Question

The stepwise formation of $[Cu(NH_3)_4]^{2+}$ is given. The value of stability constants $K_1, K_2, K_3$ and $K_4$ are $10^4, 1.58 \times 10^3, 5 \times 10^2$ and $10^2$ respectively. The overall equilibrium constant for dissociation of $[Cu(NH_3)_4]^{2+}$ is $x \times 10^{-12}$. The value of $x$ is __________. (Rounded off to the nearest integer)

Hint:

The instability constant (or dissociation constant) is the reciprocal of the cumulative stability constant ($\beta$).

Answer 1

Correct Answer: 1

Step 1: The overall stability constant $\beta_4 = K_1 \times K_2 \times K_3 \times K_4$.
Step 2: $\beta_4 = 10^4 \times (1.58 \times 10^3) \times (5 \times 10^2) \times 10^2 = 7.9 \times 10^{11}$.
Step 3: The overall dissociation constant $K_d = \frac{1}{\beta_4} = \frac{1}{7.9 \times 10^{11}} \approx 1.265 \times 10^{-12}$.
Step 4: Comparing with $x \times 10^{-12}$, $x = 1.265$.
Step 5: Nearest integer is 1.