Consider the following first order gas phase | vedclass

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(A) For the reaction $A_{(g)} \rightarrow 2B_{(g)} + C_{(g)}$,let the initial pressure of $A$ be $P_0$.At $t = 0$: $P_A = P_0, P_B = 0, P_C = 0, P_{to

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$3$

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(A) For the reaction $A_{(g)} ightarrow 2B_{(g)} + C_{(g)}$,let the initial pressure of $A$ be $P_0$.At $t = 0$: $P_A = P_0, P_B = 0, P_C = 0, P_{total} = P_0$.At $t = 23 \ s$: $P_A = P_0 - x, P_B = 2x, P_C = x, P_{total} = P_0 + 2x = 200 \ torr$.At $t = \infty$: $P_A = 0, P_B = 2P_0, P_C = P_0, P_{total} = 3P_0 = 300 \ torr$.Thus,$P_0 = 100 \ torr$.Substituting $P_0$ in $P_{total} = P_0 + 2x = 200$,we get $100 + 2x = 200$,so $x = 50 \ torr$.The pressure of $A$ at $t = 23 \ s$ is $P_A = P_0 - x = 100 - 50 = 50 \ torr$.For a first-order reaction,$k = \frac{2.303}{t} \log \frac{P_0}{P_A} = \frac{2.303}{23} \log \frac{100}{50} = \frac{2.303}{23} \log(2) = \frac{2.303 	imes 0.301}{23} \approx 0.0301 \ s^{-1} = 3.01 	imes 10^{-2} \ s^{-1}$.The nearest integer is $3$.

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