Consider the following first order gas phase reaction at constant temperature $$A(g) \to 2B(g) + C(g)$$. If the total pressure of the gases is found to be 200 torr after 23 sec. and 300 torr upon the complete decomposition of A after a very long time, then the rate constant of the given reaction is ______ $$\times 10^{-2} \text{ s}^{-1}$$ (nearest integer) [Given : $$\log_{10}(2) = 0.301$$]

$$A(g) \to 2B(g) + C(g)$$. Initial: P₀, 0, 0. At time t: P₀-x, 2x, x. Total = P₀+2x.

Complete decomposition: P₀+2P₀ = 3P₀ = 300 ⟹ P₀ = 100 Torr.

At t=23s: P₀+2x = 200 ⟹ 2x = 100 ⟹ x = 50. So P_A = 100-50 = 50 Torr.

$$k = \frac{1}{t}\ln\frac{P_0}{P_A} = \frac{1}{23}\ln\frac{100}{50} = \frac{\ln 2}{23} = \frac{2.303\log 2}{23} = \frac{2.303\times0.301}{23} = \frac{0.6932}{23} = 0.03014$$ s⁻¹.

$$\approx 3 \times 10^{-2}$$ s⁻¹.

The answer is $$\boxed{3}$$.