Order Of Reaction

The question asks us to identify the correct difference between first-order and second-order reactions. Let's explore these concepts step-by-step:

Understanding Reaction Orders:

• First-order reactions: The rate of reaction depends linearly on the concentration of one reactant. The rate law for a first-order reaction is expressed as , where is the rate constant and is the concentration of reactant A.
• Second-order reactions: The rate depends on either the concentration of two different reactants or the square of the concentration of a single reactant. The rate law for a second-order reaction can be written as or .

Half-life Comparison:

• First-order reactions: The half-life ( ) of a first-order reaction is given by . Importantly, this indicates that the half-life is constant and does not depend on the initial concentration .
• Second-order reactions: For a second-order reaction, the half-life is given by . In this case, the half-life is inversely proportional to the initial concentration of the reactant, indicating dependence on .

Evaluating the Given Options:

• The first option is incorrect because both first- and second-order reaction rates depend on reactant concentrations.
• The second option is incorrect because both first- and second-order reactions can be catalyzed.
• The third option is the correct answer, as it correctly states the difference in half-life dependencies between first- and second-order reactions: "the half-life of a first-order reaction does not depend on ; the half-life of a second-order reaction does depend on ".
• The fourth option is incorrect because it contradicts the nature of first- and second-order reactions' dependencies on concentration.

Thus, the correct answer is: the half-life of a first-order reaction does not depend on [A]₀ ; the half-life of a second-order reaction does depend on [A]₀.

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 of a zero-order reaction is given by:

Where:

• is the initial concentration of the reactant.
• 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 .

Therefore, when the initial concentration of the reactant is doubled ( ), the half-life becomes:

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.