A) 1.5
B) 3.5
C) 2.5
D) 4.0
Correct Answer: B
Solution :
In solution \[{{X}_{a}}=0.3\] \[\therefore \,\,\,\,\,\,\,\,{{X}_{b}}=0.7\] In vapors \[{{Y}_{a}}=0.6\] \[\therefore \,\,\,\,\,\,{{Y}_{b}}=0.4\] Using Dalton?s law \[{{Y}_{a}}\,=\frac{{{P}_{a}}}{{{P}_{T}}}\] i.e., \[{{Y}_{a}}\,=\frac{P_{a}^{o}\times {{X}_{a}}}{P_{a}^{o}\times \,{{X}_{a}}\,\times P_{b}^{o}\,{{X}_{b}}}\] \[\therefore \,\,\,{{Y}_{b}}\,=\frac{P_{b}^{o}\,\times {{X}_{b}}}{P_{a}^{o}\times \,{{X}_{a}}\,\times P_{b}^{o}\,{{X}_{b}}}\] \[\therefore \,\,\,\frac{{{Y}_{a}}}{{{Y}_{b}}}\,=\frac{P_{a}^{o}{{X}_{a}}}{P_{b}^{o}\,{{X}_{b}}}\] \[\therefore \,\,\frac{P_{a}^{o}}{P_{b}^{o}\,}=\frac{{{Y}_{a}}}{{{Y}_{b}}}\times \frac{{{X}_{b}}}{{{X}_{a}}}\,=\frac{0.6}{0.4}\,\times \frac{0.7}{0.4}\times \,\frac{0.7}{\,0.3}\,=3.5\]
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