Chapter 13, Problem 57A

Solution

(a)

Interpretation:

The pressure of the gas is to be calculated for a given new volume when the temperature and amount of gas are constant.

Concept introduction:

When temperature and amount of gas are constant, pressure of gas is inversely proportional to the volume of the gas. This law is known as Boyle’s Law.

According to this law,

${\mathrm{P}}_1{V}_1=P_2{V}_2$

Where

${\mathrm{P}}_1$ is initial pressure of the gas

${\mathrm{V}}_1$ is initial volume of the gas

${\mathrm{P}}_2$ is the final pressure of the gas

${\mathrm{V}}_2$ is the final volume of the gas

The new pressure of the gas is $1.64atm$.

The change in volume on changing the pressure of the gas keeping the temperature fixed is studied by a law named as Boyle’s Law. According to this law, Product of pressure and volume of a given mass of gas is constant at constant temperature.

If ${\mathrm{V}}_1$ is the volume of the gas at pressure ${\mathrm{P}}_1$ and volume is increased to ${\mathrm{V}}_2$ Then pressure is decreased to ${\mathrm{P}}_2$. The formula used to calculate ${\mathrm{P}}_2$ is

${\mathrm{P}}_1{V}_1=P_2{V}_2$

Or

${\mathrm{P}}_2=\frac{P_1{V}_1}{V_2}$

Given data is:

$\begin{array}{l}{\text{V}}_1\text{=2L}\\ {\text{P}}_1\text{=0}\text{.82atm}\\ {\text{V}}_2=1L\end{array}$

On substituting the values in the formula:

$\begin{array}{l}{P}_2=\frac{2\times 0.82}{\begin{array}{l}1\end{array}}\\ =1.64atm\end{array}$

Therefore new pressure is $1.64atm$.

(b)

Interpretation:

The temperature of the gas is to be calculated for a given new volume when the pressure and amount of gas remain constant.

Concept introduction:

When pressure and amount of gas are kept constant, increasing the temperature of gas increases its volume. This law is known as Charles’ Law.

According to this law,

$\frac{V_1}{T_1}=\frac{V_2}{T_2}$

Where

${\mathrm{T}}_1$ is initial temperature of the gas

${\mathrm{V}}_1$ is initial volume of the gas

${\mathrm{T}}_2$ is the final temperature of the gas

${\mathrm{V}}_2$ is the final volume of the gas

The initial temperature of the gas is $186.25K$

The change in volume on changing the temperature of the gas keeping the pressure and amount of gas fixed is studied by a law named as Charles’ Law. According to this law, The volume of a given mass of gas is directly proportional to the Kelvin temperature at constant pressure.

If ${\mathrm{V}}_1$ is the volume of the gas at temperature ${\mathrm{T}}_1$ and temperature is changed to ${\mathrm{T}}_2$ then volume is changed to ${\mathrm{V}}_2$. The formula used to calculate ${\mathrm{V}}_2$ is

$\frac{V_1}{T_1}=\frac{V_2}{T_2}$

Or

${\text{T}}_{\text{1}}\text{=}\frac{{\text{T}}_{\text{2}}{\text{V}}_{\text{1}}}{{\text{V}}_{\text{2}}}$

Given data is:

${\mathrm{V}}_1=250mL$

$V_2=400ml$

${\mathrm{T}}_2=298K$

On substituting the values in the formula:

$\begin{array}{c}{T}_1=\frac{250\times 298}{400}\\ =186.25K\end{array}$

Therefore temperature is $186.25K$

(c)

Interpretation:

The pressure of the gas is to be calculated for a given new volume when the temperature and amount of gas are constant.

Concept introduction:

When temperature and amount of gas are constant, pressure of gas is inversely proportional to the volume of the gas. This law is known as Boyle’s Law.

According to this law,

${\mathrm{P}}_1{V}_1=P_2{V}_2$

Where

${\mathrm{P}}_1$ is initial pressure of the gas

${\mathrm{V}}_1$ is initial volume of the gas

${\mathrm{P}}_2$ is the final pressure of the gas

${\mathrm{V}}_2$ is the final volume of the gas

The new pressure of the gas is $508.75mmHg$.

The change in volume on changing the pressure of the gas keeping the temperature fixed is studied by a law named as Boyle’s Law. According to this law, Product of pressure and volume of a given mass of gas is constant at constant temperature.

If ${\mathrm{V}}_1$ is the volume of the gas at pressure ${\mathrm{P}}_1$ and volume is increased to ${\mathrm{V}}_2$ Then pressure is decreased to ${\mathrm{P}}_2$. The formula used to calculate ${\mathrm{P}}_2$ is

${\mathrm{P}}_1{V}_1=P_2{V}_2$

Or

${\mathrm{P}}_2=\frac{P_1{V}_1}{V_2}$

Given data is:

$\begin{array}{l}{\text{V}}_1\text{=0}\text{.55}\text{L}\\ {\text{P}}_1\text{=740}\text{mmHg}\\ {\text{V}}_2=0.80L\end{array}$

On substituting the values in the formula:

$\begin{array}{l}{P}_2=\frac{740\times 0.55}{\begin{array}{l}0.80\end{array}}\\ =508.75mmHg\end{array}$

Therefore new pressure is $508.75mmHg$.