For a saturated solution of AgCl at $$25$$°C, specific conductance $$3.41$$ × $$10-6$$ $$ohm-1$$ $$cm-1$$ and of water used for preparing. The solution is $$1.60$$ × $$10-6$$ $$ohm-1$$ $$cm-1$$. If λAgCl∞ $$=$$ $$138.3$$ $$ohm-1$$ $$cm2$$ $$eq-1$$, the Ksp of AgCl is $$0.17$$ × $$10-x$$ $$M2$$.The value of x is

Question

For a saturated solution of AgCl at $$25$$°C, specific conductance $$3.41$$ × $$10-6$$ $$ohm-1$$ $$cm-1$$ and of water used for preparing. The solution is $$1.60$$ × $$10-6$$ $$ohm-1$$ $$cm-1$$. If λAgCl∞ $$=$$ $$138.3$$ $$ohm-1$$ $$cm2$$ $$eq-1$$, the Ksp of AgCl is $$0.17$$ × $$10-x$$ $$M2$$.The value of x is

Infinity Learn · Accepted Answer

For AgCl, molarity $$=$$ normality κ$$=3.41$$×$$10$$−$$6$$−$$1.6$$×$$10$$−$$6=1.81$$×$$10$$−$$6$$Ω−$$1cm$$−$$1For$$ saturated solution of sparingly soluble salt,λ$$V=$$λ∞  and   solubility $$=$$ normality ∴ λ$$V=$$λ∞$$=1000$$×Ks∴ $$s=1000$$×Kλ∞$$=1000$$×$$1.81$$×$$10$$−$$6138.3=1.31$$×$$10$$−$$5$$ Now, $$Ksp(AgCl)=s2=1.31$$×$$10$$−$$52=0.1716$$×$$10$$−$$9$$∴ $$x=9$$

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