Multiple choice

The vapour pressure of two volatile liquid mixtures is $p_t =5.3+2x_B$ (in mm of Hg), where $X_B$ is mole fraction of B in mixture. What is the ratio of mole functions of A & B in liquid phase ( $P_A and P_B$ are vapour pressures of A&B)

  1. $\frac { 73 }{ 53 }$
  2. $\frac { 73 }{ 53 } \times \frac { P_{ A } }{ { P }_{ B } }$
  3. $\frac { 53 }{ 73 }$
  4. $\frac { 53 }{ 73 } \times \frac { P_{ A } }{ { P }_{ B } }$
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A Correct answer
AI explanation

The given equation for total vapor pressure is p sub t equals 5.3 plus 2 times x sub B, and since the mole fraction of A is 1 minus x sub B, we can rewrite the total pressure as p sub A times x sub A plus p sub B times x sub B. By substituting x sub A, we get p sub t equals p sub A plus (p sub B minus p sub A) times x sub B, meaning the intercept 5.3 represents p sub A and the slope 2 means p sub B is 2 units greater than p sub A, giving values of 5.3 and 7.3 for the pure pressures. The ratio of the mole fractions of A to B in the liquid phase is found by dividing their partial pressures by their pure component pressures and setting them proportional, which ultimately reduces to p sub B divided by p sub A, yielding the ratio 73 to 53.

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