Given:

The urea solution and unknown solution are isotonic.

The molarity of urea solution, M1 = 0.5 M

The mass of unknown solute, w = 10 gm

The volume of the unknown solution, V = 100 ml

To Find:

The molar mass of the unknown solute.

Calculation:

The molarity of the unknown solution is given as:

M2 = (w×1000)/(M.wt×V)

⇒ M2 = (10×1000)/(M.wt×100)

⇒ M2 = 100/M.wt

- As the urea solution and unknown solution are isotonic, it means their osmotic pressure is equal.

⇒ Π(urea) = Π(unknown)

⇒ M1RT = M2RT

⇒ M1 = M2

⇒ 0.5 = 100/M.wt

⇒ M.wt = 100/0.5

⇒ M.wt = 200 gm/mol

- So, the molar mass of the unknown solute is 200 gm/mol.