# Heat of Solution Formula

The change in enthalpy associated with the dissolution of a substance in a solvent at constant pressure resulting in infinite dilution is known as heat of solution. The enthalpy of solution is expressed in KJ/mol at constant temperature.

When a solute is dissolved in a solvent to make its solution, enthalpy change occurs. The heat evolved or absorbed when a solid or gas is dissolved in the solvent is called the heat of solution or more accurately the heat of dissolution.

It is a common experience that when a solute is dissolved in a solvent to make its solution, enthalpy change takes place. When a solid or gas is dissolved in the solvent the heat evolved or absorbed is called the heat of solution more correctly the heat of dissolution.

The measurement of heat of solution is expressed in a calorimeter; practical difficulty is experienced in calculating the changes in temperature when a large number of moles of the solvent are present.

The heat of solution formula is given by,

ΔHwater = masswater × ΔTwater × specific heatwater

Where,

ΔH = heat change,

masswater = sample mass,

ΔT = temperature difference,

Specific heat = 0.004184 kJ/g∘C.

Example 1

The heat absorbed when hydrated salt (Na2CO3.10H2O) is dissolved at 291K isothermally in a large quantity of water is 65 KJ per mole solute. Determine the heat of crystallization of 1kg Na2CO3.10H2O

Solution:

Given data:

m = 65 kJ per mol

ΔT = 291K

Specific heat = 0.004184 KJ/g∘C

Substitute in the given formula, we get

ΔHwater= masswater  × ΔTwater × specific heatwater

= 65 × 291 × 0.004184

Therefore, ΔHwater = 79.140 kJ/Kg solute.

Example 2

Determine the heat of solution of boric acid by applying the heat of formation data:

m = 1095 kJ/mol,

ΔT = 298K,

Specific heat = 0.004184 kJ/g∘C.

Solution:

Given parameters are,

m = 1095 kJ/mol,

ΔT = 298K,

Specific heat = 0.004184 kJ/g∘C,

Substitute in the given formula

ΔΔHwater = masswater × ΔTwater × specific heatwater

= 1095 × 298 × 0.004184

Therefore, ΔHwater = 1365.28 kJ/Kg/solute.