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)"g"//"L"`
B. `2.1xx10^(-5)"g"//"L"`
C. `1.9xx10^(-3)"g"//"L"`
D. `2.1xx10^(-6)"g"//"L"`

Answer

C

Explanation

`K=1.826xx10^(-6)//Omega"cm"`
`lambda_("Ag")^(0)=61.92,lambda_("Cl")^(0)=76.34`
`:.lambda_("AgCl")^(0)=61.92+76.34`
`=138.26`
`lambda_(v)=lambda^(0)` of sparingly soluble salt
Molar mass of AgCl
`=108+35.5=143.5`
`lambda_(v)=(Kxx1000)/(C)`
`:.138.26=(1.826xx10^(-6)xx1000)/(C)`
`:." "C=1.3207xx10^(-5)"mol"//"dm"^(3)`
`N=1.3207xx10^(-5)xx143.5`
`=189.52xx10^(-5)`
`:.N=1.9xx10^(-3)"g"//"dm"^(3)"or g"//"L"`