The Ksp for silver sulfate (Ag2SO4) is 1.2 x 10-5 . Calculate the solubility of

Question

The Ksp for silver sulfate (Ag2SO4) is 1.2 x 10-5 . Calculate the solubility of silver sulfate in each of the following a. water b. 0.10 M AgNO3 c. 0.20 M K2SO4 .

Explanation / Answer

let X be the solubility of silver sulfate in mol/L then from Ag2SO4 ---> 2Ag+ + SO4-2 a) in water [SO4--]=X and [Ag+]=2X so Ksp = [Ag+]^2 * [SO4--] = (2X)^2 * X = 4X^3 = 1.2E-5 and X = 0.0144 M b) here [SO4--] = X but [Ag+] = (2X+0.10) from the silver nitrate so Ksp = (2X+0.10)^2 * X = 4X^3 + 0.4X^2 + 0.10X = 1.2E-5 giving 4X^3 + 0.4X^2 + 0.10X - 1.2E-5 = 0 the only positive root is X = 1.15E-3 M c) here [SO4--] = (X+0.20) and [Ag+] = 2X so Ksp = (2X)^2 * (X+0.20) = 4X^3 + 0.8X^2 = 1.2E-5 giving 4X^3 + 0.8X^2 + 0X - 1.2E-5 = 0 the only positive root is X = 3.84E-3 M

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