Question

For the 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 $\frac{1}{2}$ of the reaction
• D. the pre-exponential factor in the Arrhenius equation has the dimension of time, $T^1$

Answer 1

Answer: (D)

the pre-exponential factor in the Arrhenius equation has the dimension of time, $T^1$

Answer 2

For a first order reaction :
$kt=In\frac{1}{1-\alpha}$ where, $\alpha$ = degree of dissociation.
$\Rightarrow 1-\alpha=e^{-kt}\Rightarrow \alpha=1-e^{-kt}$
Also $\frac{1}{[A]}=\frac{e^{kt}}{[A]_0},$ i.e. plot of reciprocal of concentration of reactant vs time will be exponential.
Time for $75\%=\frac{1}{k}In\frac{100}{100-75}=\frac{2 In 2}{k}=2(t_{1/2})$
The Arrhenius equation is :
In k= In $A-\frac{E_0}{RT}$
The dimensions of k and A must be same. For first order reaction, dimensions of k is $t^{-1}$.