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A topic from the subject of Kinetics in Chemistry.

  • 1 year ago
  • 9 min read
Zero-Order Reactions in Chemistry
Introduction

Zero-order reactions are chemical reactions where the reaction rate is independent of the concentration of the reactants. The reaction proceeds at a constant rate regardless of how much reactant is present.

Basic Concepts

The rate law for a zero-order reaction is:

Rate = k

where:

  • k is the rate constant (with units of concentration/time, e.g., M/s).

Unlike other reaction orders, the concentration of the reactant [A] does not appear in the rate equation because it has a zero-order effect. This implies that the rate is solely determined by factors other than reactant concentration, such as the availability of a catalyst or surface area (in heterogeneous catalysis).

Integrated Rate Law

The integrated rate law for a zero-order reaction, derived from the rate law, is:

[A]t = [A]0 - kt

where:

  • [A]t is the concentration of reactant A at time t
  • [A]0 is the initial concentration of reactant A
  • k is the rate constant
  • t is time

This equation shows a linear relationship between concentration and time. Plotting [A]t versus t yields a straight line with a slope of -k and a y-intercept of [A]0.

Half-Life

The half-life (t1/2) of a zero-order reaction, the time it takes for the concentration of the reactant to decrease by half, is given by:

t1/2 = [A]0 / 2k

Notice that the half-life of a zero-order reaction depends on the initial concentration of the reactant.

Equipment and Techniques

Zero-order reactions can be studied using various techniques, including:

  • Spectrophotometry (measuring absorbance to monitor concentration changes)
  • Gas chromatography (separating and quantifying gaseous reactants/products)
  • Titration (determining the concentration of a reactant or product through neutralization or other chemical reactions)

The best technique depends on the specific reaction and the reactants/products involved.

Types of Experiments

Experiments to study zero-order reactions include:

  • Initial rate experiments (measuring the rate at the beginning of the reaction)
  • Half-life experiments (measuring the time it takes for the concentration to halve)
  • Product formation experiments (measuring the amount of product formed over time)
Data Analysis

Data analysis for zero-order reactions often involves:

  • Linear regression (fitting a straight line to a plot of [A]t vs. t)

The slope of this line directly provides the rate constant, k.

Applications

Zero-order reactions are found in several applications, including:

  • Enzyme-catalyzed reactions at high substrate concentrations (where the enzyme is saturated)
  • Some photochemical reactions (where the rate is determined by light intensity)
  • Heterogeneous catalysis (where the reaction occurs on a surface)
  • Controlled drug release (maintaining a constant drug concentration over time)
Conclusion

Zero-order reactions, while less common than first or second-order reactions, are important in various chemical and biological systems. Their unique characteristics, particularly the constant rate regardless of reactant concentration, make them valuable in specific applications.

Zero-Order Reactions
Key Points
  • Zero-order reactions have a rate that is independent of the concentration of reactants.
  • The rate constant for a zero-order reaction has units of concentration per time, such as M/s.
  • Zero-order reactions are not common, but they can occur under specific conditions, such as when a reaction's rate-limiting step involves a unimolecular process or when the surface area of a catalyst is saturated.
Main Concepts

The rate of a chemical reaction describes how quickly reactants are converted into products. It's often expressed as the change in concentration of a reactant or product per unit time. The rate law mathematically defines the relationship between the reaction rate and the concentrations of the reactants.

Zero-order reactions are unique because their rates are completely unaffected by the concentrations of the reactants. This means the reaction proceeds at a constant speed regardless of how much reactant is present.

The rate law for a zero-order reaction is:

rate = k[A]0 = k

Where:

  • rate is the rate of the reaction.
  • k is the rate constant (with units of concentration/time, e.g., M/s).
  • [A] is the concentration of reactant A (raised to the power of zero, indicating no concentration dependence).

Because [A]0 = 1, the rate is simply equal to the rate constant, k.

While uncommon, zero-order reactions can occur in specific situations. These include:

  • Reactions with a saturated catalyst: When a catalyst is completely covered by reactant molecules (saturated), further increases in reactant concentration cannot increase the rate because there are no more catalyst sites available.
  • Reactions with a limiting reagent other than the reactant of interest: If another reactant is present in a much smaller amount than the reactant considered, the rate is limited by the concentration of that other, more limiting species and thus is zero order with respect to the more plentiful reactant.
  • Photochemical reactions: The rate of a photochemical reaction often depends only on the intensity of the light and not on the concentration of the reactant.
  • Enzyme-catalyzed reactions at high substrate concentrations: At high substrate concentrations, enzymes are saturated, and the reaction rate becomes independent of substrate concentration.
Example:

The decomposition of gaseous hydrogen iodide (HI) on a metal surface under specific conditions can exhibit zero-order kinetics:

2HI(g) → H2(g) + I2(g)

At high HI concentrations or a saturated catalyst surface, the rate of this reaction can become independent of the HI concentration, resulting in a zero-order rate law.

Zero-Order Reactions

A zero-order reaction is a chemical reaction where the rate of the reaction is independent of the concentration of the reactants. This means the reaction proceeds at a constant rate regardless of how much reactant is present. The rate law for a zero-order reaction is expressed as:

Rate = k

where:

  • Rate is the rate of the reaction (e.g., in M/s)
  • k is the rate constant (in M/s)

Experiment Example: Decomposition of N2O5

The decomposition of dinitrogen pentoxide (N2O5) is a classic example of a zero-order reaction under certain conditions (specifically, at high concentrations and in the presence of a catalyst). The reaction can be represented as:

2N2O5(g) → 4NO2(g) + O2(g)

Experimental Setup:

  • A sample of N2O5 gas is placed in a closed container at a constant temperature.
  • The concentration of N2O5 is measured at regular intervals using a suitable technique (e.g., spectrophotometry).

Data Analysis:

A plot of [N2O5] versus time will yield a straight line with a negative slope. The absolute value of the slope is equal to the rate constant, k. The fact that the plot is linear indicates the zero-order nature of the reaction.

Another Example: Photochemical Reactions

Many photochemical reactions exhibit zero-order kinetics. In these reactions, the rate is determined by the intensity of the light source rather than the concentration of the reactants. As long as the light intensity is constant, the reaction proceeds at a constant rate regardless of the reactant concentration.

Note: Zero-order reactions are less common than first-order or second-order reactions. They typically occur under specific conditions, such as when the reactant is adsorbed onto a surface (heterogeneous catalysis) or when the reaction is light-limited (photochemistry).

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