The stepwise formation of [Cu(NH₃)₄]²⁺ is given below:
Cu²⁺ + NH₃ ⇌(K₁) [Cu(NH₃)]²⁺ ; [Cu(NH₃)]²⁺ + NH₃ ⇌(K₂) [Cu(NH₃)₂]²⁺ ; [Cu(NH₃)₂]²⁺ + NH₃ ⇌(K₃) [Cu(NH₃)₃]²⁺ ; [Cu(NH₃)₃]²⁺ + NH₃ ⇌(K₄) [Cu(NH₃)₄]²⁺
The value of stability constants K₁, K₂, K₃ and K₄ are 10⁴, 1.58 x 10³, 5 x 10² and 10² respectively.
The overall equilibrium constants for dissociation of [Cu(NH₃)₄]²⁺ is x × 10⁻¹².
The value of x is ________. (Rounded off to the nearest integer)

Solution

Chemistry ma’am · 4 steps

Multiply the four step constants to get overall formation, then flip it for dissociation.

1. Add the steps. Adding the four steps gives Cu²⁺ + 4NH₃ ⇌ [Cu(NH₃)₄]²⁺. When equations are added, their equilibrium constants multiply, so the overall formation constant is β₄ = K₁ K₂ K₃ K₄.
2. Put in numbers. β₄ = 10⁴ × 1.58 × 10³ × 5 × 10² × 10². The numbers give 1.58 × 5 = 7.9 and the powers give 10⁴⁺³⁺²⁺² = 10¹¹, so β₄ = 7.9 × 10¹¹.
3. Reverse the reaction. Dissociation is the formation reaction written backwards. Reversing a reaction inverts its equilibrium constant.

   K_(diss) = 1/β₄ = 1/(7.9 × 10¹¹) = 1.27 × 10⁻¹²

4. So. x = 1.27, which rounds to 1.

The idea to keep. Stepwise constants multiply to give the overall constant, and reversing a reaction means taking the reciprocal. Formation and dissociation constants are always inverses of each other.

Answer from the NTA final answer key. Solution by PrepWiser.