Question

The vapour pressure of water at 200C is 17.54 mm. When 20 gm. of a

nonvolatile solute is dissolved in 100 gm. of water, the vapour pressure is

lowered by 0.30 mm what is the molecular weight of substance?​

Answer 1

(There is an error in the question. The temperature is supposed to be 20°C and not 200C)

As given in the question, we have;

$P^o = 17.54 mm$

∴ $P_s$ = $(17.54 - 0.30) mm = 17.24 mm$

Also, we have,

$w$ (amount of solute) = 20 g

$W$ (amount of water) = 100 g

Molecular weight of water = $M$ = 18

Molecular weight of substance = $m$ = ?

Thus, use the following equation to derive the molecular weight of the substance;

$\frac{P^o - P_s}{P_s} = \frac{w}{m}$ × $\frac{M}{W}$

⇒ $\frac{17.54-17.24}{17.24} = \frac{20}{m}$ × $\frac{18}{100}$

⇒ $\frac{0.30}{17.24} = \frac{360}{100m}$

⇒ $m = \frac{360 * 17.24}{100 * 0.30} = 206.88$

Ans) Molecular weight of the substance = 206.88