Chapter U3.13, Problem 1E

Interpretation Introduction

Interpretation: The combined gas law needs to be explained. The condition when it is applied needs to be determined.

Concept Introduction: The combined gas law is combination of three gas laws that is Boyle’s law, Charles’ law and Gay-Lussac’s law. According to this law the ratio of temperature to the product of pressure and volume is a constant.

Explanation of Solution

The three gas laws are explained as follows:

Boyle’s law:

This law explains the change in pressure of the gas with volume of the container at constant temperature. As volume of the container decreases, pressure tends to increase.

This is mathematically represented as follows:

  $P_1{V}_1=P_2{V}_2$

Here, P₁ is initial pressure, P₂ is final pressure, V₁ is initial volume and V₂ is final volume.

Charles’s law:

At constant pressure, volume and temperature of the gas are directly proportional to each other.

This is mathematically represented as follows:

  $\frac{V_1}{T_1}=\frac{V_2}{T_2}$

Here, V₁ is initial volume, V₂ is final volume, T₁ is initial temperature and T₂ is final temperature.

Gay-Lussac’s law:

At constant volume, pressure and temperature of the gas are directly proportional to each other.

This is mathematically represented as follows:

  $\frac{P_1}{T_1}=\frac{P_2}{T_2}$

Here, T₁ is initial volume, T₂ is final volume, P₁ is initial pressure and P₂ is final pressure.

When the three gases are combined, the combined gas law will be:

  $\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$

Here, P₁, V₁, T₁, P₂, V₂ and T₂ is initial pressure, initial volume, initial temperature, final pressure, final volume and final temperature respectively.