Q76 / 200 · NEET 2012 (Screening) · Chemistry

$p_A$ and $p_B$ are the vapour pressure of pure liquid components, $A$ and $B$, respectively of an ideal binary solution. If $x_A$ represents the mole fraction of component $A$, the total pressure of the solution will be

  • A
    $p_A+x_A\left(p_B-p_A\right)$
  • B
    $p_A+x_A\left(p_A-p_B\right)$
  • C
    $p_B+x_A\left(p_B-p_A\right)$
  • Correct answer
    D
    $p_B+x_A\left(p_A-p_B\right)$

Solution

Total pressure, $p_T=p_A^{\prime}+p_B^{\prime}$ We know that, $p_A^{\prime}=p_A x_A$ $p_B^{\prime}=p_B x_B$ Substituting the values of $p_A^{\prime}$ and $p_B^{\prime}$ in Eq. (i) $\begin{aligned} p_T & =p_A x_A+p_B x_B \\ {\left[x_A+x_B\right.} & \left.=1 \Rightarrow x_A=1-x_B \text { or } x_B=1-x_A\right] \\ & =p_A x_A+p_B\left(1-x_A\right) \\ & =p_A x_A+p_B-p_B x_A \\ \therefore p_T & =p_B+x_A\left(p_A-p_B\right) \end{aligned}$

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

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