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For an ideal binary solution, if a graph is drawn between $1/x_A$ and $1/y_A$, where $x_A$ is the mole fraction of A in the liquid phase and $y_A$ is the mole fraction of A in the vapour phase, the resulting straight line has which slope and intercept, respectively?

1. $p_B^0/p_A^0$, $(p_B^0 - p_A^0)/p_B^0$
2. $p_A^0 - p_B^0$, $(p_A^0 - p_B^0)/p_B^0$
3. $p_B^0 - p_A^0$, $(p_B^0 - p_A^0)/p_B^0$
4. $p_A^0/p_B^0$, $(p_A^0 - p_B^0)/p_A^0$

Correct answer: $p_A^0/p_B^0$, $(p_A^0 - p_B^0)/p_A^0$

Solution

For an ideal solution, $y_A=\dfrac{x_A p_A^0}{x_A p_A^0+(1-x_A)p_B^0}$. Rearranging gives $\dfrac{1}{y_A}=\dfrac{p_A^0-p_B^0}{p_A^0}+\dfrac{p_B^0}{p_A^0}\cdot\dfrac{1}{x_A}$, so the slope and intercept follow directly.

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