Chemical Kinetics - Result Question 78
77. While studying the decomposition of gaseous $N _2 O _5$, it is observed that a plot of logarithm of its partial pressure versus time is linear. What kinetic parameters can be obtained from this observation?
(1985, 2M)
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Solution:
- For a first order process : $\ln \frac{[A] _0}{[A]}=k t \Rightarrow \ln [A]=\ln [A] _0-k t$
If the reactant is in a gaseous state
and $k t _{1 / 10}-\ln \frac{[A] _0}{[A] _0 / 10}=\ln 10$
Therefore, $\frac{t {1 / 8}}{t {1 / 10}}=\frac{\ln 8}{\ln 10}=\log{e} 8=3 \log{e} 2=3 \times 0.3=0.9$
$\Rightarrow \quad \frac{t _{1 / 8}}{t _{1 / 10}} \times 10=0.9 \times 10=9$
$\ln p=\ln p _0-k t$ $\quad$ …….. (i)
where $p$ is the partial pressure of reactant remaining unreacted at instant ’ $t$ ’ and $p _0$ is its initial partial pressure.
Also, from equation (i), $\ln p$ vs $t$ would give a straight line. Therefore, decomposition of $N_2O_5$ follows first order kinetics.
BETA
