Consider a general first order reaction \(\text{A(g)} \rightarrow \text{B(g)} + \text{C(g)}\). 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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For decomposition of gas A into n gaseous products (\(A \rightarrow n Products\)): \(k = \frac{2.303}{t} \log \left( \frac{(n-1)P_0}{nP_0 - P_t} \right)\). Here \(n=2\), so \(k \propto \log \frac{P_0}{2P_0 - P_t}\).