How is a rate constant (k) determined experimentally?

A rate constant (k) is determined experimentally by measuring the rate of reaction at different concentrations of reactants.

In more detail, the rate constant is a fundamental parameter in the rate equation of a chemical reaction. It is a measure of the speed at which a reaction occurs. The rate equation is typically expressed as Rate = k[A]^m[B]^n, where [A] and [B] are the concentrations of the reactants, m and n are the orders of reaction with respect to A and B, and k is the rate constant.

To determine the rate constant experimentally, one would typically conduct a series of experiments where the concentrations of the reactants are varied and the rate of reaction is measured. This can be done by monitoring the change in concentration of a reactant or product over time, or by measuring a physical property that changes as the reaction proceeds, such as pressure or colour intensity.

Once the rate of reaction has been measured for different concentrations of reactants, the data can be analysed to determine the orders of reaction with respect to each reactant. This is usually done by plotting graphs of rate against concentration and observing the shape of the graph. For example, if the graph is a straight line passing through the origin, the order of reaction is one. If the graph is a curve, the order of reaction is two or more.

Once the orders of reaction have been determined, they can be substituted into the rate equation along with the measured rates and concentrations. This will give a series of equations with k as the only unknown. Solving these equations simultaneously will yield the value of the rate constant.

It's important to note that the rate constant is temperature dependent. Therefore, all experiments used to determine k should be conducted at the same temperature. If the temperature changes, the rate constant will also change. This is described by the Arrhenius equation, which relates the rate constant of a reaction to the temperature at which it is carried out.