Question

Derive the relation between molarity and molality?

Answer 1

Molarity:

• It is denoted by M.
• Molarity (M) is defined as the number of moles of solute dissolved in per liter of solution.

Molarity = moles of solute / litres of solution

For example, the molecular mass of Sulphuric acid is 98. Now if 98 grams of sulphuric acid is present in 1 liter of the solution then it is 1 molar solution of Sulphuric acid and therefore molarity will be 1.

Molality:

• It is denoted by m.
• Molality (m) is defined as the number of moles of solute dissolved in per kilogram of solvent.

Molality = moles of solute / kilograms of solvent

For example, the molecular mass of Sulphuric acid is 98. If 98 grams of sulphuric acid is present in 1 kg of water then it is 1 molal solution of Sulphuric acid in water and therefore molality will be 1.

Relation between molarity and molality:
Let,
The mass of the given solute = W
The volume of the solution = V
Molality = m
The molar mass of solute = M'
Molarity = M
Therefore, molarity, M will be = W/M′×1000/V.........(1)
And molality, m will be = W/M′×1000/W′………..(2)
As we know, Density = mass/volume
d=M/V
From here, d=W+W′/V

Now, from equation (1), we get
V=W×1000/m×M′ .........(3)
And from equation (2), we get
W′=W×1000/m×M′
Therefore,
W+W′=W+W×1000/m×M′×1000/M′[mM′1000m+1m]W′.........(4)

Now, by dividing equation (4) by (3), we get
d/m=1/m+M′/10001/m
d/m−M′/1000×m
M×1000/(d×1000)−M(M′)
Hence, this is the relation between molality and molarity.