YESPYQ Start Practice
🛠️ JEE🧪 Chemistry

The plots of \(\frac{1}{{\mathrm{X}}_{\mathrm{A}}}and\frac{1}{{Y}_{A}}(where{\mathrm{X}}_{\mathrm{A}}\mathrm{and}{\mathr…

Q1 FREE PREVIEW

The plots of \(\frac{1}{{\mathrm{X}}_{\mathrm{A}}}and\frac{1}{{Y}_{A}}(where{\mathrm{X}}_{\mathrm{A}}\mathrm{and}{\mathrm{Y}}_{\mathrm{A}}\mathrm{are}\mathrm{the}\mathrm{mole}\mathrm{fraction}\mathrm{of}\mathrm{liquid}\mathrm{A}\mathrm{in}\mathrm{liquid}\mathrm{and}\mathrm{vapour}\mathrm{phase}\mathrm{respectively})\) is linear with slope and intercepts respectively

(Memory Based JEE Mains 23/01/2025 ,Shift -2)

a

\({{\mathrm{P}}_{\mathrm{A}}}^{0}/{{\mathrm{P}}_{\mathrm{B}}}^{0}\mathrm{and}\frac{{{\mathrm{P}}_{\mathrm{A}}}^{0}-{{\mathrm{P}}_{\mathrm{B}}}^{0}}{{{\mathrm{P}}_{\mathrm{B}}}^{0}}\)

b

\({{\mathrm{P}}_{\mathrm{A}}}^{0}/{{\mathrm{P}}_{\mathrm{B}}}^{0}\mathrm{and}\frac{{{\mathrm{P}}_{\mathrm{B}}}^{0}-{{\mathrm{P}}_{\mathrm{A}}}^{0}}{{{\mathrm{P}}_{\mathrm{B}}}^{0}}\)

c

\({{\mathrm{P}}_{\mathrm{B}}}^{0}/{{\mathrm{P}}_{\mathrm{A}}}^{0}\mathrm{and}\frac{{{\mathrm{P}}_{\mathrm{A}}}^{0}-{{\mathrm{P}}_{\mathrm{B}}}^{0}}{{{\mathrm{P}}_{\mathrm{B}}}^{0}}\)

d

\({{\mathrm{P}}_{\mathrm{B}}}^{0}/{{\mathrm{P}}_{\mathrm{A}}}^{0}\mathrm{and}\frac{{{\mathrm{P}}_{\mathrm{B}}}^{0}-{{\mathrm{P}}_{\mathrm{A}}}^{0}}{{{\mathrm{P}}_{\mathrm{B}}}^{0}}\)

✓ Correct answer: b)

\({{\mathrm{P}}_{\mathrm{A}}}^{0}/{{\mathrm{P}}_{\mathrm{B}}}^{0}\mathrm{and}\frac{{{\mathrm{P}}_{\mathrm{B}}}^{0}-{{\mathrm{P}}_{\mathrm{A}}}^{0}}{{{\mathrm{P}}_{\mathrm{B}}}^{0}}\)

Explanation

By the Rault's law

\({\mathrm{P}}_{\mathrm{A}}={\mathrm{P}}_{\mathrm{A}}^{\mathrm{o}}{\mathrm{X}}_{\mathrm{A}}....(1)\\ {\mathrm{P}}_{\mathrm{B}}={\mathrm{P}}_{\mathrm{B}}^{\mathrm{o}}{\mathrm{X}}_{\mathrm{B}}.....(2)\\ \mathrm{Now}\\ {\mathrm{P}}_{\mathrm{A}}={\mathrm{Y}}_{\mathrm{A}}{\mathrm{P}}_{\mathrm{T}}\Rightarrow {\mathrm{P}}_{\mathrm{T}}=\frac{{\mathrm{P}}_{\mathrm{A}}}{{\mathrm{Y}}_{\mathrm{A}}}\\ {\mathrm{P}}_{\mathrm{B}}={\mathrm{Y}}_{\mathrm{B}}{\mathrm{P}}_{\mathrm{T}}\Rightarrow {\mathrm{P}}_{\mathrm{T}}=\frac{{\mathrm{P}}_{\mathrm{B}}}{{\mathrm{Y}}_{\mathrm{B}}}\\ \frac{{\mathrm{P}}_{\mathrm{A}}}{{\mathrm{Y}}_{\mathrm{A}}}=\frac{{\mathrm{P}}_{\mathrm{B}}}{{\mathrm{Y}}_{\mathrm{B}}}\\ \frac{{\mathrm{P}}_{\mathrm{A}}^{\mathrm{o}}{\mathrm{X}}_{\mathrm{A}}}{{\mathrm{Y}}_{\mathrm{A}}}=\frac{{\mathrm{P}}_{\mathrm{B}}^{\mathrm{o}}{\mathrm{X}}_{\mathrm{B}}}{{\mathrm{Y}}_{\mathrm{B}}}\left(\mathrm{From}\left(1\right)\mathrm{and}\left(2\right)\right)\\ \frac{{\mathrm{P}}_{\mathrm{A}}^{\mathrm{o}}{\mathrm{X}}_{\mathrm{A}}}{{\mathrm{Y}}_{\mathrm{A}}}=\frac{{\mathrm{P}}_{\mathrm{B}}^{\mathrm{o}}\left(1-{\mathrm{X}}_{\mathrm{A}}\right)}{1-{\mathrm{Y}}_{\mathrm{A}}}\\ \frac{{\mathrm{P}}_{\mathrm{A}}^{\mathrm{o}}\left(1-{\mathrm{Y}}_{\mathrm{A}}\right)}{{\mathrm{Y}}_{\mathrm{A}}}=\frac{{\mathrm{P}}_{\mathrm{B}}^{\mathrm{o}}\left(1-{\mathrm{X}}_{\mathrm{A}}\right)}{{\mathrm{X}}_{\mathrm{A}}}\\ \frac{{\mathrm{P}}_{\mathrm{A}}^{\mathrm{o}}}{{\mathrm{Y}}_{\mathrm{A}}}-\frac{{\mathrm{P}}_{\mathrm{A}}^{\mathrm{o}}{\mathrm{Y}}_{\mathrm{A}}}{{\mathrm{Y}}_{\mathrm{A}}}=\frac{{\mathrm{P}}_{\mathrm{B}}^{\mathrm{o}}}{{\mathrm{X}}_{\mathrm{A}}}-\frac{{\mathrm{P}}_{\mathrm{B}}^{\mathrm{o}}{\mathrm{X}}_{\mathrm{A}}}{{\mathrm{X}}_{\mathrm{A}}}\\ \frac{{\mathrm{P}}_{\mathrm{B}}^{\mathrm{o}}}{{\mathrm{X}}_{\mathrm{A}}}=\frac{{\mathrm{P}}_{\mathrm{A}}^{\mathrm{o}}}{{\mathrm{Y}}_{\mathrm{A}}}+\left({\mathrm{P}}_{\mathrm{B}}^{\mathrm{o}}-{\mathrm{P}}_{\mathrm{A}}^{\mathrm{o}}\right)\\ \frac{1}{{\mathrm{X}}_{\mathrm{A}}}=\frac{1}{{\mathrm{Y}}_{\mathrm{A}}}\left(\frac{{\mathrm{P}}_{\mathrm{A}}^{\mathrm{o}}}{{\mathrm{P}}_{\mathrm{B}}^{\mathrm{o}}}\right)+\frac{\left({\mathrm{P}}_{\mathrm{B}}^{\mathrm{o}}-{\mathrm{P}}_{\mathrm{A}}^{\mathrm{o}}\right)}{{\mathrm{P}}_{\mathrm{B}}^{\mathrm{o}}}\\ \mathrm{Compare}\mathrm{with}\mathrm{y}=\mathrm{mx}+\mathrm{c}\)

← Previous questionNext question →

Practice more JEE Chemistry PYQs

See every question on Solutions, or browse the full JEE question bank.

See all questions on Solutions →