The specific conductance of a saturated solution of silver chloride in water at 298K is 1.26 × 10^-4 Sm^-1. The molar conductance's at infinite dilution of KCI, AgNO₃ and KNO₃ are 150 × 10^-4, 133.5 × 10^-4 and 145 × 10^-4 (all in Sm² moI^-1) respectively. False statements are

 $\begin{array}{l}\left(1\right) {\mathrm{\Lambda }}_{0\left(\mathrm{AgCl}\right)}={\mathrm{\Lambda }}_{0\left(\mathrm{KCl}\right)}+{\mathrm{\Lambda }}_0\left({\mathrm{AgNO}}_3\right)-{\mathrm{\Lambda }}_0\left({\mathrm{KNO}}_3\right)\\ =(150+133.5-145)\times {10}^{-4}=138.5\times {10}^{-4}{\mathrm{Sm}}^2{\mathrm{mol}}^{-1}\\ =138.5\times {10}^{-4}{\mathrm{Sm}}^2{\mathrm{mol}}^{-1}\times {10}^4{\mathrm{cm}}^2{\mathrm{m}}^{-2}\\ =138.5{\mathrm{Scm}}^2{\mathrm{mol}}^{-1}\end{array}$

$\begin{array}{l}\left(2\right) \mathrm{S}=\frac{\mathrm{K}}{{\mathrm{\Lambda }}_0}\frac{\left({\mathrm{Sm}}^{-1}\right)}{\left({\mathrm{Sm}}^2{\mathrm{mol}}^{-1}\right)}=\frac{1.26\times {10}^{-4}}{138.5\times {10}^{-4}}=9.1\times {10}^{-3}{\mathrm{molm}}^{-3}\\ =\frac{9.1\times {10}^{-3}\times 143.5}{1000}=1.3\times {10}^{-3}{\mathrm{kgm}}^{-3}\\ {\mathrm{K}}_{\mathrm{SP}}={\mathrm{S}}^2\\ ={\left(9.1\times {10}^{-3}\right)}^2=8.28\times {10}^{-5}{\mathrm{mol}}^2{\mathrm{litre}}^{-2}\end{array}$

$\begin{array}{l}\left(4\right) {\lambda }_{0\left({\mathrm{Cl}}^{-}\right)}={\mathrm{\Lambda }}_0\left(\mathrm{KCl}\right)-{\mathrm{\Lambda }}_0\left({\mathrm{KNO}}_3\right)+{\lambda }_0\left({\mathrm{NO}}_3^{-}\right)\\ =(150-145+71.6)\times {10}^{-4}=76.6{\mathrm{Sm}}^2{\mathrm{mol}}^{-1}\\ {\mu }_{{\mathrm{Cl}}^{-}}=\text{ionic mobility of }{\mathrm{Cl}}^{-}=\frac{76.6\times {10}^{-4}}{96,500}=\frac{76.6\times {10}^{-4}\left({\mathrm{Sm}}^2{\mathrm{mol}}^{-1}\right)}{96,500\left(\mathrm{ampsec}\right)}\\ =7.93\times {10}^{-8}{\mathrm{m}}^2{\mathrm{volt}}^{-1}{\sec }^{-1}=7.93\times {10}^{-4}{\mathrm{cm}}^2{\mathrm{volt}}^{-1}{\sec }^{-1}\end{array}$