Solutions Question 391
Question: Two components A and B form an ideal solution. The mole fraction of A and B in ideal solutions are $ X_{A} $ and $ X_{B}, $ while that of in vapour phase, these components have their mole fractions as $ Y_{A} $ and $ Y_{B} $ then, the slope and intercept of plot of $ \frac{1}{Y_{A}} $ us $ \frac{1}{X_{A}} $ will be
Options:
A) $ \frac{p_B^{0}}{p_A^{0}},\frac{p_A^{0}-p_B^{0}}{p_A^{0}} $
B) $ \frac{p_B^{0}}{p_A^{0}},\frac{p_A^{0}+p_B^{0}}{p_A^{0}} $
C) $ \frac{p_A^{0}}{p_B^{0}},\frac{p_A^{0}+p_B^{0}}{p_A^{0}} $
D) $ \frac{p_A^{0}}{p_B^{0}},\frac{p_A^{0}}{p_A^{0}-p_B^{0}} $
Show Answer
Answer:
Correct Answer: A
Solution:
Idea This problem includes the concept of Raoult’s law and their representation as equation of straight line. While solving this problem, student is advised to follow given tips.
Write the partial pressure equation using Raoult’s law.
Put the value of partial pressure to calculate mole fractions.
Rearrange the equation in $ \frac{1}{Y_{A}} $ us $ \frac{1}{X_{A}} $ and determine slope and intercept. $ p_{A}=X_{A}p_A^{0} $ $ p_{B}=X_{B}p_B^{0} $ and $ Y_{A}=\frac{p_{A}}{p_{A}+p_{B}}=\frac{p_A^{0}X_{A}}{p_A^{0}X_{A}+p_B^{0}(1-X_{A})} $
$ Y_{A}=\frac{p_A^{0}X_{A}}{X_{A}(p_A^{0}-p_B^{0})+p_B^{0}} $ $ \frac{1}{Y_{A}}=( \frac{p_A^{0}-p_B^{0}}{p_A^{0}} )+\frac{p_B^{0}}{p_A^{0}}\frac{1}{X_{A}} $
So, slope $ \frac{p_B^{0}}{p_A^{0}} $ and intercept $ \frac{p_A^{0}-p_B^{0}}{p_A^{0}} $
