The great value of chemical kinetics is that it can give us insights into the actual reaction pathways (mechanisms) that reactants take to form the products of reactions. Analyzing a reaction mechanism to determine the type of rate law that is consistent (or not consistent) with the specific mechanism can give us significant insight. For example, the reaction \[ A+ B \rightarrow C \nonumber \] might be proposed to follow one of two mechanistic pathways: \[ \underbrace{A + A \xrightarrow{k_1} A_2}_{\text{step 1}} \nonumber \] \[ \underbrace{ A_2 + B \xrightarrow{k_2} C}_{\text{step 2}} \nonumber \] or \[ \underbrace{A \xrightarrow{k_1} A^*}_{\text{step 1}} \nonumber \] \[ \underbrace{ A^* + B \xrightarrow{k_2} C}_{\text{step 2}} \nonumber \] The first rate law will predict that the reaction should be second order in \(A\), whereas the second mechanism predicts that it should be first order in \(A\) (in the limit that the steady state approximation, discussed in the following sections, can be applied to \(A_2\) and \(A^*\)). Based on the observed rate law being first or second order in A, one can rule out one of the rate laws. Unfortunately, this kind of analysis cannot confirm a specific mechanism. Other evidence is needed to draw such conclusions, such as the spectroscopic observation of a particular reaction intermediate that can only be formed by a specific mechanism. In order analyze mechanisms and predict rate laws, we need to build a toolbox of methods and techniques that are useful in certain limits. The next few sections will discuss this kind of analysis, specifically focusing on the Rate Determining Step approximation, the Steady State approximation, and the Equilibrium approximation. Each type of approximation is important in certain limits, and they are oftentimes used in conjunction with one another to predict the final forms of rate laws.