Chapter 14, Problem 54A

Interpretation Introduction

Interpretation: The final pressure of the gas in a closed container needs to be determined if the temperature decreases from 303 K to 101 K.

Concept Introduction: According to Gay Lussac’s law, at constant volume, the pressure of the given amount of gas is directly proportional to the temperature in K.

Explanation of Solution

According to the question, the initial pressure of the gas is $3.00\times {10}^2\text{ kPa}$ . The temperature of the gas lowered from 303 K to 101 K.

Here, gas is in a closed container; thus, the volume and number of moles of the gas remain the same.

The relation between the pressure and temperature of the gas at constant volume is as follows:

  $\frac{P_1}{T_1}=\frac{P_2}{T_2}$

Substitute the values,

  $\frac{3\times 10\text{kPa}}{303\text{ K}}=\frac{P_2}{101\text{ K}}$

On rearranging,

  $\begin{array}{c}{P}_2=\frac{3\times 10\text{kPa}}{303\text{ K}}\times 101\text{ K}\\ \text{=100 kPa}\end{array}$

The final pressure of the gas is 100 kPa.