Chemistry · Ch 1 — Solutions

Solubility of a Gas in a Liquid

1.3.2

Solubility of a Gas in a Liquid

Many gases dissolve in liquids, though to very different extents. Oxygen dissolves in water only slightly — yet that small amount of dissolved oxygen is what supports all aquatic life. Hydrogen chloride gas, by contrast, is extremely soluble in water. For gases, solubility is strongly controlled by both pressure and temperature.

Effect of pressure

Consider a gas sitting above a liquid in a closed vessel, at pressure $p$ and temperature $T$ , with the dissolved gas and the gas above the liquid in dynamic equilibrium — gas particles enter the solution as fast as they leave it. Now compress the gas into a smaller volume. This packs more gas particles into each unit of volume above the liquid, so they strike the liquid surface more often and enter the solution faster. More gas dissolves until a new equilibrium is set up at the higher pressure. In short, the solubility of a gas increases as the pressure of the gas above the liquid increases.

Figure 1.1Effect of pressure on the solubility of a gas. The concentration of dissolved gas is proportional to the pressure on the gas above the solution.

Fig. 1.1 — Effect of pressure on the solubility of a gas. The concentration of dissolved gas is proportional to the pressure on the gas above the solution.

Drawn by us to help you understand the concept clearly, and verified to make sure it's accurate. For exams, practice from your NCERT textbook's own diagram.

What the Figure Shows

The figure is a two-part schematic, labelled (a) and (b), of a vessel closed by a

movable piston (the hatched band). Below the piston there are two regions:

Upper region — the gaseous phase: gas particles (dots) at pressure $p$ , directly beneath the piston.
Lower region — the solution: the liquid, with the dots inside it showing the gas that has dissolved.

In panel (a), a single weight $W_1$ rests on the piston and the system is at

dynamic equilibrium — gas particles enter and leave the solution at the same

rate. In panel (b), three weights ( $W_1$ , $W_2$ , $W_3$ ) sit side by side on the

piston. The piston has moved down, compressing the gas into a thinner band, so

the gas particles above the solution are visibly closer together — and more dots now appear inside the solution: more gas has dissolved.

The Physical Idea

Compressing the gas increases the number of gaseous particles per unit volume

over the solution, and with it the rate at which particles strike the liquid

surface and enter it. Dissolving therefore outpaces escape until a new equilibrium is reached at a higher dissolved-gas concentration — the

solubility of the gas increases with pressure.

The key takeaway: higher pressure → higher concentration of dissolved gas.

The Key Formula

This proportionality is Henry's law, stated quantitatively in the text:

p = K_H \, x

where:

$p$ = partial pressure of the gas in the vapour phase …

Henry's law

Henry was the first to put this relationship on a quantitative footing. His law states that, at constant temperature, the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the surface of the liquid. (Dalton, working at the same time, reached the same conclusion independently.)

If the mole fraction of the dissolved gas is used as the measure of its solubility, Henry's law can be stated in its most commonly used form: the partial pressure of a gas in the vapour phase is proportional to the mole fraction of that gas in the solution.

p = K_H\, x

A plot of the partial pressure of the gas against its mole fraction in solution is therefore a straight line, and the slope of that line is $K_H$ .

Figure 1.2Experimental results for the solubility of HCl gas in cyclohexane at 293 K. The slope of the line is the Henry's Law constant, K_H.

Fig. 1.2 — Experimental results for the solubility of HCl gas in cyclohexane at 293 K. The slope of the line is the Henry's Law constant, K_H.

Drawn by us to help you understand the concept clearly, and verified to make sure it's accurate. For exams, practice from your NCERT textbook's own diagram.

The figure is a linear graph with a best-fit straight line passing through the origin.

x-axis: Mole fraction of HCl in its solution in cyclohexane, ranging from 0 to 0.020.
y-axis: Partial pressure of HCl gas above the solution, in torr, ranging from 0 to 1000.
Data points: Experimental scatter points lying close to the best-fit straight line (one point sits visibly just above it — real data, not a perfect fit).
Slope of the line: The Henry’s law constant, $K_H$ , for HCl in cyclohexane at 293 K.

Physical idea: The graph demonstrates Henry’s law — at constant temperature, the partial pressure of a gas above a liquid is directly proportional to its mole fraction in the liquid. The straight line through the origin confirms this proportionality: as the mole fraction of dissolved HCl doubles, its partial pressure also doubles.

Key formula from the textbook:

p = K_H \, x

where:

$p$ = partial pressure of the gas in the vapour phase (in torr or bar)
$x$ = mole fraction of the gas in the solution …

Meaning of the Henry's law constant $K_H$

Different gases have different $K_H$ values at the same temperature, so $K_H$ depends on the nature of the gas (representative values for various gases in water are collected in the accompanying table).

Table 1.2Values of Henry's Law Constant for Some Selected Gases in Water

Gas	Temperature/K	$K_H$ /kbar
He	293	144.97
$H_2$	293	69.16
$N_2$	293	76.48
$N_2$	303	88.84
$O_2$	293	34.86
$O_2$	303	46.82
Argon	298	40.3
$CO_2$	298	1.67
Formaldehyde	298	$1.83\times10^{-5}$

The size of $K_H$ tells us how soluble a gas is. Rearranging Henry's law,

x = \frac{p}{K_H}

shows that, at a given pressure, a larger $K_H$ means a smaller mole fraction dissolved — that is, a lower solubility. So a high $K_H$ corresponds to a poorly soluble gas.

Temperature dependence of $K_H$

$K_H$ also changes with temperature. For gases such as $N_2$ and $O_2$ , $K_H$ rises as the temperature is raised. Since a higher $K_H$ means lower solubility, this tells us that the solubility of these gases falls as the temperature increases — dissolved gas escapes more readily from warmer water.

Effect of temperature

The temperature trend for gases is the opposite of the endothermic-solid case. When a gas dissolves, its molecules pass from the gas phase into the liquid — a process much like condensation, which releases heat, so dissolution of a gas is generally exothermic. Treating this as a dynamic equilibrium and applying Le Chatelier's principle, raising the temperature drives the exothermic dissolution backwards, and solubility decreases as temperature rises.

Note

This is why aquatic organisms fare better in cold water than in warm water: cold water holds more dissolved oxygen.

Applications of Henry's law

Henry's law explains several everyday, industrial and biological observations:

Carbonated drinks: To force more $CO_2$ into soft drinks and soda water, the bottle is sealed under high pressure, which raises the gas's solubility. Opening the bottle drops the pressure and the excess gas fizzes out. …

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Solubility of a Gas in a Liquid