Chapter 13.1, Problem 8PP

Interpretation Introduction

Interpretation:

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

Concept introduction:

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

According to this law,

$\frac{P_1}{T_1}=\frac{P_2}{T_2}$

Where

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

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

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

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

Answer to Problem 8PP

The new pressure of the gas is $1.96atm$

Explanation of Solution

Given information:

The initial pressure ${\mathrm{P}}_1=1.88atm$

The initial temperature is ${\mathrm{T}}_1=25°C$

The final temperature is $T_2=37°C$

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

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

$\frac{P_1}{T_1}=\frac{P_2}{T_2}$

Or

${\mathrm{P}}_2=\frac{T_2{P}_1}{T_1}$

Where

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

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

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

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

On converting the temperature from Celsius to kelvin,

$\begin{array}{l}T(K)=T(°C)+273\\ T_1(K)=25+273\\ =298K\\ T_2(K)=37+273\\ =310K\end{array}$

On substituting the values in the formula:

$\begin{array}{c}{P}_2=\frac{1.88\times 310}{\begin{array}{l}298\\ \end{array}}\\ =1.96atm\end{array}$

Therefore, new pressure is $1.96atm$

Conclusion

The pressure of the gas is $1.96atm$.