Question

A substance having rate constant k and initial concentration reacts according to zero order kinetics. What will be the time for the reaction to go to completion?
 A. $${\displaystyle \frac{a}{k}}$$
 B. $${\displaystyle \frac{k}{a}}$$
 C. $${\displaystyle \frac{a}{2k}}$$
 D. $${\displaystyle \frac{2k}{a}}$$

Answer 1

Hint: Zero-order reactions are those reactions where the rate of reaction is independent of the increase or decrease in the concentration of reactants. Therefore, it is found that the rate of such reactions is always equal to their rate constants.

Complete step-by-step answer:
The kinetic equation of zero order is x = kt, where x is the quantity of reactant that is converted into product, k is the rate constant of the reaction and t is time taken to process the reaction.
 $$100\mathrm{\%}$$ completion reaction occurs when the initial concentration of reactants is completely converted into a product. Let us assume that the initial concentration of reactant is $$a={\left[A\right]}_0$$. When this initial concentration gives rise to a product which is equal to it, then it is called a complete reaction. At this point, the value of x changes to a.
 $$a=k\times t_{100}$$ or we can write it as $$t_{100}={\displaystyle \frac{a}{k}}$$.
Therefore, for a reaction to be $$100\mathrm{\%}$$completed, the time required in zero order reaction is $$t_{100}={\displaystyle \frac{a}{k}}$$.

Hence, the correct option is (A).

Note: The unit of the rate constant can be given by the ratio of concentration by time i.e. M/s or molarity per second.Zero order reactions are generally those reactions in which catalysts are used to process the reaction.