Relation between molarity and molality

The relation between molarity and molality is due to concentration of solution because the term molarity and molality are the ways to determine the concentration of any solution. In other words,

Molarity divided by Molality is always equal to the weight of the solute divided by volume of the solution. Hence, the relation between molarity and molality is given by,

M/m = w/v

As we know above the concentration is the similar terms in both molarity and molality. But what is concentration. so lets start with concentration.

Concentration means the maximum amount of solute present in a unit volume of solution is known as concentration. concentration can be determined by the following ways:-

Mole Fraction (x)
Molarity (M)
Molality (m)
Mass percentage (w/w)
Volume percentage (v/v)
Part-per million (ppm)

But here we will only talk about molarity and molality. so lets start with what is molarity? and what is molality?

Relation between molarity and molality - Derivation

What is molarity?

Molarity is defined as the total number of moles of solute present in 1 litre of solution. Molarity is one of the ways to determine the concentration of a solution. It is denoted by ‘M’.

Molarity depends on the temperature. that means molarity is inversely proportional to the temperature. When temperature increases then molarity decreases due to increase in volume and vice-versa.

Molarity (M) = No. of moles of solute/ volume of solution

M = n/V

M ∝ 1/V

∴ M ∝ 1/T [ ∵ V ∝ T ]

What is Molality?

Molality is defined as the total number of moles of solute present in per kg of solvent. In other words molality is equal to the number of moles of solute divided by weight of solvent. it is also the one of the ways to determine the cncentration of solution. It is denoted by ‘m’.

Molality (m) = No. of moles of solute / weight of solvent

m = n / w

Derivation of relation between molarity and molality

Let,

molarity of a solution be M.

molality of the solution be m.

Moles of solute be n = w2/m2.

Volume of solution be V.

Weight of solvent be W.

then,

Molarity = No. of moles of solute ∕ volume of solution (in L)

Molarity = No. of moles of solute × 1000 ∕ volume (in mL)

M = n × 1000 ∕ V (in mL)

M = w2/m2 × 1000 ∕ V (in mL) [ ∵ n = w2/m2 ]

∴ M V = w2/m2 × 1000 ————————- (1)

Now,

Molality = No. of moles of solute ∕ weight of solvent ( in kg)

Molality = No. of moles of solute × 1000 ∕ weight (in g)

m = n × 1000 ∕ W (in g)

m = w2/m2 × 1000 ∕ W (in g) [ ∵ n = w2/m2 ]

∴ m W = w2/m2 × 1000 ————————- (2)

From equation (1) and (2) we get,

M V (in mL) = m W (in g) ———————(A)

Hence, the relation between molarity and molality formula is M V (in mL) = m W (in g).