A(g) $$\to$$ 2B(g) + C(g) is a first order reaction. The initial pressure of the system was found to be $$800$$ mm Hg which increased to $$1600$$ mm Hg after $$10$$ min. The total pressure of the system after $$30$$ min will be _____ mm Hg. (Nearest integer)

A(g) → 2B(g) + C(g) is a first order reaction.

Initial pressure of A = 800 mm Hg. If $$x$$ is the pressure of A that has reacted:

$$P_{total} = (800 - x) + 2x + x = 800 + 2x$$

At t = 10 min: $$P_{total} = 1600$$ mm Hg

$$800 + 2x = 1600$$

$$x = 400$$ mm Hg

Pressure of A remaining at t = 10 min: $$800 - 400 = 400$$ mm Hg.

For first order: $$P_A = P_0 \times e^{-kt}$$

At t = 10: $$400 = 800 \times e^{-10k}$$

$$e^{-10k} = \frac{1}{2}$$

$$t_{1/2} = 10$$ min

At t = 30 min (3 half-lives): $$P_A = \frac{800}{2^3} = 100$$ mm Hg

Amount reacted: $$x = 800 - 100 = 700$$ mm Hg

$$P_{total} = 800 + 2(700) = 800 + 1400 = 2200$$ mm Hg

The total pressure after 30 min is $$\mathbf{2200}$$ mm Hg.