An aqueous solution of a metal bromide `MBr_(2) (0.05 M)` is saturated with `H_(2) S.` What is the minimum pH at which MS will precipitate? `K_(p)` for `MS = 6.0 xx 10 ^(-21) ` concentration of saturated `H _(2) S =0.1 M , k_(1) = 10 ^(-7) and K _(2) = 1. 3 xx 10 ^(-13) ` for `H _(2) S.`

Options

A. `0.9826`
B. `1.3213`
C. `2.6931`
D. `2.1897`

Answer

A

Explanation

`M Br _(2) (g) hArr MBr _(2) (aq) hArr M ^(2+) + 2 Br ^(-)`
`MBr _(2) + H _(2 ) S to MS + 2 HB r `
`K _(sp ) of MS = [M ^(2+)] [S ^(2-)] , 6 xx 10 ^(-21) = [ 0.05] [S ^(2-)]`
`therefore [S ^(2-)] =1.2 xx 10 ^(-19) M`
Now for `H _(2) S, H _(2)S hArr 2 H^(+) + S ^(2-) , K _(1) xx K_(2) = ([H ^(+)] ^(2) [S ^(2-)])/( [H _(2) S])`
`10 ^(-7) xx 1. 3 xx 10 ^(-13)= ([ H ^(+)] ^(2) [1.2 xx 10 ^(-19)])/([0.1]) . [H^(+)] = 1. 04 xx 10 ^(-1) and pH = 0. 08 26`