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Dalton's Law of Partial Pressures

The vapour pr...

Question

The vapour pressure of a solution of methanol and ethanol at $20^{'} C$ was found to be $70 m m$ of Hg. Adding $10 g$ of urea to $80 g$ of this solution lowers the vapour pressure to $64.6 m m$ of Hg. Determine composition of the original solution

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Solution

$\begin{matrix} P_{1}^{\circ} (m e t h a n o l), P_{2}^{\circ} (e t h a n o l) P_{T} = {P_{1}}^{\circ} x_{1} + P_{2}^{\circ} x_{2} = {P_{1}}^{\circ} (1 - x_{2}) + P_{2}^{\circ} x_{2} P_{T} = {P_{1}}^{\circ} - {P_{1}}^{\circ} x_{2} + P_{2}^{\circ} x_{2} P_{T} = {P_{1}}^{\circ} + x (P_{2}^{\circ} - P_{1}^{\circ}) 70 m m H s = 88.7 + x_{2} (88.7 - 44.5) 70 = 88.7 - 44.2 x_{2} 18.7 = 44.2 x_{2} x_{2} = 0.42 \Rightarrow E t h a n o l M e t h a n o l x_{1} + x_{2} = 1 x_{1} = 1 - 0.42 x_{1} = 0.58 \end{matrix}$

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