A zero-order reaction is a chemical reaction where the rate of the reaction is independent of the concentration of the reactants. In other words, the reaction rate remains constant regardless of how much of the reactants are present.
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In a zero-order reaction, the rate of the reaction is constant and does not depend on the concentration of the reactants.
The rate law for a zero-order reaction is expressed as $\text{rate} = k$, where $k$ is the rate constant.
The integrated rate law for a zero-order reaction is $[A] = [A]_0 - kt$, where $[A]$ is the concentration of the reactant, $[A]_0$ is the initial concentration, $k$ is the rate constant, and $t$ is the time.
Zero-order reactions are often observed in catalytic reactions, where the catalyst concentration remains constant throughout the reaction.
The half-life of a zero-order reaction is independent of the initial concentration and is given by $t_{1/2} = [A]_0 / (2k)$.
Review Questions
Explain the key features of a zero-order reaction and how it differs from other reaction orders.
In a zero-order reaction, the reaction rate is constant and does not depend on the concentration of the reactants. This is in contrast to first-order and second-order reactions, where the rate is proportional to the concentration of one or more reactants, respectively. The rate law for a zero-order reaction is simply $\text{rate} = k$, where $k$ is the rate constant. The integrated rate law for a zero-order reaction is $[A] = [A]_0 - kt$, which shows that the concentration of the reactant decreases linearly with time. This is different from the exponential decay observed in first-order reactions and the more complex relationships seen in higher-order reactions.
Describe the conditions under which a reaction is likely to be zero-order and provide examples of such reactions.
A reaction is likely to be zero-order when the concentration of the reactants is much higher than the concentration of the products or intermediates. This is often the case in catalytic reactions, where the catalyst concentration remains constant throughout the reaction. Examples of zero-order reactions include the decomposition of hydrogen peroxide (H$_2$O$_2$) catalyzed by the enzyme catalase, the reduction of nitrogen oxides (NO$_x$) in automobile catalytic converters, and the hydrolysis of sucrose (table sugar) catalyzed by the enzyme invertase. In these cases, the rate of the reaction is independent of the concentration of the reactants, as long as there is an excess of the reactants present.
Explain how the half-life of a zero-order reaction is calculated and how it differs from the half-life of a first-order reaction.
The half-life of a zero-order reaction is given by the equation $t_{1/2} = [A]_0 / (2k)$, where $[A]_0$ is the initial concentration of the reactant and $k$ is the rate constant. This is different from the half-life of a first-order reaction, which is given by $t_{1/2} = \ln(2) / k$. In a zero-order reaction, the half-life is independent of the initial concentration, as the rate is constant throughout the reaction. In contrast, the half-life of a first-order reaction depends on the initial concentration, as the rate decreases exponentially with time. The linear decrease in concentration observed in zero-order reactions also means that the half-life is simply the time it takes for the concentration to decrease by half, whereas in first-order reactions, the half-life is the time it takes for the concentration to decrease to half of its initial value.