Q62 / 180 · JIPMER 2015 · Chemistry

For an ideal binary liquid solution with $p_x^0 \gt p_y^0$ in which relation between $X_x$ (mole fraction of $X$ in liquid phase) and $Y_X$ (mole fraction of $X$ in vapour phase) is correct, $X_y$ and $Y_y$ are mole fraction of $Y$ in liquid and vapour phase respectively

  • A
    $X_x \gt Y_x$
  • B
    $X_x=Y_x$
  • Correct answer
    C
    $\frac{X_x}{X_y} \lt \frac{Y_x}{Y_y}$
  • D
    $X_x, Y_x, X_y$ and $Y_y$ cannot be correlated

Solution

$\begin{aligned} & p_x^1=p_x^0 \cdot X_x=p_T \cdot Y_x \\ & p_y^1=p_y^0 \cdot X_y=p_T \cdot Y_y\end{aligned}$ Therefore, $\frac{p_x^0}{p_y^0} \cdot \frac{X_x}{X_y}=\frac{Y_x}{Y_y}$ $\begin{array}{ll}\because & \frac{p_x^0}{p_y^0}\gt1 \\ \therefore & \frac{X_x}{X_y} \lt \frac{Y_x}{Y_y}\end{array}$

Hence, the correct answer is option: 'C'.

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