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 understand how the half-life of a zero-order reaction changes with the initial concentration of the reactant, let's delve into the fundamental principles of chemical kinetics regarding zero-order reactions.

Concept of Zero Order Reaction:

• In a zero-order reaction, the rate of reaction is independent of the concentration of the reactants.
• The rate law is expressed as: \( R = k \), where \( k \) is the rate constant.

Half-life of Zero Order Reaction:

• The formula for the half-life of a zero-order reaction is given by: \( t_{\frac{1}{2}} = \frac{[A]_0}{2k} \)
• Here, \( [A]_0 \) is the initial concentration of the reactant and \( k \) is the rate constant.

Impact of Doubling Initial Concentration:

• Let's consider the effect of doubling the initial concentration of the reactant on the half-life.
• If the initial concentration is doubled, i.e., \( [A]_0 \) becomes \( 2[A]_0 \), substitute it in the half-life formula:
• The new half-life, \( t_{\frac{1}{2},\text{new}} = \frac{2[A]_0}{2k} = \frac{[A]_0}{k} \), which is twice the original half-life.

From this, we can conclude that when the initial concentration of the reactant is doubled, the half-life period of a zero-order reaction is doubled. Therefore, the correct answer is \( \text{is doubled} \).

Explanation of Other Options:

• Is halved: This option would be correct for reactions whose rate is inversely proportional to concentration, not for zero-order.
• Is tripled: Incorrect as per the derived formula.
• Remains unchanged: Incorrect because the concentration directly affects the numerator in the zero-order half-life formula.