Question

For a reaction following first-order kinetics, which of the following statements is/are correct ?

• A. The time taken for the completion of 50% of the reaction is $t_{1/2}$.
• B. A plot of the reciprocal of the concentration of the reactants against time gives a straight line.
• C. The degree of dissociation is equal to $1-e^{-kt}$.
• D. A plot of $\left[A{]}_0/\right[A]$ versus time gives a straight line.

Answer 1

The correct option is A The time taken for the completion of 50% of the reaction is $t_{1/2}$.

The time taken for the completion of $50$% of the reaction is called as the half-life period. It is represented as $t_{1/2}$.

Thus option A is correct.

A plot of the logarithm of the concentration of the reactants against time gives a straight line.

Thus option B is incorrect.

The integrated rate law for the first order reaction is $\left[A\right]=[A{]}_0{e}^{-kt}$.
Substitute $\left[A\right]=a-x$ and $[A{]}_0=a$ in the above expression.
$a-x=a{e}^{-kt}$.
Rearrange above expression.
$x=a(1-e^{-kt})$.

Hence option C is incorrect.

A plot of $log\left[A{]}_0/\right[A]$ versus time gives a straight line.

Hence, option D is incorrect.