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  4. An ideal solution is formed by mixing 23g C2H5OH with 16.0g of CH3OH at the same temperature. The vapour pressures of pure C2H5OH and CH3OH are 40mm of Hg and 80mm of Hg respectively and total vapour pressure of the solution is x cm of Hg. Find x .

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Q. An ideal solution is formed by mixing 23g $C_{2}H_{5}OH$ with 16.0g of $CH_{3}OH$ at the same temperature. The vapour pressures of pure $C_{2}H_{5}OH$ and $CH_{3}OH$ are 40mm of $Hg$ and 80mm of $Hg$ respectively and total vapour pressure of the solution is $x \, cm$ of $Hg. \, $ Find $x$ .

NTA AbhyasNTA Abhyas 2022

Solution:

$n_{ C _2 H _5 OH }=\frac{23}{46}=\frac{1}{2} \cdot n_{ CH _3 OH }=\frac{16}{32}=\frac{1}{2}$
$P_A=P_A^0 \times X_A \quad \Rightarrow \quad P_A=40 \times \frac{1}{2}=20 m \cdot n$
$P_B=P_B^\rho \Rightarrow \quad P_B=80 \times \frac{1}{2}=40 m \cdot n \quad+60 m \cdot n =6 cm$