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(B) For the reaction $A_{(g)} \rightarrow 2 B_{(g)} + C_{(g)}$:Let the initial pressure of $A$ be $P_0 = 0.1 \ atm$.At time $t = 115 \ s$,let the decr

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$2$

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(B) For the reaction $A_{(g)} ightarrow 2 B_{(g)} + C_{(g)}$:Let the initial pressure of $A$ be $P_0 = 0.1 \ atm$.At time $t = 115 \ s$,let the decrease in pressure of $A$ be $x$.Then,the pressures are: $P_A = P_0 - x$,$P_B = 2x$,and $P_C = x$.The total pressure $P_t = (P_0 - x) + 2x + x = P_0 + 2x$.Given $P_t = 0.28 \ atm$ at $t = 115 \ s$,we have $0.1 + 2x = 0.28$,which gives $2x = 0.18$,so $x = 0.09 \ atm$.The pressure of $A$ at $t = 115 \ s$ is $P_A = 0.1 - 0.09 = 0.01 \ atm$.For a first-order reaction,the rate constant $k = \frac{1}{t} \ln \frac{P_0}{P_A} = \frac{1}{115} \ln \frac{0.1}{0.01} = \frac{1}{115} \ln(10)$.Using $\ln(10) \approx 2.303$,$k = \frac{2.303}{115} \approx 0.02002 \ s^{-1} = 2.002 	imes 10^{-2} \ s^{-1}$.The nearest integer is $2$.

$S.No.$	$Time/s$	$Total Pressure/(atm)$
$1.$	$0$	$0.1$
$2.$	$115$	$0.28$

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