Relationship between Molarity and Molality when density of solution is less than 1gm/ml

When the density of a solution is less than 1gm/ml, it means that the solvent is lighter than water and the solution is considered as a dilute solution. In such cases, the relationship between molarity and molality is affected as the density of the solution is not a constant value. Let's understand this in detail.

Molarity
Molarity is defined as the number of moles of solute per liter of solution. It is represented by the symbol 'M'. The formula for molarity is given as:

Molarity (M) = Number of moles of solute / Volume of solution in liters

Molality
Molality is defined as the number of moles of solute per kilogram of solvent. It is represented by the symbol 'm'. The formula for molality is given as:

Molality (m) = Number of moles of solute / Mass of solvent in kilograms

Relationship between Molarity and Molality
The relationship between molarity and molality is affected when the density of the solution is less than 1gm/ml. This is because the volume of the solution changes with temperature and pressure, whereas the mass of the solvent remains constant. Therefore, the density of the solution changes with temperature and pressure.

To understand this, let's consider an example. Suppose we have a solution of sucrose in water. The density of the solution is 0.98gm/ml. We want to calculate the molarity and molality of the solution.

Molarity (M) = Number of moles of solute / Volume of solution in liters
Molality (m) = Number of moles of solute / Mass of solvent in kilograms

Since the density of the solution is less than 1gm/ml, the volume of the solution will change with temperature and pressure. Therefore, we cannot use the volume of the solution to calculate molarity. Instead, we need to use the mass of the solution.

Molarity (M) = Number of moles of solute / Mass of solution in kilograms

On the other hand, since the mass of the solvent remains constant, we can use the mass of the solvent to calculate molality. Therefore, the formula for molality remains the same.

Molality (m) = Number of moles of solute / Mass of solvent in kilograms

In conclusion, when the density of a solution is less than 1gm/ml, the relationship between molarity and molality is affected as the volume of the solution changes with temperature and pressure, whereas the mass of the solvent remains constant. Therefore, we need to use the mass of the solution to calculate molarity, whereas we can use the mass of the solvent to calculate molality.

Density of solution = 1gm/ml
volume of solution = 1litre
molarity= no. of moles of solute/volume of solution in litre
volume = 1litre
therefore molarity = no. of moles of solute (1)
Now,
molality = no. of moles of solute / mass of solvent in Kg
now from (1)
molality = molarity /mass of solvent in Kg