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+)] [S^(2-)]`
`5 xx 10^(-21) = (0.05) [S^(2-)]`
For precipitation `Q_(sp) = K_(sp)`
`:. [S^(2-)] = (5 xx 10^(-21))/(5xx10^(-2)) = 10^(-19)`
For `H_(2)S:`
`H_(2)S hArr H^(o+) +HS^(Theta) (K_(1))`
`HS^(Theta) hArr H^(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 logaritham both sides]
`-2 log [H^(o+)] = 3`
`pH = (3)/(2) = 1.5`