Indicate the order of reaction consistent with each observation.
a. The half-life of the reaction gets shorter as the initial concentration is increased.
b. A plot of the natural log of the concentration of the reactant versus time yields a straight line.

Verified step by step guidance

1. Identify the relationship between half-life and concentration for different orders of reaction.
2. Recall that for a zero-order reaction, the half-life decreases as the initial concentration increases.
3. For a first-order reaction, the half-life is independent of the initial concentration.
4. For a second-order reaction, the half-life increases as the initial concentration decreases.
5. Conclude that the observation of the half-life getting shorter as the initial concentration increases is consistent with a zero-order reaction.

Key Concepts

Order of Reaction

The order of a reaction refers to the power to which the concentration of a reactant is raised in the rate law. It provides insight into how the rate of reaction is affected by the concentration of reactants. Common orders include zero, first, and second, each indicating different relationships between concentration and reaction rate.

Half-Life of a Reaction

The half-life of a reaction is the time required for the concentration of a reactant to decrease to half of its initial value. For different orders of reactions, the half-life behaves differently; for example, in first-order reactions, the half-life is constant, while in second-order reactions, it increases with decreasing concentration.

Kinetics and Concentration

In chemical kinetics, the relationship between reaction rate and concentration is crucial. If the half-life of a reaction decreases as the initial concentration increases, it suggests a reaction order greater than one, typically indicating a second-order reaction. This behavior highlights how changes in concentration can significantly influence reaction dynamics.