Integrated rate law equation for a first order gas phase reaction is given by (where \(P_i\) is initial…

Integrated rate law equation for a first order gas phase reaction is given by (where \(P_i\) is initial pressure and \(P_t\) is total pressure at time \(t\))
  1. \(k=\frac{2.303}{t} \times \log \frac{P_i}{\left(2 P_i-P_tight)}\)
  2. \(k=\frac{2.303}{t} \times \log \frac{2 P_i}{\left(2 P_i-P_tight)}\)
  3. \(k=\frac{2.303}{t} \times \log \frac{\left(2 P_i-P_tight)}{P_i}\)
  4. \(k=\frac{2.303}{t} \times \frac{P_i}{\left(2 P_i-P_tight)}\)

Solution

\(\begin{array}{llll}\mathrm{A} ightarrow & \mathrm{B} & + & \mathrm{C} \\ \mathrm{P}_{\mathrm{i}} & \mathrm{0} & & \mathrm{0} \\ \mathrm{P}_{\mathrm{i}}-\mathrm{x} & \mathrm{x} & & \mathrm{x}\end{array}\) The formula used here is: \(\begin{aligned} & k=\frac{2.303}{t} \log \frac{P_i}{P_t} \\ & P_t=P_i+x \\ & P_i-x=P_i-P_t+P_i \\ & =2 P_i-P_t \\ & k=\frac{2.303}{t} \times \log \frac{P_i}{\left(2 P_i-P_tight)} \end{aligned}\) Hence, the answer is option A. ,

Asked in: JEE-TOPICTESTS-CHEMISTRY

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