What are the assumptions made in deriving the rate expression for a reaction?

The assumptions made in deriving the rate expression for a reaction include the collision theory, steady state approximation, and elementary reaction assumption.

The first assumption is based on the collision theory. This theory assumes that for a reaction to occur, reactant particles must collide with each other. Not only that, but these collisions must also have sufficient energy (greater than the activation energy) and the correct orientation. This is important in deriving the rate expression as it helps to explain why increasing the concentration of reactants or the temperature can increase the rate of reaction.

The second assumption is the steady state approximation. This is used in complex reactions that involve intermediates. The assumption is that the concentration of these intermediates remains constant over the course of the reaction. This is because their rate of formation is equal to their rate of consumption. This assumption allows us to simplify the rate equations and make them more manageable.

The third assumption is the elementary reaction assumption. This assumes that the reaction occurs in a single step with a single transition state. This is used to derive the rate law from the stoichiometry of the reaction. However, many reactions occur in multiple steps, each with its own transition state. For these reactions, the rate law must be derived from the rate-determining step, which is the slowest step in the reaction.

In addition, it is also assumed that the reaction is not influenced by external factors such as pressure and catalysts. These factors can alter the rate of reaction and therefore would affect the rate expression. However, in many cases, these factors are kept constant to simplify the derivation of the rate expression.

In conclusion, these assumptions are necessary to derive the rate expression for a reaction. They simplify the complex nature of chemical reactions and allow us to predict the rate of reaction under different conditions. However, they are approximations and may not always hold true, especially for complex reactions. Therefore, the derived rate expression should always be validated with experimental data.