The following data were obtained during the first order thermal decomposition of a gas A at constant volume: S.No. Time/sec Total Pressure/atm --- --- --- 1 0 0.1 2 115 0.28 The rate constant of the reaction is \ \ \ \ \ \ \ \ × 10 -2 s -1 (nearest integer)

Chemistry · Chemical Kinetics

JEE Main 2024 — 1 February, Shift 2 — Question 77

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

S.No.	Time/sec	Total Pressure/atm
1	0	0.1
2	115	0.28

The rate constant of the reaction is $\_\_\_\_\_\_\_\_$$\times 10^{-2} \mathrm{~s}^{-1}$ (nearest integer)

Numerical answer — enter this value.

P_0=0.1\ \mathrm{atm},\quad P_t=0.28\ \mathrm{atm},\quad t=115\ \mathrm{s}

P_\infty=0.3\ \mathrm{atm}

k=\frac{1}{t}\ln\!\left(\frac{P_\infty-P_0}{P_\infty-P_t}\right)

k=\frac{1}{115}\ln\!\left(\frac{0.3-0.1}{0.3-0.28}\right)

k=\frac{1}{115}\ln(10)

k=\frac{2.303}{115}=0.020\ \mathrm{s^{-1}}

\boxed{k=2\times10^{-2}\ \mathrm{s^{-1}}}

Answer key and solution verified before publishing.

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