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Consider a first order gas phase decomposition reaction given below :

A(g)\rightarrow B(g)+C(g)

The initial pressure of the system before decomposition of A was pi. After lapse of time ‘t’, total pressure of the system increased by x units and became ‘pt'. The rate constant k for the reaction is given as _________.

(i) k=\frac{2.303}{t} log\;\frac{P_{i}}{P_{i}-x}

(ii) k=\frac{2.303}{t} log\;\frac{P_{i}}{2P_{i}-P_{t}}

(iii) k=\frac{2.303}{t} log\;\frac{P_{i}}{2P_{i}+P_{t}}

(iv) k=\frac{2.303}{t} log\;\frac{P_{i}}{P_{i}+x}

Answers (1)

The answer is the option (ii)

  A(g) B(g) C(g)
Initial Pressure: Pi 0 0
Pressure after time (t): (Pi - x) x x

P_{i}=P_{i}+x

x=P_{t}-P_{i}

P_{A}= \text {Pressure of A after time t}= \text {P}_{i}-\text {x}=\text {P}_{i}-(\text {P}_{i}-\text {P}_{i})=2\text {P}_{i}-\text {P}_{t}

k=\frac{2.303}{t}log\frac{[A]_{0}}{[A]}=\frac{2.303}{t}log\frac{P_{i}}{2P_{i}-P_{t}}

 

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