What is the solubility of M(OH)2 in a 0.202 M solution of M(NO3)2?

To determine the solubility of M(OH)2 in a 0.202 M solution of M(NO3)2, you need to consider the solubility product constant (Ksp), which describes the equilibrium between the solid and dissolved ions in a sparingly soluble salt.

The general equation for the solubility equilibrium of M(OH)2 is:

M(OH)2(s) ⇌ M2+(aq) + 2OH-(aq)

The Ksp expression for this equilibrium is:

Ksp = [M2+][OH-]²

To solve the problem, you will need the value of the Ksp for M(OH)2 and the concentration of the M2+ ion (in this case, the M2+ ion comes from M(NO3)2).

1. Find the Ksp value for M(OH)2: This information should be given in the problem or can be found in a reference source.

2. Determine the concentration of M2+ ion (in this case, the metal cation from M(NO3)2): Since you have a 0.202 M solution of M(NO3)2, the concentration of the M2+ ions will also be 0.202 M. This is because one mole of M(NO3)2 releases one mole of M2+ ion into solution.

3. Set up an ICE (Initial, Change, Equilibrium) table:

M(OH)2(s) ⇌ M2+(aq) + 2OH-(aq)

Initial: 0 0 0
Change: -x +x +2x
Equilibrium: -x x 2x

The change in concentration of the M2+ ion is equal to the solubility of M(OH)2, and the change in concentration of the OH- ion is twice the solubility. Since two OH- ions are produced for every M(OH)2 molecule that dissolves.

4. Substitute the equilibrium concentrations into the Ksp expression:

Ksp = [M2+][OH-]²

Ksp = (x)(2x)² = 4x³

5. Substitute the M2+ ion concentration (0.202 M) into the expression and solve for x:

Ksp = 4x³
0.202 = 4x³

Solving for x will give you the solubility of M(OH)2 in the 0.202 M solution of M(NO3)2. Evaluate this expression using algebraic methods or numerical methods to find the value of x.

Once you have the value of x, you can multiply it by the molar mass of M(OH)2 to determine the solubility of M(OH)2 in the given solution of M(NO3)2.

One must have the Ksp of M(OH)2 to work this problem.

ezjyfkgiukb