# Factors affecting solubility of gases in liquid

### Factors affecting solubility of gases in liquid

Almost all gases are soluble in water in varying amounts. The existence of aquatic life in lakes, rivers etc. is due to the dissolution of oxygen gas of air in water.

Solubility of a gas may be defined as the volume of the gas measured at S.T.P. dissolved per unit volume of the solvent. This method of expressing the concentration is called absorption coefficient of the gas and is usually represented by .

Solubility of a gas in a liquid at a particular temperature is also expressed in term of molarity and mole fraction.

#### Nature of the gas and the solvent

Typically, those gases that are easily liquefied (or have high critical temperatures) are more soluble in the solvent. Furthermore, gases that can react chemically or are capable of forming ions in aqueous solution are more soluble in water than in any other solvent.

Example:

• Gases like H2, O2, N2 dissolve in water in very small amounts whereas the gases like SO2, H2S, HCl, NH3 etc. are highly soluble.
• O2, N2 and CO2 are more soluble in ethyl alcohol than in water while gases such as NH3 and H2S are more soluble in water than in ethyl alcohol.

#### Effect of Temperature

Gases dissolve in a liquid by exothermic process. Therefore, according to Le-Chatelier’s principle, an increase in temperature will result in a decrease in the solubility of a gas if the process is exothermic. [or equilibrium will shift to a direction in which the heat is absorbed]

Solvent + Solute ⇌ Solution + Heat

This is why aquatic species are more comfortable in cold water rather than warm water. However, it may be noted that there are certain gases such as hydrogen and inert gases whose solubility increase slightly with increase of temperature especially in the non-aqueous solvents like alcohols, acetone etc.

#### Effect of Pressure

The solubility of gases increases with increase of pressure. This behaviour is also in accordance with Le-Chatelier’s principle.

To understand this, consider a gas in dynamic equilibrium with a solution. The lower part represents the solution and the upper part is gaseous system. Now increase the pressure over the solution. This will increase the number of gaseous particles per unit volume over the solution. Hence, more molecules will dissolve and solubility of a gas increase until a new equilibrium is reached.

William Henry gave quantitative relationship between the solubility of a gas in a solvent and the pressure of a gas on a solution, known as Henry’s law.

According to this law, the mass of a gas dissolved per unit volume of the solvent at a given temperature is directly proportional to the pressure of the gas in equilibrium with the solution.

m ∝ p      or        m = k.p

Where :  m = mass of the gas dissolved in a unit volume of the solvent,  P = pressure of gas in equilibrium  and K = proportionality constant.

Henry’s Law may also be stated as follow:

The solubility of a gas in a liquid at a particular temperature is directly proportional to the pressure of the gas on that solution at equilibrium.

Dalton, a contemporary of Henry, also concluded independently that if a mixture of gases is in equilibrium with a liquid at a particular temperature, the solubility of any gas in the mixture is directly proportional to the partial pressure of that gas in the mixture.

If we express the solubility of a gas in terms of mole fractions, then Henry’s law can be written as:

χ ∝ p    or    χ = K’.p

[KH =  $$\frac{1}{K’}$$]          p = $$\frac{1}{K’}$$.χ

###### p = KH.χ

Thus, most commonly used form of Henry’s law may be defined as : The pressure of a gas over a solution in which the gas is dissolved is directly proportional to the mole fraction of the gas dissolved in the solution.

###### Mathematical Modifications to Henry's Law

According to Henry’s Law :  Pgas = KH . χgas

χgas  =   $$\frac{n_{gas}}{n_{solution}}~=~\frac{n_{gas}}{n_{solvent}~+~n_{gas}}$$

[nsolvent >> ngas  , So, nsolvent + ngas ≅ nsolvent ]

Pgas =  $$\frac{K_{H}~\times ~n_{gas}}{n_{solvent}}$$

Pgas =  $$\frac{K_{H}~\times ~n_{gas}~\times ~M_{A}}{W_{A}}$$

Pgas =  $$\frac{K_{H}~\times ~W_{gas}~\times ~M_{A}}{M_{gas}~\times ~W_{A}}$$