First order reaction

First Order Reaction

A first order reaction is a type of chemical reaction where the rate of reaction is directly proportional to the concentration of one reactant. This means that the reaction rate depends linearly on the concentration of a single reactant raised to the first power. First order reactions are common in chemical kinetics and are characterized by a specific rate law and integrated rate equation.

Rate Law

For a first order reaction, the rate law can be expressed as:

\( \text{Rate} = k[A] \)

where:

• \( k \) is the rate constant,
• \( [A] \) is the concentration of the reactant A.

The units of the rate constant \( k \) for a first order reaction are \( \text{s}^{-1} \).

Integrated Rate Equation

The integrated rate equation for a first order reaction is derived by integrating the rate law. It is given by:

\( [A] = [A]_0 e^{-kt} \)

or in logarithmic form:

\( \ln[A] = \ln[A]_0 - kt \)

where:

• \( [A]_0 \) is the initial concentration of the reactant,
• \( t \) is the time,
• \( e \) is the base of the natural logarithm.

This equation shows that the natural logarithm of the concentration of the reactant decreases linearly with time.

Half-Life

The half-life of a first order reaction, denoted as \( t_{1/2} \), is the time required for the concentration of the reactant to decrease to half of its initial value. For a first order reaction, the half-life is independent of the initial concentration and is given by:

\( t_{1/2} = \frac{0.693}{k} \)

This property makes first order reactions particularly simple to analyze.

Examples

First order reactions are common in both chemical and biological systems. Some examples include:

• Radioactive decay of isotopes, where the rate of decay is proportional to the number of undecayed nuclei.
• The hydrolysis of aspirin in water.
• The decomposition of hydrogen peroxide in the presence of a catalyst.

Graphical Representation

In a plot of \( \ln[A] \) versus time \( t \), a first order reaction will yield a straight line with a slope of \( -k \). This linear relationship is a key diagnostic feature of first order kinetics.

Also see

• Chemical kinetics
• Second order reaction
• Zero order reaction
• Reaction rate
• Rate equation