When 30 mL of 5.93 millimolar solution of `AgNO_(3)` was added to 2.0 mL of 8.89 millimolar solution of KCl, the mixture turns turbid. The solubility product of AgCl is

Options

A. `1.96 xx 10^(-6) mol^(2)L^(-1)`
B. `3.92 xx 10^(-6) mol^(2)L^(-1)`
C. `1.96 xx 10^(-6)mol^(-1) L^(-1)`
D. `3.92 xx 10^(-6) mol^(-1)L^(-1)`

Answer

A

Explanation

After mixing, `[Ag^(+)]=M_(2)` (say)
`M_(1)V_(1)=M_(2)V_(2)" "i.e. 30 xx 5.93 xx 10^(-3)=32 xx M_(2)`
or `M_(2)=5.56 xx 10^(-3)M`
After mixing `[Cl^(=-)]=M_(2)' `(say)
`2.0 xx 8.89 xx 10^(-3) 32 xx M_(2)'`
or `M_(2)' =5.56 xx 10^(-4)M`
`:. ` Ionic prodcut of `AgCl=[Ag^(+)][Cl^(-)]`
`=(5.56 xx 10^(-3) mol L^(-1))(5.56 xx 10^(-4)mol L^(-1))`
`=3.09 xx 10^(-6) mol ^(2) L^(-1)`
which exceeds (A) but not (B)