Question

The solubility product constant for strontium sulfate is 3.44*10^-7. Using the Debye-Hukel limiting law to estimate activity coefficients,

a.       Calculate the solubility of strontium sulfate in a solution of 0.100 m KCl

b.      Calculate the solubility of strontium sulfate in pure water.

Answer 1

Ksp = 3.44*10^-7

Ksp = [Sr+2][SO4-2]

activity:

a)

KCl --< 0.1 m assume 0.1 M (1kg of water approx, then 1 liter of water/solution)

IS = 1/2*((0.1)(1) + (0.1)(1)) = 0.1

Recall that:

-log(γ) = 0.51*(Zi^2)*sqrt(I.S.) / ( 1 + (α * sqrt(I.S)/305))

Where

γi = activity coefficient for species “i”

αi = theoretical diameter in pm (10^-12 m)

Zi = Charge of ion

I.S. = ionic Strength (usually used as μ as well)

If we wanted only γ-Sr+2

γ = 10^-(0.51*(Zi^2)*sqrt(I.S.) / ( 1 + (α * sqrt(I.S)/305)))

for SR+2 , Zi = +2, IS = 0.1, α = 500

Y_Sr2+ = 10^-(0.51*(2^2)*sqrt(0.1) / ( 1 + (500* sqrt(0.1 )/305))) = 0.3759 M

for SO4-2+2 , Zi = -2, IS = 0.1, α = 400

Y_SO42- = 10^-(0.51*(2^2)*sqrt(0.1) / ( 1 + (400* sqrt(0.1 )/305))) = 0.3499

Now

Ksp = [Sr+2][SO4-2]

3.44*10^-7 = (Y_Sr2+)([SR+2]) (Y_SO42-)([SO4-2])

3.44*10^-7 = 0.3759 ([SR+2]) (0.3499)([SO4-2])

( 3.44*10^-7)/(0.3759 *0.3499) = [SR+2][SO4-2]

0.000002615 = S*S

S = sqrt(0.000002615) = 0.0016170 M

b)

Ksp = [Sr+2][SO4-2]

Ksp = S*S

S = sqrt(3.44*10^-7)

S =0.0005865 M for SrSO4