The rate constant of the reaction is

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Solution

Q.
The following data were obtained during the first order thermal decomposition of a gas A at constant volume:

$A (g) \to 2 B (g) + C (g)$

S.No. Time/s Total pressure/(atm)

1. 0 0.1

2. 115 0.28

The rate constant of the reaction is ______ $\times 10^{- 2} s^{- 1}$ (nearest integer). [2024]

Ans.
(2)

   $A (g)$ $\to$ $2 B (g)$ $+$ $C (g)$

  t = 0 0.1 0 0

t = 115s (0.1 - p) 2p p

  Total pressure at 115s = (0.1 + 2p) atm = 0.28 atm

P = 0.09 atm

  For first order reaction rate constant k is given as:

   $k = \frac{2.303}{t} \log_{10} \frac{P_{o}}{P_{t}}$

  Where $p_{o}$ is initial pressure of reactant and $p_{t}$ is pressure of reactant at time $t$ .

   $k = \frac{2.303}{115} \log_{10} \frac{0.1}{0.1 - 0.09} s^{- 1} = \frac{2.303}{115} \log_{10} 10 s^{- 1} \approx 2 \times 10^{- 2} s^{- 1}$

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