Let the solubilities of AgCl in `H_(2)O`, 0.01 M `CaCl_(2)`, 0.01 M NaCl and 0.05 M `AgNO_(3)` be `S_(1), S_(2), S_(3), S_(4)` respectively. What is the correct relationship between these quantities ?

Options

A. `S_(1) gt S_(2) gt S_(3) gt S_(4)`
B. `S_(1) gt S_(2) = S_(3) gt S_(4)`
C. `S_(1) gt S_(3) gt S_(2) gt S_(4)`
D. `S_(4) gt S_(2) gt S_(3) gt S_(1)`

Answer

C

Explanation

AgCl in water : `[Ag^(+)][Cl^(-)] = 10^(-10)`
`S xx S = S^(2) = 10^(-10)`
`S = 10^(-5)` mol `"dm"^(-3) = S_(1)`
AgCl in 0.01 M `CaCl_(2) : [Ag^(+)][0.02] = 10^(-10)`
More the concentration of common ion less the solubility of AgCl.
`[Ag^(+)] = (10^(-10))/(2 xx 10^(-2)) = 0.5 xx 10^(-8) = 5 xx 10^(-9)` mol `"dm"^(-3) = S_(2)`
AgCl in 0.01 M NaCl : `[Ag^(+)][10^(-2)] = 10^(-10)`
`[Ag^(+)] = (10^(-10))/(10^(-2)) = 10^(-8)` mol `"dm"^(-3) = S_(3), AgCl` in 0.05 M `AgCO_(3) : [0.05][Cl^(-)] = 10^(-10)`
`[Cl^(-)] = (10^(-10))/(5 xx 10^(-2)) = 0.2 xx 10^(-8) = 2 xx 10^(-9)` mol `"dm"^(-3) = S_(4)`. Hence , `S_(1) gt S_(3) gt S_(2) gt S_(4)`.