Question

For a $1^{st}$ order chemical reaction.

• A. The product formation rate is independent of reactant concentration
• B. The time taken for the completion of half of the reaction $\left(t_{1/2}\right)$ is 69.3% of the rate constant(k)
• C. The dimension of Arrhenius pre-exponential factor is reciprocal of time
• D. The concentration vs time plot for the reactant should be linear with a negative slope

Answer 1

The correct option is C The dimension of Arrhenius pre-exponential factor is reciprocal of time

a) For $1^{st}$ order reaction product formation is depends upon reactant concentration. The rate of a first order reaction is given by $r=k\left[A\right]$, where [A] is concentration of the reactant.
b) For first order reaction,
$t_{1/2}=\frac{0.693}{k}$
= 69.3 % of $\frac{1}{k}$
c) According to Arrhenius equation,
$k=A{e}^{-E_a/RT}$
Since it is a first order reaction, so unit of rate constant k is $se{c}^{-1}$. So the dimension of Arrhenius pre-exponential factor is reciprocal of time.
d) For first order reaction,
$A=A_o{e}^{-kt}$
So, the concentration vs time plot for the reactant should be exponential.