The rate law for a reaction can be determined only from experiment and not from the balanced equation. Two experimental procedures were outlined in Chapter \(12 .\) What are these two procedures? Explain how each method is used to determine rate laws.

The Method of Initial Rates is an experimental procedure that involves studying the initial rate of a reaction under different initial concentrations of reactants. It is based on the assumption that the initial rate of the reaction is proportional to the initial concentrations of reactants raised to some power, according to the rate law. To use the Method of Initial Rates: 1. Perform the reaction with different initial concentrations of reactants and keep other variables constant. 2. Measure the initial rate of the reaction for each set of initial concentrations. 3. Compare the initial rates and initial concentrations of reactants to determine the order of the reaction with respect to each reactant. 4. Combine the individual orders to determine the overall rate law for the reaction.

The Integrated Rate Law Method is another experimental procedure used to determine the rate law of a reaction. This method involves measuring the concentrations of reactants or products as a function of time and using this data to determine the order and rate constant for the reaction. To use the Integrated Rate Law Method: 1. Perform the reaction and measure the concentration of a reactant or product at different time intervals. 2. Plot the data as a function of time in a way that corresponds to different possible reaction orders (for example, as a linear or logarithmic plot). 3. Determine which plot provides the best linear-fit, indicating the order of the reaction. 4. Use the slope of the linear-fit line to calculate the rate constant. 5. Combine the order and rate constant to obtain the overall rate law for the reaction. In conclusion, the two experimental procedures used to determine rate laws for a reaction are the Method of Initial Rates and the Integrated Rate Law Method. Both methods involve collecting experimental data and analyzing it to find the relationship between reactant concentrations and reaction rates, allowing us to determine the rate law for the reaction.