Solubility: Solid, Gas & Liquid in a Liquid and Henry's Law | Chemistry Class 12 - NEET PDF Download

What is Solubility?

Solubility of a substance is the maximum amount of solute that can dissolve in a specified quantity of solvent at a particular temperature to form a homogeneous solution.

A solution is a homogeneous mixture of one or more solutes in a solvent. A familiar example is sugar dissolving in tea. The ability of sugar molecules to mix uniformly with water is described by solubility. A solute may be solid, liquid or gas; the solvent is usually a liquid.

On this basis, factors affecting solubility vary with the physical state of the solute:

• Solids in liquids
• Liquids in liquids
• Gases in liquids

The maximum amount of solute which can be dissolved in a specified amount of solvent at a given temperature is called the solubility of that solute in the solvent.

Dissolution

Dissolution means the process by which particles of a solute are separated and dispersed uniformly in a solvent to form a solution. When a solid is added to a liquid, some of its particles leave the solid phase and enter the solution; this increase in dissolved particles is called dissolution.

Crystallisation

Crystallisation is the reverse process: particles of solute in solution come together to form solid particles which separate out from the solution.

When dissolution and crystallisation proceed at the same rate, the system attains a dynamic equilibrium in which the number of solute particles entering the solution equals the number leaving it.

Dynamic equilibrium

At dynamic equilibrium the concentration of solute in the solution remains constant at the given temperature and pressure, because the forward and reverse processes occur at equal rates.

Solute + Solvent ⇌ Solution

A similar equilibrium exists when a gas dissolves in a liquid.

Saturated and Unsaturated Solutions

Saturated solution: A solution in which no more solute can dissolve under the given conditions of temperature and pressure; it is the composition at dynamic equilibrium.

Unsaturated solution: A solution that can dissolve more solute under the given conditions.

1. Solubility of a Solid in a Liquid

Conditions for a solute to dissolve in a solvent

• The solute and solvent should have compatible polarity: polar with polar, non-polar with non-polar.
• The intermolecular attractions in the solute and solvent should be of similar type and strength (often summarised as "like dissolves like").

Factors affecting solubility of a solid in a liquid

1. Nature of solute and solvent

   Only solutes with intermolecular forces similar to the solvent dissolve readily. Polar solids dissolve in polar solvents; non-polar solids dissolve in non-polar solvents.

   Example: Sugar and common salt dissolve readily in water, while naphthalene and anthracene do not. Naphthalene and anthracene dissolve in benzene, whereas sugar and salt do not.

2. Effect of temperature

   Temperature often changes the solubility of solids significantly.

   If the dissolution process is endothermic (ΔH > 0), solubility generally increases with temperature in accordance with Le Châtelier's principle. If the dissolution is exothermic (ΔH < 0), solubility tends to decrease with increasing temperature.

3. Effect of pressure

   Pressure has negligible effect on solid solubility because solids and liquids are essentially incompressible under ordinary pressures.

2. Solubility of Gases in Liquids

The solubility of gases in liquids is strongly affected by both pressure and temperature, and by the chemical nature of the gas and solvent.

The solubility of a gas is commonly expressed in terms of an absorption coefficient (or simply solubility): the volume of gas (in mL, at STP) that dissolves in 1 mL of solvent at the experimental temperature and one atmosphere pressure.

If v is the volume of gas (reduced to STP) dissolved in volume V of solvent under pressure P (in atm), the absorption coefficient α is given by

α = v / (V P)

Factors affecting solubility of gases in liquids

1. Effect of pressure

   Solubility of a gas increases with the partial pressure of that gas above the liquid. In a closed container at equilibrium the rate at which gas molecules enter the liquid equals the rate at which they leave it. Increasing external pressure increases the concentration of gas molecules above the solution and therefore increases the rate at which gas molecules enter the solution until a new equilibrium is reached. Thus higher pressure → higher solubility of gas.

2. Effect of temperature

   Solubility of most gases in liquids decreases with increasing temperature. For many gases the dissolution is effectively exothermic; by Le Châtelier's principle increasing temperature shifts equilibrium to reduce the amount dissolved.

3. Nature of the gas and solvent

   Gases that are easily liquefied are generally more soluble. Gases that react chemically with the solvent are also more soluble (for example, HCl and NH3 in water). Oxygen, nitrogen and carbon dioxide show different solubilities in different solvents: they are often more soluble in organic solvents such as ethanol than in water at the same T and P.

3. Solubility of Liquids in Liquids

Two liquids are mutually soluble when molecules of one are uniformly dispersed among molecules of the other. Water is a very good solvent for many substances and is often called the "universal solvent".

Solubility is commonly measured in g per litre (g L-1). Substances that dissolve 0.1 g or more in 100 mL of water are termed soluble; those that dissolve less than 0.1 g in 100 mL are called sparing soluble or slightly soluble.

Depending on solubility we can obtain saturated solutions, and occasionally supersaturated solutions (solutions that contain more dissolved solute than in the normal saturated state and are metastable-excess solute may crystallise out).

Factors affecting solubility of a liquid in a liquid

1. Temperature

   Generally, solubility of liquids in liquids increases with temperature because higher thermal energy helps solvent molecules overcome intermolecular forces and mix with solute molecules. Exceptions may occur depending on specific interactions.

2. Intermolecular forces and bonding

   Hydrogen bonding, dipole-dipole interactions and dispersion forces between solute and solvent molecules influence solubility. For example, alcohols (which can hydrogen bond) are quite soluble in water.

3. Pressure

   Pressure has a negligible effect on liquid-liquid solubility except when compressibility becomes relevant (uncommon under ordinary conditions).

4. Nature (polarity) of liquids

   "Like dissolves like": polar solvents dissolve polar solutes; non-polar solvents dissolve non-polar solutes.

Henry's Law

Henry's law gives a quantitative relation between the partial pressure of a gas above a liquid and the amount of that gas dissolved in the liquid. It is stated as:

The solubility of a gas in a liquid at a fixed temperature is directly proportional to the partial pressure of that gas above the liquid.

If m is the mass (or concentration) of gas dissolved per unit volume of solvent and P is the partial pressure of the gas in equilibrium with the solution, then

m ∝ P

and hence

m = K P

where K (or KH) is the Henry's law constant for that gas-solvent system at the given temperature. When P = 1 atm, m = K.

Factors affecting the Henry's law constant

1. Nature of the gas

   Different gases have different solubilities; molecular size, polarity and the tendency to interact with the solvent all affect KH.

   
2. Nature of the solvent

   Solvent polarity and structure determine how well it solvates the gas. Polar solvents favour soluble polar gases.

3. Temperature

   KH is temperature dependent. For many gas-solvent systems solubility decreases with increasing temperature, so KH changes accordingly and must be quoted with the temperature.

4. Units and reference state

   KH values depend on the units used for concentration and pressure; always use consistent units and the temperature at which KH is given.

Different gases and solvents therefore have different Henry's law constants, and graphs of solubility versus pressure have different slopes for different systems.

Effect of pressure on solubility of gases in liquids

1. Increasing the partial pressure of a gas above the liquid increases its solubility in the liquid; decreasing pressure reduces solubility.

   

2. At a given pressure, a larger Henry's law constant (KH) corresponds to lower solubility (m = KH P), and a smaller KH corresponds to higher solubility.

Example 1. If N₂ gas is bubbled through water at 293 K, how many millimoles of N₂ gas would dissolve in 1 litre of water? Assume that N₂ exerts a partial pressure of 0.987 bar. Given that Henry's law constant for N₂ at 293 K is 76.48 kbar.

Solution.

The mole fraction of the dissolved gas is given by Henry's law in the form x(gas) = p(gas) / K_H.

x(Nitrogen) = 0.987 bar / 76.48 kbar = 0.987 / 76.48 × 10^3 = 1.29 × 10^-5.

One litre of water contains approximately 55.5 mol of water molecules.

If n is the number of moles of N₂ dissolved, then the mole fraction x(Nitrogen) ≈ n / 55.5 (neglecting n relative to 55.5).

Therefore n = x(Nitrogen) × 55.5 = 1.29 × 10^-5 × 55.5 = 7.16 × 10^-4 mol.

The number of millimoles = 7.16 × 10^-4 × 1000 = 0.716 mmol.

Applications of Henry's law

1. Carbonated beverages:

   Carbon dioxide solubility increases with pressure, so soft drinks are bottled under high pressure to increase CO₂ dissolved in the liquid.

2. Scuba diving and the bends:

   At greater depths partial pressures of atmospheric gases increase and more gas dissolves in blood. Rapid ascent reduces pressure and dissolved gases can form bubbles (decompression sickness or "bends"). Scuba breathing mixes (dilution with helium) and controlled ascent rates reduce risk. Typical breathing mix compositions are chosen to reduce nitrogen narcosis and bubble formation.

   
3. High altitude and anoxia:

   At high altitude the partial pressure of oxygen in air is lower, so less O₂ dissolves in blood, causing breathlessness and weakness (anoxia). Mountaineers use oxygen cylinders to raise the inspired partial pressure of O₂.

   
4. Respiration and blood oxygenation:

   In the lungs, where the partial pressure of oxygen is high, haemoglobin forms oxyhaemoglobin; in tissues where partial pressure is low, oxygen is released for cellular use.

   Respiration and the Oxygenation of Blood

Limitations of Henry's Law

Henry's law is valid only when the following conditions are met:

• The pressure is not too high,
• The temperature is not very low,
• The gas does not chemically react with the solvent (no chemical combination).

Example 2. Calculate the concentration of CO₂ in a soft drink that is bottled at a partial pressure of CO₂ of 4 atm over the liquid at 25°C. The Henry's Law constant for CO₂ in water at 25°C is 3.1 × 10^-2 mol litre^-1 atm^-1.

Solution.

Apply Henry's law: S = K P.

S = (3.1 × 10^-2 mol L^-1 atm^-1) × 4 atm.

S = 0.124 mol L^-1 (≈ 0.12 mol L^-1).

Try Yourself!

Q.1. At 20° C the solubility of nitrogen gas in water is 0.0150 g/litre when the partial pressure N₂ is 580 torr. Find the solubility N₂ in H₂O at 20°C when its partial pressure is 800 torr.

Ans. 0.0207 g/litre.