Chapter 14.4, Problem 42LC

Interpretation Introduction

Interpretation: To determine how the partial pressure of a gas in the mixture can be calculated.

Concept Introduction: In a gaseous mixture, each component's pressure was equal to what it would be if it were the only gas present in the container. The various partial pressures add up to form the total pressure.

Answer to Problem 42LC

The total pressure will be ${\text{P}}_{\text{Total}}{\text{=P}}_{\text{1}}{\text{+P}}_{\text{2}}{\text{+P}}_{\text{3}}\mathrm{.....}{\text{P}}_{\text{n}}$ .

Explanation of Solution

According to Dalton's law of partial pressures, each gas inside a mixture exerts the same amount of pressure as it should if it were the only one in the container.

Let the partial pressure of the gas will be ${\text{P}}_{\text{1}}$ , ${\text{P}}_{\text{2}}$ and ${\text{P}}_{\text{3}}$ then the total partial pressure will be:

  $\begin{array}{c}{\text{P}}_{\text{total}}{\text{=P}}_{\text{`1}}{\text{+P}}_{\text{2}}\text{+}\mathrm{...........}{\text{P}}_{\text{N}}\\ \text{= }\frac{{\text{n}}_{\text{1}}\text{RT}}{\text{V}}\text{+}\frac{{\text{n}}_{\text{2}}\text{RT}}{\text{V}}\text{+}\mathrm{...........}\frac{{\text{n}}_{\text{n}}\text{RT}}{\text{V}}\\ \text{= }\left(\frac{\text{RT}}{\text{V}}\right)\left({\text{n}}_{\text{1}}{\text{+n}}_{\text{2}}\text{+}\mathrm{...................}{\text{n}}_{\text{n}}\right)\end{array}$