Q. $\bigwedge_{{ClCH}_{2}COONa}^{\infty} = 224\mathrm{\Omega}^{- 1}\ {cm}^{2}\ g\ {equiv}^{- 1}$ $\bigwedge_{NaCl}^{\infty} = 38.5\mathrm{\Omega}^{- 1}\ {cm}^{2}\ g\ {equiv}^{- 1}$ $\bigwedge_{HCl}^{\infty} = 203\mathrm{\Omega}^{- 1}\ {cm}^{2}\ g\ {equiv}^{- 1}$ What is the value of $\lambda_{ClCH_{2}COOH} = ?$

A) $288.5\mathrm{\Omega}^{- 1}\ {cm}^{2}\ g\ {equiv}^{- 1}$
B) $289.5\mathrm{\Omega}^{- 1}\ {cm}^{2}\ g\ {equiv}^{- 1}$
C) $388.5\mathrm{\Omega}^{- 1}\ {cm}^{2}\ g\ {equiv}^{- 1}$
D) $59.5\mathrm{\Omega}^{- 1}\ {cm}^{2}\ g\ {equiv}^{- 1}$
Explanation

(c)
According to Kohlrausch’s law
$\Lambda_{{ClCH}_{2}COOH}^{\infty} = \ \Lambda_{{ClCH}_{2}COO^{-}}^{\infty} + \ \Lambda_{H^{+}}^{\infty}$
Given from Kohlrausch law,
$\Lambda_{{ClCH}_{2}COONa}^{\infty} = 224\mathrm{\Omega}^{- 1}\ {cm}^{2}\ g\ {eq}^{- 1}$
$\Lambda_{{ClCH}_{2}COONa}^{\infty} = \Lambda_{{ClCH}_{2}COO^{-}}^{\infty} + \ \Lambda_{{Na}^{+}}^{\infty}\$…(i)
$\Lambda_{HCl}^{\infty} = 203\mathrm{\Omega}^{- 1}\ {cm}^{2}\ g\ {eq}^{- 1}$
$\Lambda_{HCl}^{\infty} = \ \Lambda_{H}^{\infty} + \Lambda_{Cl}^{\infty}$ …(ii)
$\Lambda_{NaCl}^{\infty} = 38.5\ \mathrm{\Omega}^{- 1}\ {cm}^{2}\ g\ {eq}^{- 1}$
$\Lambda_{NaCl}^{\infty} = \Lambda_{Na^{+}}^{\infty} + \ \Lambda_{Cl}$ ….(iii)
Adding Eqs. (i) and (ii) and subtracting Eq. (iii)
$\Lambda_{{ClCH}_{2}COO^{-}}^{\infty} + \ \Lambda_{H^{+}}^{\infty} = \ \Lambda_{{ClCH}_{2}COONa}^{\infty}\ + \ \Lambda_{HCl}^{\infty}\ - \ \Lambda_{NaCl}^{\infty}\$
= 224 + 203 – 38.5
= 427 – 38.5
$= \ 388.5\mathrm{\Omega}^{- 1}\ {cm}^{2}\ g\ {eq}^{- 1}$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.