An aqueous solution of metal chloride `MCI_(2)(0.05M)` is saturated with `H_(2)S (0.1M)`. The minimum `pH` at which metal sulphide will be precipiated is
`[K_(sp)MS = 5 xx 10^(-21),K_(1)(H_(2)S) = 10^(-7),K_(2)(H_(2)S) = 10^(-14)`.

Options

A. `3.25`
B. `2.50`
C. `1.50`
D. `1.25`

Answer

C

Explanation

`K_(sp)MS = [M^(2+)][SO_(4)^(2-)]`
`5xx10^(-21) = (0.05)[S^(2-)]`
For precipitation `Q_(sp) = K_(sp)`
`:. [S^(2-)] = (5 xx 10^(-21))/(5 xx 10^(-2)) = 10^(-19)`
For `H_(2)S`:
`H_(2)ShArr H^(o+)+HS^(T)(K_(1))`
`HS^(T)hArrH^(o+)+S^(2-)(K_(2))`
`K_(1) xx K_(2) = ([H^(o+)]^(2)[S^(2-)])/(H_(2)S)`
`10^(-7) xx 10^(-14) = ([H^(o+)]^(2)[10^(-19)])/(0.1)`
`[H^(o+)]^(2) = 10^(-3) rArr ` [Taking negative logarthim both sides]
`-2"log"[H^(o+)] = 3, pH = 3/2 = 1.5`