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Solubility Product

100.0 mL of a...

Question

$100.0 m L$ of a clear saturated solution of $A g_{2} S O_{4}$ is added to $250.0 m L$ of a clear saturated solution of $P b C r O_{4}$ . Will any precipitate form and if so what? Given, $K_{s p}$ values of $A g_{2} S O_{4}, A g_{2} C r O_{4}, P b C r O_{4}$ are $1.4 \times 10^{- 5}, 2.4 \times 10^{- 12}, 2.8 \times 10^{- 13}$ and $1.6 \times 10^{- 8}$ respectively.

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Solution

$A g_{2} S O_{4} ⇌ 2 A g^{+} + S O_{4}^{2 -}$
$K s p = [A g^{+}] [S O_{4}^{2 -}] = 1.4 \times 10^{- 5}$
let $S$ mol dissolves
$[A g^{+}] = 2 S$
$[S O_{4}^{2 -}] = S$
$4 S^{3} = 1.4 \times 10^{- 5}$ $= [A g^{+}] = 0.0304 M$
$S = 0.0152 M$
Mixed Solutions $⇌ M_{1} V_{1} = M_{2} V_{2}$
$[A g^{+}] = \frac{0.0304 \times 100}{350} = 8.68 \times 10^{- 3} M$
$[S O_{4}^{2 -}] = 4.34 \times 10^{- 3} M$
$P b C r O_{4} ⇌ P b^{2 +} + C r O_{4}^{2 -}$
$K s p = [P b^{2 +}] [C r O_{4}^{2 -}] = (2.8 \times 10^{- 13})$
$S^{2} = 2.8 \times 10^{- 13} ⟶ S = 5.29 \times 10^{- 7} M$
Upon Dilution $⟶ \frac{5.29 \times 10^{- 7} \times 250}{350} = 3.78 \times 10^{- 7} M = [P b^{2 +}] = [C r O_{4}^{2 -}]$
Will $A g_{2} C r O_{4}$ ppt?
$K s p = [A g^{+}]^{2} [C r O_{4}^{2 -}] = 1.1 \times 10^{- 12}$
$[8.86 \times 10^{- 3}]^{2} [3.78 \times 10^{- 7}] = 2.8 (5) \times 10^{- 11}$ which is $> 1.1 \times 10^{- 12}$ (so some $A g_{2} C r O_{4}$ will ppt).

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Similar questions

Q. 100 mL of a clear saturated solution of

A g_{2} S O_{4}

is added to 250 mL of a clear saturated solution of

P b C r O_{4}

. What is the precipitate formed? Given,

K_{s p}

A g_{2} S O_{4}, A g_{2} C r O_{4}, P b C r O_{4}

P b S O_{4}

1.4 \times 10^{- 5}, 2.4 \times 10^{- 12}, 2.8 \times 10^{- 13}

1.6 \times 10^{- 5}

Q. 100 mL of a clear saturated solution of

A g_{2} S O_{4}

is added to 250 mL of a clear saturated solution of

P b C r O_{4}

. What is the precipitate formed? Given,

K_{s p}

A g_{2} S O_{4}, A g_{2} C r O_{4}, P b C r O_{4}

P b S O_{4}

1.4 \times 10^{- 5}, 2.4 \times 10^{- 12}, 2.8 \times 10^{- 13}

1.6 \times 10^{- 5}

100 m L

of a saturated solution of

A g_{2} S O_{4}

250 m L

of a saturated solution of

P b C r O_{4}

. Will any precipitate form and if so what?

K_{s p}

A g_{2} S O_{4}, A g_{2} C r O_{4}, P b C r O_{4}

P b S O_{4}

1.4 \times 10^{- 5},

2.4 \times 10^{- 12},

2.8 \times 10^{- 13}

1.6 \times 10^{- 8}

100.0

mL of a saturated solution of

A g_{2} S O_{4}

250.0

mL of saturate solution of

P b C r O_{4}

. Will any precipitate from and if so what?

K_{s p}

A g_{2} S O_{4}, A g_{2} C r O_{4}, P b C r O_{4},

P b S O_{4}

1.4 \times 10^{- 5},

2.4 \times 10^{- 12},

2.8 \times 10^{- 13}

1.6 \times 10^{- 8}

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A g_{2} S O_{4}

2.5 \times 10^{- 2} M

. The value of its solubility product is

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