How do you derive the rate expression from experimental data?

The rate expression is derived from experimental data by plotting concentration against time and determining the order of reaction.

In more detail, the rate expression for a chemical reaction describes how the rate of the reaction depends on the concentrations of the reactants. It is usually in the form of rate = k[A]^m[B]^n, where k is the rate constant, [A] and [B] are the concentrations of the reactants, and m and n are the orders of reaction with respect to A and B, respectively.

To derive the rate expression from experimental data, you first need to conduct a series of experiments where you vary the concentrations of the reactants and measure the rate of the reaction. You then plot the concentration of a reactant against time and observe the shape of the graph. If the graph is a straight line, the reaction is first order with respect to that reactant. If the graph is a curve that can be linearised by taking the logarithm of the concentration, the reaction is second order with respect to that reactant. If the rate of the reaction does not change when the concentration of the reactant is changed, the reaction is zero order with respect to that reactant.

Once you have determined the order of reaction with respect to each reactant, you can write the rate expression. For example, if the reaction is first order with respect to A and second order with respect to B, the rate expression would be rate = k[A][B]^2.

Finally, you can determine the value of the rate constant, k, by substituting the concentrations and the rate of the reaction into the rate expression. This should be done for several sets of experimental data to ensure accuracy. The average value of k obtained from these calculations is then used in the final rate expression.

Remember, the rate expression is an important tool in predicting how the rate of a reaction will change under different conditions, so understanding how to derive it from experimental data is a key skill in chemistry.