Concentration and Rate Law

The rate of a reaction often depends on the reactant concentrations. For any reaction, the relationship between the reaction rate and the reactant concentrations can be expressed mathematically using a rate law or the rate equation.

In a rate law, k is the proportionality constant, or the rate constant, and n is the reaction order with respect to a single reactant, whose value is often an integer. In rate laws for multi-reactant reactions, the overall reaction order is the sum of all reactant orders.

For each reactant, the reaction rate, rate constant, concentration, and the reaction order are all determined experimentally. The rate law expresses the relationship between all these parameters.

Individual reactant orders commonly take the values 0, 1, or 2, and based on the overall reaction order, chemical reactions can be categorized as zero-order, first-order, or second-order reactions.

A single-reactant, or unimolecular, chemical reaction for which the reaction rate remains constant throughout its duration is a zero-order reaction. The reactant order in a zero-order reaction is zero, and according to the rate law, the reactant concentration is raised to the zeroth power.

Since the value of any number raised to the zeroth power is one, the reaction rate of a zero-order reaction is equal to the rate constant and, hence, independent of the reactant concentration. Therefore, in a zero-order reaction, even as the reactant's concentration decreases, the reaction rate does not slow down.

A unimolecular chemical reaction where the reaction rate is directly proportional to the reactant's concentration is a first-order reaction. The reactant order for a first-order reaction is one, and as per the rate law the reactant’s concentration is raised to the first power.

Since the value of any number raised to the power of one remains the same, the reaction rate of a first-order reaction directly depends on the reactant concentration. As the reactant concentration decreases, the reaction rate decreases proportionally in a linear manner.

A unimolecular chemical reaction where the reaction rate is dependent on the square of the reactant’s concentration is a second-order reaction. The reactant order is two, and the reactant concentration is raised to the second power.

Accordingly, the reaction rate in a second-order reaction directly depends on the square of the reactant concentration. As the reactant concentration decreases, the reaction rate decreases exponentially in a quadratic manner.