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Compare the two quantities below.
Column A: $1 - \dfrac{1}{27}$
Column B: $\dfrac{8}{9} + \dfrac{1}{81}$
Column A: $1 - \dfrac{1}{27} = \dfrac{27-1}{27} = \dfrac{26}{27}$
Convert to 81 denominator: $\dfrac{26}{27} = \dfrac{78}{81}$
Column B: $\dfrac{8}{9} + \dfrac{1}{81} = \dfrac{72}{81} + \dfrac{1}{81} = \dfrac{73}{81}$
Since $\dfrac{78}{81} > \dfrac{73}{81}$, Column A is greater.
Mole fraction in liquid: $x_A = 0.40,\ x_B = 0.60$
By Raoult's Law:
$P_A = x_A \cdot P_A^0 = 0.40 \times 7000 = 2800\ \text{Pa}$
$P_B = x_B \cdot P_B^0 = 0.60 \times 12000 = 7200\ \text{Pa}$
$P_{\text{total}} = 2800 + 7200 = 10000\ \text{Pa}$
In vapour phase: $y_A = \dfrac{P_A}{P_{\text{total}}} = \dfrac{2800}{10000} = \mathbf{0.28}$
$y_B = 1 - 0.28 = \mathbf{0.72}$
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