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CaCO (3) and BaCO (3) have solubility p...

`CaCO _(3) and BaCO _(3)` have solubility product values `1xx10^(-8) and 5 xx10^(-9)` respectively. If water is shaken up with both solids till equilibrium is reached, the concentration of `CO_(3)^( 2-)`ion is

A

`1.5 xx 10 ^(-8)`

B

`1. 225 xx 10 ^(-4)`

C

`2.25 xx 10 ^(-9)`

D

`2.5 xx 10 ^(-8)`

Text Solution

Verified by Experts

The correct Answer is:
B
Sinve `K _(sp) of CaCO _(3) and BaCO _(3)` are very close . So oncentration of any species connot be negleted. Let the solubility of `Ca CO _(3) and Ba CO _(3)` are x and y M.
`therefore Ca CO _(3) hArr underset(x) (Ca ^(2+))+ underset(x) ( Ca _(3) ^(2-)) , BaCo _(3) hArr Ba ^(2+) + CO _(3) ^( 2-)`
Total `[CO _(3) ^(2-) ] = (x+y) `
`therefore K _(sp ) of Ca CO _(3) = [ Ca ^(2+)] [ CO _(3) ^(2-) ] = x (x + y) , K _(sp) of Ba CO _(3) = [Ba ^(2+)][CO _(3) ^( 2- ) ]= y (x + y)`
`therefore x (x + y) = 10 ^(-8) , y ( x + y) = 5 xx 10 ^(-9)`
`(5 xx 10 ^(-9))/( 10 ^(-3)) = (y ( x + y))/( x (x + y)) (y)/(x) 5 xx 10 ^(-1) implies y = 0. 5 x`
Subsituate the vaue of `y, x (x + 0.5 x ) = 1 0 ^(-8) x = 0.8 xx 10 ^(-4) , y = 0.5xx 08 xx 10 ^(-4)`
`therefore [ Ca ^(2-)] = x = 0.8 xx 10 ^(-4) therefore [Ba ^(2+)] = y = 0.4 xx 10 ^(-4) [ CO _(3) ^(2-)] = (x + y) = 1.2 xx 10 ^(-4)`
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