Question

Equal weights of two substances X and Y are dissolved in equal volumes of water. The osmotic pressure of the solution containing Y is five times the osmotic pressure of the solution containing X. What is the molecular weight of X if that of Y is 60?

Answer 1

Given: Equal weights of two substances, X and Y are dissolved in equal volumes of water. (so volume V is constant)

Osmotic pressure of Y’s solution is 5 times that of X

Molecular weight of Y = 60 g/mol

We need to find the molecular weight of X

By using Van’t Hoff law:

`pi = w/M RT`

Since w, R, T, and V are the same for both, osmotic pressure is inversely proportional to molecular weight:

`((pi_Y)/(pi_X)) = ((M_X)/(M_Y))`

`(pi_Y)/(pi_X)` = 5    ...(given)

M_Y = 60

so,

`5 = M_X/60`

M_X = 5 × 60

M_X = 300 g/mol

The molecular weight of X is 300 g/mol.