Question

Ignoring activities, determine the molar solubility of copper (I) azide (CuN₃) in a solution with a pH of 3.696. K_sp (CuN₃) = 4.9x10^{-9 ;} K_a (HN₃₎= 2.2x10^-5.

List of steps my teacher suggests we follow:

1. Write the pertinent reactions.

2. Write the charge balance equation.

3. Write the mass balance equations.

4. Write the equilibrium constant expressions for each reaction.

5. Count the equations and unknowns.

6. Solve for all unknowns.

How far I've gotten:

1. Pertinent reactions:

CuN₃ (s) <-> Cu⁺ (aq) + N₃^- (aq) K_sp= 4.9x10^-9

N₃^- (aq) + H₂O (l) <-> HN₃ (aq) + OH^- (aq) K_b = (K_w/K_a) = (1.0x10^-14/2.2x10^-5) = 4.55 x 10^-10

H₂O (l) <-> H⁺ (aq) + OH^- (aq) K_w = 1.0x10^-14

2. Write the charge balance equation:

Because the pH is fixed with no info given regarding the buffer used to fix the pH, there is no charge balance equation for this problem.

3. Write the mass balance equation(s):

[Total Cu⁺] = [Total N₃^-]

[Cu⁺] = [N₃^-] +[HN₃]

4. Write the equilibrium constant expressions for each reaction:

K_sp = 4.9x10^-9 = [Cu⁺] [N₃^-]

K_b = 4.55x10^-10 = ([HN₃] [OH^-] / [N₃^-])

K_w = 1.0x10^-14 = [H⁺] [OH^-]

Now use the charge balance, mass balance, and equilibrium constant expressions to solve for [Cu⁺], which is the molar solubility of CuN_3.

I tried to finish it 5 times and haven't been able to make any progress.