Chapter 4, Problem 4D.9E

(a)

Interpretation Introduction

Interpretation:

The solubility of $C{O}_2$ in water at ${25}^{o}C$ when its partial pressure is $3.8kPa$ has to be determined.

Concept introduction:

Partial pressure of a gas in a mixture of gases is the pressure of that gas when it alone.

Partial pressure of a gas in terms of its mole fraction and total pressure is,

`            ${\text{P}}_{\text{A}}\text{=}{\text{χ}}_{\text{A}}\text{×}{\text{P}}_{\text{TOTAL}}$

Henry’s law states that the partial pressure of the gas in vapour phase (p) is proportional to the mole fraction of the gas (x) in the solution.

$\text{p}={\text{K}}_{\text{H}}\text{x}\boxed{\begin{array}{l}\text{where,}\\ {\text{K}}_{\text{H}}\text{:}\text{Henry's}\text{constant}\\ \text{x}\text{:}\text{mole}\text{fraction}\\ \text{p}\text{:}\text{partial}\text{pressure}\end{array}}$

Henry’s law: The solubility of a gas in liquid is directly proportional to the gas pressure.

$\begin{array}{l}{\text{S}}_{\text{g}}{\text{= k}}_{\text{H}}{\text{P}}_{\text{g}}\text{,}\\ \text{where,}\\ {\text{S}}_{\text{g}}\text{is}\text{the}\text{gas}\text{solubility}\text{(in}\text{mol/kg)}\\ {\text{k}}_{\text{H}}\text{is Henry's constant }\\ {\text{P}}_{\text{g}}\text{ is the partial pressure of the gaseous solute}\text{.}\end{array}$

(b)

Interpretation Introduction

Interpretation:

The solubility of $C{O}_2$ in water at ${25}^{o}C$ when its partial pressure is $50.0kPa$ has to be determined.

Concept introduction:

Partial pressure of a gas in a mixture of gases is the pressure of that gas when it alone.

Partial pressure of a gas in terms of its mole fraction and total pressure is,

`            ${\text{P}}_{\text{A}}\text{=}{\text{χ}}_{\text{A}}\text{×}{\text{P}}_{\text{TOTAL}}$

Henry’s law states that the partial pressure of the gas in vapour phase (p) is proportional to the mole fraction of the gas (x) in the solution.

$\text{p}={\text{K}}_{\text{H}}\text{x}\boxed{\begin{array}{l}\text{where,}\\ {\text{K}}_{\text{H}}\text{:}\text{Henry's}\text{constant}\\ \text{x}\text{:}\text{mole}\text{fraction}\\ \text{p}\text{:}\text{partial}\text{pressure}\end{array}}$

Henry’s law: The solubility of a gas in liquid is directly proportional to the gas pressure.

$\begin{array}{l}{\text{S}}_{\text{g}}{\text{= k}}_{\text{H}}{\text{P}}_{\text{g}}\text{,}\\ \text{where,}\\ {\text{S}}_{\text{g}}\text{is}\text{the}\text{gas}\text{solubility}\text{(in}\text{mol/kg)}\\ {\text{k}}_{\text{H}}\text{is Henry's constant }\\ {\text{P}}_{\text{g}}\text{ is the partial pressure of the gaseous solute}\text{.}\end{array}$