Calculation of Relative Lowering of Vapour Pressure

When a non-volatile solute is dissolved in a solvent, the vapour pressure of the solution decreases as compared to the pure solvent. The relative lowering of the vapour pressure can be calculated using the following formula:

Relative lowering of vapour pressure (ΔP/P₀) = (moles of solute/mass of solvent in kg) x (RT/M)

Where,
ΔP = Change in vapour pressure
P₀ = Vapour pressure of pure solvent
moles of solute = Number of moles of solute dissolved in the solvent
mass of solvent = Mass of solvent in kg
R = Universal gas constant
T = Temperature in Kelvin
M = Molar mass of solvent

Given Data
Molality of the solution = 0.70

Calculation
Since the molality of the solution is given, we can use the formula:

Molality (m) = (moles of solute/mass of solvent in kg)

Rearranging the formula, we get:

moles of solute = m x mass of solvent in kg

We know that molality (m) = 0.70, and we assume that the mass of solvent is 1 kg (since it is not given). Therefore,

moles of solute = 0.70 x 1 = 0.70 moles

The molar mass of water is 18 g/mol. Therefore, the molar mass of 1 kg (1000 g) of water is:

M = mass/molar mass = 1000/18 = 55.56 moles

Substituting the values in the formula, we get:

ΔP/P₀ = (0.70/1) x (0.0821 x 298/55.56)

ΔP/P₀ = 0.0231

Therefore, the relative lowering of vapour pressure is 0.0231.

Explanation
When a non-volatile solute is dissolved in a solvent, the vapour pressure of the solution decreases as compared to the pure solvent. This is because the solute particles occupy some of the space on the surface of the solvent, thereby reducing the number of solvent particles that can escape into the vapour phase. The relative lowering of the vapour pressure is a measure of the extent to which the vapour pressure of the solution is lowered as compared to the pure solvent. It is defined as the ratio of the change in vapour pressure to the vapour pressure of the pure solvent. The formula for calculating the relative lowering of vapour pressure takes into account the molality of the solution, the mass of the solvent, the molar mass of the solvent, the universal gas constant, and the temperature.

0.7 molal means 0.7 mole solute in 1000g solvent( water). so, moles of solvent = 1000/18 =55.5. relative lowering in vapour pressure = X( mole fraction of solute) = 0.7/ 0.7+ 55.5 = 0.017.