Table 12.2 illustrates how the average rate of a reaction decreases with time. Why does the average rate of a reaction generally decrease with time? How does the instantaneous rate of a reaction depend on time? Why are initial rates of a reaction primarily used by convention?

The average rate of a chemical reaction refers to the speed at which reactants are transformed into products over a certain time interval. As the reaction progresses, the concentrations of the reactants decrease, which generally leads to a slower reaction rate. Since there are fewer reactant particles available to collide and react, the overall average rate of the reaction decreases with time.

The instantaneous rate of a reaction is the rate at which reactants are consumed or products are generated at an exact moment in time. Mathematically, it is the derivative of the concentration of reactants or products with respect to time (\(\frac{d[R]}{dt}\) or \(\frac{d[P]}{dt}\) respectively). Depending on the reaction and the orders of the reactants, the instantaneous rate may either decrease, increase, or remain constant with time. However, oftentimes, it will follow a similar trend to the average rate, decreasing as the reaction progresses and reactant concentrations drop.

Initial rates are reaction rates measured at the beginning of a reaction when the concentration of reactants is at its highest. There are a few reasons why initial rates are primarily used by convention: 1. The initial rate offers a consistent starting point for comparing reactions, as it eliminates the impact of changing concentrations as the reaction progresses. 2. Initial rates are easier to determine experimentally and can provide a clear indication of how changing reactants' concentrations affect the overall rate of a chemical reaction. 3. The initial rates are useful to determine the rate law (order and rate constant) in kinetics studies, helping researchers to understand the reaction mechanisms. In summary, understanding the behavior of reaction rates, such as average and instantaneous rates, is crucial in the study of chemical kinetics. Initial rates are primarily used to simplify and standardize the study of reactions and better understand their mechanisms.