For a first-order reaction, the half-life period ($t_{1/2}$) is related to the specific rate constant ($k$) by the equation independent of the initial concentration: $k = \frac{0.693}{t_{1/2}}$

Given: $t_{1/2} = 1386 \text{ s}$

Substituting the value: $k = \frac{0.693}{1386 \text{ s}}$ $k = \frac{0.693}{2 \times 693} = \frac{1}{2000}$ $k = 0.0005 \text{ s}^{-1} = 5.0 \times 10^{-4} \text{ s}^{-1} = 0.5 \times 10^{-3} \text{ s}^{-1}$

Thus, the specific rate constant is $0.5 \times 10^{-3} \text{ s}^{-1}$ .