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The pH of a saturated solution of a meta...

The pH of a saturated solution of a metal hydroxide of formula `X(OH)_(2)` is 12.0 at 298 K. What is the solubility product of a metal hydroxide at 298 K (in `mol ^(3) L ^(-3))`?

A

`2 xx 10 ^(-6)`

B

`5xx 10 ^(-7)`

C

`5 xx 10 ^(-5)`

D

`2 xx 10 ^(-5)`

Text Solution

Verified by Experts

The correct Answer is:
D
Given, `pH = 12`
`therefore [H ^(+)] = 1 xx 10 ^(-pH) = 1 xx 10 ^(-12)`
We know that
`[H^(+)] [OH ^(-)] = K _(w) = 1 xx 10 ^(-14)`
`therefore [OH^(-)] = (1 xx 10 ^(-14))/( [H^(+)] ) = (1 xx 10 ^(-14) )/( 1 xx 10 ^(-12)) = 1 xx 10 ^(-2)`
`X (OH) _(2)` dissolves as
`X (OH) _(2) to X ^(2+) + 2 O ^(-)`
`x 1 xx 10 ^(-2)`
`therefore X ^(2+) = ([OH ^(-)])/( 2) = (1 xx 10 ^(-2))/(2) = 5 xx 10 ^(-3)`
`K _(sp) = [C ^(2+) ] [2OH ^(-) ]^(2)`
`= ( 5 xx 10 ^(-3)) (1 xx 10 ^(-2)) ^(2)`
`= ( 5 xx 10 ^(-3)) (1 xx 10 ^(-4))`
`= 5 xx 10 ^(-7) mol ^(3) L ^(-3)`
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