ =273\text{K}\end{array}$

$\begin{array}{c}{T}_2\left(\text{K}\right)=273\text{°C}+273\\ =546\text{K}\end{array}$

Solve for $V_2$.

$V_2=\frac{V_1{T}_2}{T_1}$

Substitute $1000{\text{cm}}^{\text{3}}$ for $V_1$, $273\text{K}$ for $T_1$ and $546\text{K}$ for $T_2$ to find the final volume of hydrogen.

$\begin{array}{c}{V}_2=\frac{\left(1000{\text{cm}}^{\text{3}}\right)\left(546\text{K}\right)}{273\text{K}}\\ =2000{\text{cm}}^{\text{3}}\end{array}$

Conclusion:

Therefore, the volume of hydrogen when the temperature is $273\text{°C}$ but pressure is kept constant is $2000{\text{cm}}^{\text{3}}$.