Question

For a first order reaction,
(IIT-JEE, 1998)

• A. The degree of dissociation is equal to $(1–e^{-kt})$
• B. A plot of reciprocal concentration of the reactant versus time gives a straight line.
• C. The time taken for the completion of 75% of the reaction is thrice the time taken for ½ of the reaction.
• D. The pre-exponential factor in the Arrhenius equation has the dimension of time $T^{-1}$.

Answer 1

Answer: (A), (D)

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

$k=\frac{2.303}{t}log\frac{A_0}{A}$

$orkt=ln\frac{A^0}{A}=ln\frac{1}{1-a}$

If a is the degree of dissociation,

$e^{kt}=\frac{1}{1-a}$

$or1-a=e^{-kt}$

$a=1-e^{-kt}$

$\therefore k=A{e}^{-E_a/RT}$ (Arrhenius equation)

Pre-exponential factor has the same dimensions as the rate constant, and for a first order reaction that is $\left(t^{-1}\right).$