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JEE Main 20249 AprilEvening Shift
Exam
JEE Main
Year
2024
Date
9 April
Shift
Evening Shift
Subject
Chemistry
Chapter
Electrochemistry

JEE Main 2024 · 9 April · Evening Shift · Chemistry · Electrochemistry

Which out of the following is a correct equation to show change in...

Which out of the following is a correct equation to show change in molar conductivity with respect to concentration for a weak electrolyte, if the symbols carry their usual meaning :

Options

  1. A(\Lambda_{\mathrm{m}}-\Lambda_{\mathrm{m}}^0+\mathrm{AC}^{\frac{1}{2}}=0)
  2. B(\Lambda_m^2 \mathrm{C}-\mathrm{K}_{\mathrm{a}} \Lambda_{\mathrm{m}}^{\circ 2}+\mathrm{K}_{\mathrm{a}} \Lambda_{\mathrm{m}} \Lambda_{\mathrm{m}}=0)
  3. C(\Lambda^2{ }_m \mathrm{C}+\mathrm{K}_{\mathrm{a}} \Lambda_{\mathrm{m}}^{\circ 2}-\mathrm{K}_{\mathrm{a}} \Lambda_{\mathrm{m}} \Lambda_{\mathrm{m}}^{\circ}=0)
  4. D(\Lambda_{\mathrm{m}}-\Lambda_{\mathrm{m}}^{\circ}-\mathrm{AC}^{\frac{1}{2}}=0)

Correct answer

B. (\Lambda_m^2 \mathrm{C}-\mathrm{K}_{\mathrm{a}} \Lambda_{\mathrm{m}}^{\circ 2}+\mathrm{K}_{\mathrm{a}} \Lambda_{\mathrm{m}} \Lambda_{\mathrm{m}}=0)

Step-by-step solution

HA(aq)⇌H+(aq)+A−(aq)Ka=α2C1−αα2C+Kaα−Ka=0(λmλm∞)2C+Kaλmλm∞−Ka=0λm2C+Kaλmλm∞−Ka(λm∞)2=0\begin{aligned} & \mathrm{HA}(\mathrm{aq}) \rightleftharpoons \mathrm{H}^{+}(\mathrm{aq})+\mathrm{A}^{-}(\mathrm{aq}) \\ & \mathrm{K}_{\mathrm{a}}=\frac{\alpha^2 \mathrm{C}}{1-\alpha} \\ & \alpha^2 \mathrm{C}+\mathrm{K}_{\mathrm{a}} \alpha-\mathrm{K}_{\mathrm{a}}=0 \\ & \left(\frac{\lambda_{\mathrm{m}}}{\lambda_{\mathrm{m}}^{\infty}}\right)^2 \mathrm{C}+\mathrm{K}_{\mathrm{a}} \frac{\lambda_{\mathrm{m}}}{\lambda_{\mathrm{m}}^{\infty}}-\mathrm{K}_{\mathrm{a}}=0 \\ & \lambda_{\mathrm{m}}^2 \mathrm{C}+\mathrm{K}_{\mathrm{a}} \lambda_{\mathrm{m}} \lambda_{\mathrm{m}}^{\infty}-\mathrm{K}_{\mathrm{a}}\left(\lambda_{\mathrm{m}}^{\infty}\right)^2=0\end{aligned}
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