At 300 K . the vapour pressures of $A$ and $B$ liquids are 500 and 400 mm Hg respectively. Equal moles of A and B are mixed to form an ideal solution, The mole fraction of $A$ and $B$ in vapor state is respectively

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Aicharya · Accepted Answer

$\begin{array}{lll}\mathrm{P}_{\mathrm{A}}^0=500 & \mathrm{n}_{\mathrm{A}}=1 & \mathrm{x}_{\mathrm{A}}=0.5 \\ \mathrm{P}_{\mathrm{B}}^0=400 & \mathrm{n}_{\mathrm{B}}=1 & \mathrm{x}_{\mathrm{B}}=0.5\end{array}$ $\begin{aligned} \therefore & P_A=P_A^0 x_A \\ & P_A=500 \times 0.5=250 \\ & P_B=400 \times 0.5=200 \\ & P_T=P_A+P_B=250+200=450 \end{aligned}$
In vapour state $\begin{aligned} & \mathrm{P}_{\mathrm{A}}=\mathrm{P}_{\mathrm{T}} \times \mathrm{x}_{\mathrm{A}}^{\prime} \\ & \mathrm{x}_{\mathrm{A}}^{\prime}=\frac{\mathrm{P}_{\mathrm{A}}}{\mathrm{P}_{\mathrm{T}}}=\frac{250}{450}=0.555 \\ & \mathrm{x}_{\mathrm{B}}^{\prime}=\frac{\mathrm{P}_{\mathrm{B}}}{\mathrm{P}_{\mathrm{T}}}=\frac{200}{450}=0.444 \end{aligned}$

At 300 K . the vapour pressures of $A$ and $B$ liquids are 500 and 400 mm Hg respectively. Equal moles of A…

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