A ( g ) 2 B ( 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)

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Solution

Q.
$A (g) \to 2 B (g) + C (g)$ 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) [2023]

Ans.
(2200)

$\begin{matrix} A (g) & ⟶ & 2 B (g) & + & C (g) \\ t = 0800 & - & - \\ t = (10 min) & 800 - P & 2 P & P \end{matrix}$

$P_{T} = 800 - P + 2 P + P$

$= 800 + 2 P = 1600$

So $P = 400 mm$

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

Given time = 30 min.

So for 1st order reaction $C_{t} = \frac{C_{0}}{{(2)}^{n}}$

$n = \frac{t}{t_{1 / 2}} = \frac{30}{10} = 3$ ; $n =$ number of half life

$C_{t} = \frac{800}{{(2)}^{3}} = 100 mm of Hg$

So After 30 minutes, $P = 700 mm$

$P_{A} = 800 - 700 = 100,$ $P_{B} = 1400,$ $P_{C} = 700$

$P_{T}$ of reaction mixture $= 100 + 1400 + 700 = 2200 mm of Hg$

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