How many grams of silver sulfate can be dissolved in 450. ml of .200 M sodium sulfate solution? Ksp for Ag2SO4= 1.2*10^-5

Do not understand this solubility question. Please help.

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

I......solid.......0........0
C......solid.......2x.......x
E......solid.......2x.......x

Substitute the E line into the Ksp expression and solve for x = solubility.

To solve this solubility question, we need to use the concept of the solubility product constant (Ksp) and the given concentration of the sodium sulfate solution (.200 M). The solubility product constant (Ksp) describes the equilibrium between the solid and the dissolved ions in a saturated solution.

Here's the step-by-step approach to solving this problem:

1. Write the balanced chemical equation for the dissolution of silver sulfate (Ag2SO4) in water:
Ag2SO4(s) ⇌ 2Ag+(aq) + SO4^2-(aq)

2. Identify the stoichiometry of the dissolved ions from the balanced equation. In this case, for every 1 mole of silver sulfate dissolved, 2 moles of Ag+ and 1 mole of SO4^2- ions are produced.

3. Determine the molar solubility of silver sulfate (Ag2SO4) by assuming x moles of Ag2SO4 dissolve in the given volume (450 ml or 0.450 L) of the sodium sulfate solution. Thus, the concentrations of Ag+ and SO4^2- ions will be 2x M and x M, respectively.

4. Calculate the molar solubility (x) using the solubility product constant (Ksp) expression:
Ksp = [Ag+]^2 * [SO4^2-]
Ksp = (2x)^2 * (x) = 1.2 * 10^-5

5. Solve the equation obtained in step 4 for x.

Let's now solve the equation:

1.2 * 10^-5 = 4x^3

Dividing both sides by 4 gives:
3 * 10^-6 = x^3

Taking the cube root of both sides:
x = (3 * 10^-6)^(1/3)

Calculating the value of x gives us:
x ≈ 0.014 M

Therefore, the molar solubility of silver sulfate is approximately 0.014 M.

To find the number of grams, we can use the molar mass of silver sulfate (Ag2SO4), which is 311.8 g/mol:

Mass = Molar solubility * Volume * Molar mass
= 0.014 M * 0.450 L * 311.8 g/mol

Calculating this will give us the number of grams of silver sulfate that can be dissolved in the given solution.