What is the [OH-] of a saturated solution of Zn(OH)2? Ksp=1.8 x 10^-14. i'm just confused on how to start this problem i don't want the answer just the steps how to get there please

Zn(OH)2(s) ==> Zn^+2 + 2OH^-

Ksp = (Zn^+2)(OH^-)^2
In a saturated solution, (Zn) = x and (OH^-) = 2x
Substitute into Ksp expression and solve for x and multiply by 2 to find 2x.

To determine the concentration of hydroxide ions ([OH-]) in a saturated solution of Zn(OH)2 using the solubility product constant (Ksp), follow these steps:

Step 1: Write the balanced equation for the dissociation of Zn(OH)2.
Zn(OH)2 (s) ⇌ Zn2+ (aq) + 2OH- (aq)

Step 2: Write the expression for the solubility product constant (Ksp) equation.
Ksp = [Zn2+][OH-]2

Step 3: Since Zn(OH)2 is a strong base that fully dissociates in water, assume that the concentration of hydroxide ions (OH-) formed is equal to the concentration of Zn2+ ions released.

Step 4: Use the stoichiometry of the balanced equation to express the concentration of OH- ions in terms of x (concentration of Zn2+ ions).

[OH-] = 2x

Step 5: Substitute the concentration of OH- ions in terms of x in the Ksp expression.

Ksp = [Zn2+][OH-]2
Ksp = (x)(2x)2
Ksp = 4x3

Step 6: Use the given value of Ksp to solve for x (concentration of Zn2+).

Ksp = 1.8 x 10^-14
4x3 = 1.8 x 10^-14
x3 = 1.8 x 10^-14 / 4
x3 = 4.5 x 10^-15

Step 7: Take the cube root of both sides to solve for x.

x = (4.5 x 10^-15)^(1/3)
x ≈ 1.53 x 10^-5

Step 8: Finally, substitute the value of x back into the expression for the concentration of OH- ions.

[OH-] = 2x
[OH-] ≈ 2(1.53 x 10^-5)
[OH-] ≈ 3.06 x 10^-5

Therefore, the concentration of hydroxide ions ([OH-]) in a saturated solution of Zn(OH)2 is approximately 3.06 x 10^-5 M.

To find the hydroxide ion concentration ([OH-]) of a saturated solution of Zn(OH)2, you need to use the solubility product constant (Ksp) and understand how it relates to the concentration of ions in the solution. Here are the steps to solve this problem:

Step 1: Write the balanced chemical equation for the dissolution of Zn(OH)2.
Zn(OH)2 -> Zn2+ + 2 OH-

Step 2: Determine the expression for the solubility product constant (Ksp) using the balanced chemical equation.
Ksp = [Zn2+][OH-]^2

Step 3: Since Zn(OH)2 is a saturated solution, the concentrations of Zn2+ and OH- are equal. Therefore, let x represent the concentration of OH-. The concentration of Zn2+ will be also x.

Step 4: Substituting these values into the Ksp expression:
Ksp = (x)(x)^2
= x^3

Step 5: Substitute the given value of Ksp into the equation and solve for x.
1.8 x 10^-14 = x^3

Step 6: Take the cube root of both sides to solve for x.
x = (1.8 x 10^-14)^(1/3)

This value represents the concentration of [OH-] in the saturated solution of Zn(OH)2.