Question

Which among the following is/ are correct for a first order reaction?

• A. The degree of dissociation is equal to $(1-e^{-kt})$.
• B. A plot of reciprocal concentration of the reactant vs time gives a straight line.
• C. The time taken for the completion of 75% reaction is thrice the $t_{1/2}$ of reaction.
• D. The pre-exponential factor in the Arrhenius equation has the dimension of time, $T^{-1}$.

Answer 1

Answer: (A), (D)

The degree of dissociation is equal to $(1-e^{-kt})$.
The pre-exponential factor in the Arrhenius equation has the dimension of time, $T^{-1}$.

For a first order reaction, $A\to$ Products, we have

$In\frac{[A{]}_t}{[A{]}_0}=-ktor[A{]}_t=[A{]}_0{e}^{-kt}$

In terms of degree of dissociation,

$[A{]}_t=[A{]}_0(1-\alpha )$

Hence, $\left[A{]}_0\right(1-\alpha )=[A{]}_0{e}^{-kt}$
or $\alpha =1-e^{-kt}$

The Arrehnius equation is k = $A{e}^{-E_a/RT}$

The dimension of pre-exponential factor A in the above expression is the same as that of rate constant k. For a first order reaction, the dimension of k is $t^{-1}$.