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) \[\frac{p_{A}^{0}}{p_{B}^{0}},\frac{p_{A}^{0}}{p_{A}^{0}-p_{B}^{0}}\]
Correct Answer: A
Solution :
| [a] 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 \[{{Y}_{A}}=\frac{{{p}_{A}}}{{{p}_{A}}+{{p}_{B}}}=\frac{p_{A}^{0}{{X}_{A}}}{p_{A}^{0}{{X}_{A}}+p_{B}^{0}(1-{{X}_{A}})}\] |
| \[{{Y}_{A}}=\frac{p_{A}^{0}{{X}_{A}}}{{{X}_{A}}(p_{A}^{0}-p_{B}^{0})+p_{B}^{0}}\] |
| \[\frac{1}{{{Y}_{A}}}=\left( \frac{p_{A}^{0}-p_{B}^{0}}{p_{A}^{0}} \right)+\frac{p_{B}^{0}}{p_{A}^{0}}\frac{1}{{{X}_{A}}}\] |
| So, slope \[\frac{p_{B}^{0}}{p_{A}^{0}}\] and intercept \[\frac{p_{A}^{0}-p_{B}^{0}}{p_{A}^{0}}\] |
| TEST Edge Students are advised to study Raoult's law for non-ideal solution which may be asked frequently. |
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