Describe at least two experiments you could perform to determine a rate law.

One common experimental approach to determine a rate law is the method of initial rates. In this method, we monitor the initial rate of reaction under different initial concentrations of reactants. By comparing how the initial rates change as the reactant concentrations are varied, we can deduce the order of the reaction with respect to each reactant and thus determine the rate law. Here's how to perform an initial rates experiment: a. Set up the reaction with different initial concentrations of the reactants, while keeping the other conditions like temperature and pressure constant. b. Monitor the concentration of one of the reactants or products as a function of time, over multiple trials with different initial concentrations. c. Calculate the initial rate of the reaction for each trial, ideally in the early stages of the reaction when the rate is approximately constant. d. Plot the initial rate as a function of the initial concentration(s) of the reactant(s) and find the relationship between them. e. Determine the order of reaction with respect to each reactant, and obtain the rate constant (k) by fitting the data to the rate law expression.

Another experimental approach to determine a rate law is using integrated rate laws. Integrated rate laws relate the concentration of reactants or products to the time elapsed during the reaction. By monitoring how the concentrations change over time, we can identify the functional relationship between concentration and time to determine the reaction order and rate constant. Here's how to perform an integrated rate law experiment: a. Set up the reaction under controlled conditions (e.g. constant temperature and pressure). b. Measure the concentration of one of the reactants or products as a function of time (e.g. by using spectrophotometry, titration, or gas collection). c. Plot the concentration data versus time and fit the data to the common integrated rate law expressions for zeroth-order, first-order, and second-order reactions. d. Determine which order provides the best fit to the experimental data (e.g. by evaluating the linearity of the plots). e. From the best-fitted plot, determine the slope, which is related to the rate constant (k) for the reaction and calculate the value of k. By using one (or both) of the described experimental approaches, you can successfully determine the rate law for a given chemical reaction.