The maximum pH of a solution which is 0.10 M in `Mg ^(2+ ) ` from which `Mg (OH) _ 2` is not precipitated is : ( Given `K_(sp) " of " Mg (OH)_2 =1.2 xx 10^(-11) M) `

Options

A. `4. 96`
B. `6.96`
C. `7. 54 `
D. ` 9. 04`

Answer

D

Explanation

` Ag_2Cr O_4 hArr 2Ag^(+) +CrO_4^(-2) `
` " " 2S " " S `
` (i) 0.1 M Ag^(+) " ions is common ion "`
` 9 xx 10 ^(-12) = ( 2S)^(2) (0.1 ) ^(2) xx S rArr S =9 xx 10 ^(-10 ) M`
` (ii) 0.1 M CrO_4^(-2) " ions is common ion " `
` 9xx 10 ^(_12) =( 2S)^(2) (0.1) rArr 9 xx 10 ^(_12) = 4S^(2) 0.1 `
` S = sqrt( (9)/(4) xx 10 ^(-11)) ~~ 4.5 xx 10^(_6) M`
`[Mg^(+2) ][OH^(-)] ltKsp , (0.1) [OH^(-) ]^(2) lt 1.2 xx 10 ^(-11)`
` [OH^(-) ] lt sqrt(1.2 xx 10 ^(-10) ) , [OH^(-) ] lt 1.09 xx 10 ^(-5) POH = 4. 96 , PH = 9. 04`