The type of rate law for a reaction, either the differential rate law or the integrated rate law, is usually determined by which data is easiest to collect. Explain.

The differential rate law describes the rate of a reaction at a specific point in time. It provides the relationship between the rate of the reaction and the concentration of the reactants. The differential rate law has the general form: \[rate = k[A]^m[B]^n,\] where \(rate\) is the reaction rate, \(k\) is the rate constant, \([A]\) and \([B]\) are the concentrations of reactants, and \(m\) and \(n\) are the reaction orders with respect to the reactants A and B, respectively.

The integrated rate law is obtained by integrating the differential rate law over time. This results in a mathematical equation that expresses the concentration of reactants or products as a function of time. Integrated rate laws can be used to predict the concentration of reactants or products at any given time during a reaction or to calculate the time needed for the reaction to reach a particular stage.

When performing experiments, researchers collect data on the concentrations of reactants and products as a function of time. This can be done by various techniques such as spectroscopy, titration, or chromatography. The experimental data can then be used to determine the rate law for the reaction by fitting the data to the appropriate differential or integrated rate law equation.

The choice between differential and integrated rate laws depends on the type of data collected and the ease of fitting the data to the equations. - If the experimental data directly provides the rates of reaction at different reactant concentrations, the differential rate law is more appropriate. By plotting the reaction rate against the reactant concentrations, the order for each reactant can be deduced by finding the slope of the log-log plot, and the rate constant can be determined from the intercept. - On the other hand, if the experimental data provides reactant or product concentrations as a function of time, the integrated rate law is preferable. By plotting the concentration data against time, the rate constant and reaction order can be obtained, depending on the decay pattern. For example, if the concentration of a reactant decreases linearly with time, the reaction is first order. In conclusion, the choice between differential and integrated rate laws depends on the format and accessibility of the experimental data. The more straightforward method to apply the collected data should be employed, enabling the researcher to determine the reaction's rate law with the least amount of effort and the highest level of accuracy.