Question

When initial concentration of the reactant is doubled, the half-life period of a zero order reaction

• A. is halved
• B. is tripled
• C. is doubled
• D. remains unchanged

Answer 1

The Correct Option is C

To solve the problem, we need to understand the behavior of a zero-order reaction and its half-life. The half-life of a reaction is the time required for the concentration of a reactant to reduce to half of its initial value.

For a zero-order reaction, the rate of the reaction is independent of the concentration of the reactants. The expression for the half-life \( (t_{1/2}) \) of a zero-order reaction is given by:

\( t_{1/2} = \frac{[A]_0}{2k} \)

Where:

• \( [A]_0 \) is the initial concentration of the reactant.
• \( k \) is the rate constant of the reaction.

From the expression, it can be seen that the half-life is directly proportional to the initial concentration of the reactant \( [A]_0 \).

Therefore, when the initial concentration of the reactant is doubled (\( 2[A]_0 \)), the half-life becomes:

\( t_{1/2}' = \frac{2[A]_0}{2k} = \frac{[A]_0}{k} \)

This shows that the half-life period is doubled when the initial concentration is doubled.

Let's consider the options given:

• is halved - This is incorrect because the half-life for a zero-order reaction increases with an increase in the initial concentration.
• is tripled - This is incorrect. Although the half-life increases, it doesn't triple; it doubles with the doubling of the initial concentration.
• is doubled - This is correct as explained above.
• remains unchanged - This is incorrect because, for a zero-order reaction, the half-life changes with changes in initial concentration.

Thus, the correct choice is is doubled.