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Solubility And Henry's Law

How pressure changes how much gas dissolves in a liquid.

7 micro-lessons

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Solubility of Gases in Liquids

What affects how much gas dissolves in a liquid.

Many gases dissolve in water. While oxygen dissolves only to a small extent (just enough to sustain aquatic life), gases like hydrogen chloride (HCl) are highly soluble. The solubility of a gas is fundamentally driven by two external variables: temperature and pressure.

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Effect of Pressure on Solubility

A piston pushes down, and more gas dissolves.

Clean scientific diagram comparing two sealed containers with a liquid below and a gas above. In the first container, a movable piston sits high up, with some gas molecules floating above the liquid and a few dissolved in it. In the second container, heavy weights push the piston downward, compressing the gas into a smaller volume. As a result, the concentration of dissolved gas molecules in the liquid below is visibly much higher.

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As pressure increases, gas gets compressed into a smaller space, so more gas molecules strike the surface of the solution and dissolve—this is the basis of Henry’s law.

Henry's Law

The partial pressure equation for Henry's Law.

p = K_{H} x

$p :$ Partial pressure of the gas in the vapour phase
$K_{H} :$ Henry's law constant (depends on the nature of the gas)
$x :$ Mole fraction of the gas in the solution

Key Insight on Temperature: At a constant pressure, a higher

K_{H}

value results in a lower solubility (

x

). Experimental data shows that

K_{H}

increases with temperature, which means the solubility of gases drops as liquids get warmer.

Example 1.4: Henry's Law Calculation

Calculates millimoles of nitrogen dissolved in water.

Problem. If $\text{N}_2$ gas is bubbled through water at 293 K, how many millimoles of $\text{N}_2$ gas would dissolve in 1 litre of water? Assume that $\text{N}_2$ exerts a partial pressure of 0.987 bar. Given that Henry's law constant for $\text{N}_2$ at 293 K is 76.48 kbar.

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Henry's Constant

Calculate Henry's constant, step by step.

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We are given the molality of $H_2S$ as $0.195 \text{ m}$ at STP, meaning $0.195$ moles of $H_2S$ are dissolved in $1 \text{ kg}$ of water.

First, we calculate the number of moles of water in $1 \text{ kg}$ , which is $\frac{1000 \text{ g}}{18 \text{ g mol}^{-1}} =$ $\text{ mol}$ .

Next, the mole fraction of $H_2S$ ( $x$ ) is calculated as the ratio $\frac{0.195}{0.195 + 55.55}$ , which gives approximately $0.0035$ .

Henry's Law relates the partial pressure of the gas to its mole fraction in solution using the equation $p =$ $\cdot x$ . At STP, assuming standard pressure $p = 0.987 \text{ bar}$ , we rearrange the equation to solve for the constant.

Substituting the values gives $K_H = \frac{0.987 \text{ bar}}{0.0035}$ , resulting in approximately $282 \text{ bar}$ .

Evaluating Temperature Dependence

How does temperature change Henry's constant?

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Why are aquatic species generally more comfortable in cold water than in warm water?

Practice: Soda Water Pressure

Calculates the quantity of CO2 in soda water.

Solve the analytical step-by-step problem based on Intext 1.7.

Calculate the quantity of $CO_2$ (in grams) in 500 mL of soda water when packed under 2.5 atm $CO_2$ pressure at 298 K.

Given: $K_H = 1.67 \times 10^8$ Pa at 298 K. (Note: 1 atm = 101,325 Pa. Assume 500 mL of water = 500 g).

Knowns

List the given variables and their values.

Governing Formula

State Henry's Law.

Substitution and Unit Adjustment

Ensure pressure units match K_H before substituting.

Step-by-Step Calculation

Find the mole fraction, then relate it to the moles of CO2 (n).

Final Answer

Convert moles to grams (Molar mass of CO2 = 44 g/mol).

← previousExpressing Concentration next →Vapour Pressure And Raoult's Law

Example 1.4: Henry's Law Calculation

Calculates millimoles of nitrogen dissolved in water.

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Henry's Constant

Calculate Henry's constant, step by step.

0 of 2 blanks filled

We are given the molality of $H_2S$ as $0.195 \text{ m}$ at STP, meaning $0.195$ moles of $H_2S$ are dissolved in $1 \text{ kg}$ of water.

First, we calculate the number of moles of water in $1 \text{ kg}$ , which is $\frac{1000 \text{ g}}{18 \text{ g mol}^{-1}} =$ $\text{ mol}$ .

Next, the mole fraction of $H_2S$ ( $x$ ) is calculated as the ratio $\frac{0.195}{0.195 + 55.55}$ , which gives approximately $0.0035$ .

Substituting the values gives $K_H = \frac{0.987 \text{ bar}}{0.0035}$ , resulting in approximately $282 \text{ bar}$ .

Practice: Soda Water Pressure

Calculates the quantity of CO2 in soda water.

Solve the analytical step-by-step problem based on Intext 1.7.

Calculate the quantity of $CO_2$ (in grams) in 500 mL of soda water when packed under 2.5 atm $CO_2$ pressure at 298 K.

Given: $K_H = 1.67 \times 10^8$ Pa at 298 K. (Note: 1 atm = 101,325 Pa. Assume 500 mL of water = 500 g).

Knowns

List the given variables and their values.

Governing Formula

State Henry's Law.

Substitution and Unit Adjustment

Ensure pressure units match K_H before substituting.

Step-by-Step Calculation

Find the mole fraction, then relate it to the moles of CO2 (n).

Final Answer

Convert moles to grams (Molar mass of CO2 = 44 g/mol).