Chapter 13.2, Problem 6RQ

Interpretation Introduction

Interpretation:

The pressure of oxygen gas in the gas mixture needs to be determined by an equation.

Concept Introduction:

When a gas is collected by the displacement of water, the mixing of gas takes place. Thus, the collecting bottle contains a mixture of water vapor and collected gas. So, the total pressure exerted by the gas mixture is the sum of the partial pressure of that collected gas and the partial pressure of the water vapor.

Answer to Problem 6RQ

So, the total pressure exerted by the gas mixture is the sum of the partial pressure of oxygen and the partial pressure of the water vapor.

  $\begin{array}{l}{\mathrm{P}}_{\text{T}}={\mathrm{P}}_{{\text{O}}_{\text{2}}}+{\mathrm{P}}_{\text{water}\text{vapor}}\\ {\mathrm{P}}_{{\text{O}}_{\text{2}}}={\mathrm{P}}_{\text{T}}-23.756\end{array}$

Explanation of Solution

The given figure represents the production of oxygen by thermal decomposition of KClO₃ and oxygen is collected by bubbling it into a bottle initially filled with water. When oxygen gas is collected by the displacement of water, the mixing of gas takes place. Thus, the collecting bottle contains a mixture of water vapor and oxygen. So, the total pressure exerted by the gas mixture is the sum of the partial pressure of oxygen and the partial pressure of the water vapor.

  ${\mathrm{P}}_{\mathrm{T}}={\mathrm{P}}_{{\mathrm{O}}_2}+{\mathrm{P}}_{\mathrm{w}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{v}\mathrm{a}\mathrm{p}\mathrm{o}\mathrm{r}}$

Where the pressures P_T represents the total pressure while ${\mathrm{P}}_{\text{O}}{}_{{}_{\text{2}}}$ , and ${\mathrm{P}}_{\text{water vapor}}$ represent the partial pressures of oxygen and water vapor respectively.

At 25 °C the partial pressures of water vapor is 23.756.

So, the final equation-

  $\begin{array}{l}{\mathrm{P}}_{\text{T}}={\mathrm{P}}_{{\text{O}}_{\text{2}}}+{\mathrm{P}}_{\text{water}\text{vapor}}\\ {\mathrm{P}}_{{\text{O}}_{\text{2}}}={\mathrm{P}}_{\text{T}}-23.756\end{array}$