Consider a general first order reaction A_{(g | vedclass

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(B) For the reaction $A_{(g)} \rightarrow B_{(g)} + C_{(g)}$,let the initial pressure of $A$ be $P_0 = 200 \ mm$. At time $t = 20 \ min$,let the press

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$50.2$

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(B) For the reaction $A_{(g)} ightarrow B_{(g)} + C_{(g)}$,let the initial pressure of $A$ be $P_0 = 200 \ mm$. At time $t = 20 \ min$,let the pressure of $A$ decrease by $x$. The total pressure $P_t = (P_0 - x) + x + x = P_0 + x$. Given $P_t = 250 \ mm$,so $250 = 200 + x$,which gives $x = 50 \ mm$. The pressure of $A$ at $t = 20 \ min$ is $P_A = P_0 - x = 200 - 50 = 150 \ mm$. The rate constant $k = \frac{2.303}{t} \log(\frac{P_0}{P_A}) = \frac{2.303}{20} \log(\frac{200}{150}) = \frac{2.303}{20} \log(\frac{4}{3}) = \frac{2.303}{20} (\log 4 - \log 3) = \frac{2.303}{20} (0.60 - 0.48) = \frac{2.303 	imes 0.12}{20} = 0.013818 \ min^{-1}$. The half-life $t_{1/2} = \frac{0.693}{k} = \frac{0.693}{0.013818} \approx 50.15 \ min$. Thus,the half-life is approximately $50.2 \ min$.

Consider a general first order reaction $A_{(g)} \rightarrow B_{(g)} + C_{(g)}$. If the initial pressure is $200 \ mm$ and after $20 \ minutes$ it is $250 \ mm$,then the half-life period of the reaction (in minutes) is. $(\log 2 = 0.30, \log 3 = 0.48, \log 4 = 0.60)$

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