Chemical Kinetics - Result Question 45
####45. For the first order reaction,
(a) the degree of dissociation is equal to $\left(1-e^{-k t}\right)$
$(1998,2 M)$
(b) a plot of reciprocal concentration of the reactant $v s$ time gives a straight line
(c) the time taken for the completion of $75 %$ reaction is thrice the $\frac{1}{2}$ of the reaction
(d) the pre-exponential factor in the Arrhenius equation has the dimension of time, $T^{-1}$
Show Answer
Answer:
Correct Answer: 45. $(a, b, d)$
Solution:
- For a first order reaction :
$$ \begin{aligned} & \qquad k t=\ln \frac{1}{1-\alpha} \quad \text { where, } \alpha=\text { degree of dissociation. } \ & \Rightarrow \quad 1-\alpha=e^{-k t} \Rightarrow \alpha=1-e^{-k t} \ & \text { Also } \frac{1}{[A]}=\frac{e^{k t}}{[A] _0} \text {, i.e. plot of reciprocal of concentration of } \end{aligned} $$
reactant $v s$ time will be exponential.
Time for $75 %=\frac{1}{k} \ln \frac{100}{100-75}=\frac{2 \ln 2}{k}=2\left(t _{1 / 2}\right)$
The Arrhenius equation is :
$$ \ln k=\ln A-\frac{E _a}{R T} $$
The dimensions of $k$ and $A$ must be same. For first order reaction, dimensions of $k$ is $t^{-1}$.
