Question

The ionization constant of a weak electrolyte is $ 25\times {{10}^{-6}} $ while the equivalent conductance of its 0.01 M solution is $ 19.6\text{ }S\text{ }c{{m}^{2}}e{{q}^{-1}} $ . The equivalent conductance of the electrolyte at infinite dilution (in $ S\text{ }c{{m}^{2}}e{{q}^{-1}} $ ) will be

• A. 340
• B. 208
• C. 364
• D. 392

Answer 1

Answer: (D)

Sol. $ \underset{\begin{smallmatrix} \,\,\,\,\,\,C \\ C(1-\alpha ) \end{smallmatrix}}{\mathop{HA}}\,\underset{\begin{smallmatrix} \,\,0 \\ C\alpha \end{smallmatrix}}{\mathop{{{H}^{+}}}}\,+\underset{\begin{smallmatrix} \,\,\,0 \\ C\alpha \end{smallmatrix}}{\mathop{{{A}^{-}}}}\, $
$ K=\frac{C.\alpha .C\alpha }{C(1-\alpha )}=\frac{C{{\alpha }^{2}}}{1-\alpha }\simeq C{{\alpha }^{2}} $
$ 25\times {{10}^{-6}}={{10}^{-2}}\times {{\alpha }^{2}} $
$ \alpha =5\times {{10}^{-2}} $
$ \alpha =\frac{{{\Lambda }^{c}}}{{{\Lambda }^{\infty }}} $
$ {{\Lambda }^{\infty }}=\frac{{{\Lambda }^{c}}}{\alpha }=\frac{19.6}{5\times {{10}^{2}}}=382S\,c{{m}^{2}}e{{q}^{-1}} $