The specific conductance at 289 K of AgCl is `1.826xx10^(-6)ohm^(-1)cm^(-1)`. The ionic conductance of `Ag^(+)` and `Cl^(-)` are `61.92` and `61.92` and `76.36` respectively. What is the solubility of AgCl in water?

Options

A. `2.1xx10^(-4) gL^(-1)`
B. `2.1xx10^(-5) gL^(-1)`
C. `1.9xx10^(-3) gL^(-1)`
D. `2.1xx10^(-6) gL^(-1)`

Answer

C

Explanation

`K=1.826 xx 10^(-6) "ohm"^(-1) cm^(-1)`
`lambda_(Ag)^(0) =61.91 , lambda_(Cl)^(0) =76.34 `
`therefore lambda_(AgCl)^(0) =61.92 + 76.34 =138.26`
`lambda_(v) =lambda^(0)` for sparingly soluble salt
Molar mass of AgCl =108 + 35.5 =143.5
`lambda_(v)=(Kxx1000)/(C)`
`therefore 138.26xx10^(-6)xx(1000)/(C)`
`therefore C=1.3826xx10^(-5) " mol "dm^(-3)`
`N=1.3826 xx 10^(-5) xx 143.5 =189.52xx10^(-5)`
`therefore N=1.9 xx 10^( -5)g dm^(-3)`