Question
Given below are two statements:
Given : Molar mass of $C,H,O,Cl$ are 12, 1, 16 and $35.5\text{ }g{\text{ }mol}^{- 1}$, respectively.
Statement I: In $30\%(w/w)$ solution of methanol in ${CCl}_{4}$ (at T K ), the mole fraction of ${CCl}_{4}$ is equal to 0.33 .
Statement II : Mixture of methanol and ${CCl}_{4}$ shows positive deviation deviation from Raoult's law.
In the light of the above statements, choose the correct answer from the option given below :
Options
Solution
Sol. [Key Concept: For $30\%$ w/w methanol in ${CCl}_{4}$ the mole fraction of ${CCl}_{4} = \frac{70/154}{70/154 + 30/32} = 0.33$ (Statement I true), and the pair shows positive deviation from Raoult's law (Statement II true).]
(i) Let wt of solution $= 100\text{ }g$
wt of methanol $= 30\text{ }g$
wt of ${CCl}_{4} = 100 - 30 = 70\text{ }g$
mole fraction of ${CCl}_{4} = \frac{n_{{CCl}_{4}}}{n_{{CCl}_{4}} + n_{{CH}_{3}OH}} = \frac{\frac{70}{154}}{\frac{70}{154} + \frac{30}{32}} = 0.3267 \approx 0.33$
(ii) ${CCl}_{4}\&$ methanol is mixture of positive deviation from Raoult's law.
So, statement (I) & statement (II) are correct.
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