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

0.30 M K2SO4

Let x = solubility Ag2SO4, then

Ag2SO4 ==> 2Ag^+ + SO4^=
...x........2x......x.

........K2SO4 ==> 2K^+ + SO4^=
initial.0.30M.......0......0
equil.....0.......0.6.....0.30

Ksp = (Ag^+)^2(SO4^2-)
You know Ksp.'
(Ag^+) = 2x from Ag2SO4
(SO4^2-) = x from Ag2SO4 and 0.30M from K2SO4 so the total is x+0.30
Substitute into Ksp expression and solve for x.

To calculate the solubility of silver sulfate (Ag2SO4) in a solution of 0.30 M K2SO4, we need to consider the common ion effect.

The common ion effect states that the solubility of a salt is generally reduced when a common ion is present in the solution. Here, the common ion is the sulfate ion (SO4 2-), which is present in both silver sulfate and potassium sulfate (K2SO4).

To find the solubility of silver sulfate in the presence of K2SO4, we can use the concept of ionic product (Qsp) and compare it to the solubility product constant (Ksp).

The ionic product (Qsp) is the product of the ion concentrations raised to the power of their coefficients in the balanced chemical equation. In the case of silver sulfate, the balanced equation is:

Ag2SO4 (s) ⇌ 2 Ag+ (aq) + SO4 2- (aq)

The solubility product constant (Ksp) for Ag2SO4 is given as 1.2 × 10^-5, which is the equilibrium ionic product when the solution is saturated with Ag2SO4.

Using these values, we can set up the equation:

Qsp = [Ag+]^2 [SO4^2-]

Since the concentration of silver sulfate is unknown, let's assume it is 's'. The concentration of the sulfate ion can be calculated from the K2SO4 solution concentration, which is 0.30 M. K2SO4 dissociates completely into 2 K+ ions and 1 SO4 2- ion.

Therefore, the initial concentration of the sulfate ion (SO4 2-) = 0.30 M × 1 = 0.30 M

Substituting these values into the equation:

Qsp = (2s)^2 (0.3)

Qsp = 4s^2 × 0.30

Now, equating the calculated value of Qsp to the given Ksp value:

1.2 × 10^-5 = 4s^2 × 0.30

Simplifying the equation:

0.30s^2 = (1.2 × 10^-5)/4

0.30s^2 = 3.0 × 10^-6

Dividing both sides of the equation by 0.30:

s^2 = (3.0 × 10^-6) / 0.30

s^2 = 1.0 × 10^-5

Taking the square root of both sides:

s = √(1.0 × 10^-5)

s = 1.0 × 10^-3 M

The solubility of silver sulfate in the presence of a 0.30 M K2SO4 solution is 1.0 × 10^-3 M.