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AIIMS 201925 May

Exam: AIIMS
Year: 2019
Date: 25 May
Subject: Chemistry
Chapter: Chemical Kinetics

AIIMS 2019 · 25 May · Chemistry · Chemical Kinetics

For a first order gas phase reaction, A_ (g) 2 B_ (g) +C_ (g) P_0...

For a first order gas phase reaction,

A_{(g)} \longrightarrow 2 B_{(g)}+C_{(g)}

P_0

be initial pressure of

A

and

P_t

the total pressure at time '

t

'. Integrated rate equation is For a first order gas phase reaction, A_ (g) 2 B_ (g) +C_ (g) P_0 be initial pressure of A and P_t the total pressure

For a first order gas phase reaction, A_ (g) 2 B_ (g) +C_ (g) P_0 be initial pressure of A and P_t the total pressure

Options

A $\frac{2.303}{t} \log \left(\frac{P_0}{P_0-P_t}\right)$
B $\frac{2.303}{t} \log \left(\frac{2 P_0}{3 P_0-P_t}\right)$
C $\frac{2.303}{t} \log \left(\frac{P_0}{2 P_0-P_t}\right)$
D $\frac{2.303}{t} \log \left(\frac{2 P_0}{2 P_0-P_t}\right)$

Correct answer

B. $\frac{2.303}{t} \log \left(\frac{2 P_0}{3 P_0-P_t}\right)$

Step-by-step solution

For a first order gas phase reaction, A_ (g) 2 B_ (g) +C_ (g) P_0 be initial pressure of A and P_t the total pressure

Total pressure at time

t=P_0-P+2 P+P=P_t

\begin{aligned} & \Rightarrow P_t=P_0+2 P \\ & P_t-P_0=2 P \Rightarrow P=\frac{P_t-P_0}{2} \\ & k=\frac{2.303}{t} \log \left[\frac{P_0}{P_0-P}\right] \\ & =\frac{2.303}{t} \log \left[\frac{P_0}{P_0-\left(\frac{P_t-P_0}{2}\right)}\right] \\ & =\frac{2.303}{t} \log \left[\frac{2 P_0}{2 P_0-P_t+P_0}\right]=\frac{2.303}{t} \log \left[\frac{2 P_0}{3 P_0-P_t}\right]\end{aligned}

$$

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