Calculate the molar mass of non volatile solute when 1 g of it is dissolved in 100 g solvent decreases its freezing point by 0.2 K . [ K f = 1.2 K kg mol − 1 ]

Question

Calculate the molar mass of non volatile solute when 1 g of it is dissolved in 100 g solvent decreases its freezing point by 0.2 K . [ K f ​ = 1.2 K kg mol − 1 ]

TestHub · Accepted Answer

The depression in freezing point is given by the formula:

$Δ T_{f} = K_{f} \times m$

where $m$ is the molality of the solution.

Molality $m = \frac{w _{2} \times 1000}{M _{2} \times w _{1}}$

Substituting the given values ( $w_{2} = 1 g$ , $w_{1} = 100 g$ , $Δ T_{f} = 0.2 K$ , $K_{f} = 1.2 K kg mol^{- 1}$ ):

$0.2 = \frac{1.2 \times 1 \times 1000}{M _{2} \times 100}$

$0.2 = \frac{12}{M _{2}}$

$M_{2} = \frac{12}{0.2} = 60 g mol^{- 1}$

Answer: $60 g mol^{- 1}$

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