The overall stability constant of the complex ion $$[Cu(NH_3)_4]^{2+}$$ is $$2.1 \times 10^{13}$$. The overall dissociation constant is $$y \times 10^{-14}$$. Then $$y$$ is _________ (Nearest integer)

For the complex ion $$[Cu(NH_3)_4]^{2+}$$ we are given the overall stability (formation) constant

$$K_f = 2.1 \times 10^{13}.$$

We first recall the basic relationship between the stability (formation) constant and the overall dissociation constant. By definition,

$$K_f = \frac{1}{K_d},$$

where $$K_d$$ is the overall dissociation constant. Hence, to obtain $$K_d$$ we simply take the reciprocal of the given $$K_f$$ value.

So,

$$K_d = \frac{1}{K_f} = \frac{1}{2.1 \times 10^{13}}.$$

We now perform the algebraic inversion step by step. First, separate the numerical part from the power of ten:

$$K_d = \frac{1}{2.1} \times \frac{1}{10^{13}}.$$

Next, taking the reciprocal of $$10^{13}$$ gives $$10^{-13}$$, while the reciprocal of $$2.1$$ remains as a decimal:

$$K_d = \left(\frac{1}{2.1}\right) \times 10^{-13}.$$

Now we evaluate the decimal fraction $$\frac{1}{2.1}$$. Using direct division,

$$\frac{1}{2.1} \approx 0.47619.$$

Substituting this decimal back, we obtain

$$K_d \approx 0.47619 \times 10^{-13}.$$

For ease of comparison with the form $$y \times 10^{-14}$$, we shift the decimal one place to the right and correspondingly decrease the exponent on ten by one:

$$0.47619 \times 10^{-13} = 4.7619 \times 10^{-14}.$$

Thus, in the required form,

$$K_d = y \times 10^{-14} \quad \text{with} \quad y = 4.7619.$$

The problem asks for the nearest integer value of $$y$$. Rounding $$4.7619$$ to the nearest whole number gives

$$y \approx 5.$$

So, the answer is $$5$$.