Premed · Premed · General Chemistry 2
Lecture 2: Reaction Mechanisms and Catalysis
General Chemistry II
Learning Objectives
By the end of this lecture, students will be able to:
- Define and identify elementary steps within a reaction mechanism
- Determine the molecularity of an elementary step
- Identify the rate-determining step in a multi-step mechanism
- Derive a rate law from a proposed mechanism and compare it to experimental data
- Explain how catalysts increase reaction rates without being consumed
- Distinguish between homogeneous and heterogeneous catalysis and describe enzyme catalysis
Lecture Content
I. Reaction Mechanisms: Overview
A reaction mechanism is a detailed, step-by-step description of the molecular-level pathway by which reactants are converted into products. Each individual step in a mechanism is called an elementary step, and the overall balanced equation is simply the sum of all elementary steps. Species that are produced in one step and consumed in a subsequent step are called reaction intermediates. These intermediates do not appear in the overall balanced equation, but they are real chemical species that can sometimes be detected experimentally. This distinguishes them from transition states, which represent fleeting energy maxima along the reaction path and cannot be isolated.
A proposed mechanism must satisfy two essential criteria. First, the elementary steps must add together to yield the overall balanced equation. Second, the rate law predicted by the mechanism must agree with the experimentally determined rate law. If either criterion fails, the mechanism must be revised.
II. Elementary Steps and Molecularity
An elementary step describes a single molecular event, such as one bond breaking or forming during a single collision. The molecularity of an elementary step refers to the number of reactant molecules involved. A unimolecular step involves a single molecule (A -> products) and has a rate law of Rate = k[A]. A bimolecular step involves two molecules colliding (A + B -> products or 2A -> products), giving Rate = k[A][B] or Rate = k[A]^2. Termolecular steps, involving three molecules colliding simultaneously (A + B + C -> products), are extremely rare because three-body simultaneous collisions are highly improbable.
A crucial distinction in kinetics is that the rate law can be written directly from the stoichiometry of an elementary step, and only from an elementary step. This is emphatically not true for the overall reaction, whose rate law must be determined experimentally.
III. The Rate-Determining Step
In a multi-step mechanism, the slowest step limits the overall rate and is therefore called the rate-determining step (RDS). A useful analogy is a multi-lane highway with a bottleneck: the narrowest point determines the overall traffic flow rate. Because the rate-determining step controls the pace of the entire reaction, the overall rate law is determined by this slowest step.
When the first step is slow and subsequent steps are fast, the rate law is simply the rate law for that slow first step. For example, consider the reaction NO2 + CO -> NO + CO2, which proceeds through a slow first step (NO2 + NO2 -> NO3 + NO) followed by a fast second step (NO3 + CO -> NO2 + CO2). The overall rate law is Rate = k[NO2]^2, derived directly from the slow step.
When a fast equilibrium precedes the slow step, the situation requires more care. The rate law for the slow step may contain an intermediate whose concentration is not directly measurable. In this case, you use the equilibrium expression from the preceding fast step to express the intermediate's concentration in terms of the original reactant concentrations, then substitute this expression into the rate law.
<image>An energy diagram (reaction coordinate diagram) for a two-step reaction mechanism. The x-axis is labeled "Reaction Coordinate" and the y-axis is labeled "Potential Energy." The diagram shows two humps (transition states). The first hump is taller (labeled "Transition State 1, slow step") and the second is shorter (labeled "Transition State 2, fast step"). The valley between the two humps is labeled "Intermediate." The starting energy level is labeled "Reactants" and the final level (lower than reactants) is labeled "Products." Activation energies Ea1 and Ea2 are marked for each step, with Ea1 > Ea2. Delta H for the overall reaction is marked as negative.</image>
IV. Deriving Rate Laws from Mechanisms
Deriving a rate law from a proposed mechanism follows a systematic procedure. First, identify the slow (rate-determining) step. Then write the rate law for that step based on its molecularity. If the resulting rate law contains an intermediate, eliminate it by looking for a preceding fast equilibrium step. Write the equilibrium expression (K_eq = k_forward/k_reverse), solve for the concentration of the intermediate, and substitute back into the rate law. Finally, verify that the derived rate law matches experimental observations.
As a concrete example, consider the reaction 2NO + Br2 -> 2NOBr with a proposed mechanism consisting of a fast equilibrium first step (NO + Br2 <=> NOBr2) followed by a slow second step (NOBr2 + NO -> 2NOBr). The rate law from the slow step is Rate = k2[NOBr2][NO], but NOBr2 is an intermediate. From the fast equilibrium, K = [NOBr2]/([NO][Br2]), so [NOBr2] = K[NO][Br2]. Substituting gives Rate = k2 K [NO][Br2] * [NO] = k_obs[NO]^2[Br2]. This matches the experimentally observed rate law, Rate = k[NO]^2[Br2], supporting the proposed mechanism.
V. Collision Theory and the Arrhenius Equation
Collision theory provides a molecular-level explanation of reaction rates. For a reaction to occur, molecules must collide with sufficient kinetic energy and with the proper geometric orientation. The minimum energy required for a productive collision is called the activation energy, Ea.
The Arrhenius equation quantifies the temperature dependence of the rate constant: k = A e^(-Ea/RT). Here, A is the frequency factor (also called the pre-exponential factor), which reflects the frequency of collisions and the fraction with proper orientation. Ea is the activation energy in J/mol, R is the gas constant (8.314 J/(molK)), and T is the absolute temperature in Kelvin. The equation reveals that higher temperatures and lower activation energies both lead to larger rate constants and faster reactions.
A practical two-point form of the Arrhenius equation allows comparison of rate constants at two different temperatures: ln(k2/k1) = (Ea/R)(1/T1 - 1/T2). Additionally, plotting ln(k) versus 1/T yields a straight line with slope -Ea/R and y-intercept ln(A), providing a graphical method for determining the activation energy.
<image>Panel A: An Arrhenius plot showing ln(k) on the y-axis vs. 1/T (K^-1) on the x-axis. A straight line with a negative slope is drawn. The slope is labeled as "-Ea/R" and the y-intercept is labeled as "ln(A)." Several data points are plotted along the line. Panel B: A Boltzmann distribution of molecular kinetic energies at two temperatures T1 and T2 (where T2 > T1). The x-axis is "Kinetic Energy" and the y-axis is "Fraction of Molecules." A vertical dashed line marks Ea. The shaded area to the right of Ea is larger for T2 than T1, illustrating that more molecules exceed the activation energy at higher temperature.</image>
VI. Catalysis
A catalyst is a substance that increases the rate of a reaction without being consumed in the overall process. Catalysts work by providing an alternative reaction pathway that has a lower activation energy than the uncatalyzed route. Importantly, a catalyst does not alter the thermodynamics of a reaction: Delta G and Delta H remain unchanged. Nor does a catalyst shift the position of equilibrium, because it accelerates both the forward and reverse reactions equally. The system simply reaches equilibrium faster.
Homogeneous Catalysis
In homogeneous catalysis, the catalyst exists in the same phase as the reactants. Acid-catalyzed ester hydrolysis, where H+ ions in aqueous solution speed the reaction, is a classic example. Another important case is the catalytic destruction of stratospheric ozone by chlorine radicals. In this gas-phase process, Cl reacts with O3 to form ClO and O2, and then ClO reacts with atomic oxygen to regenerate Cl and produce another O2 molecule. The net reaction, O3 + O -> 2O2, proceeds without consuming the chlorine catalyst.
Heterogeneous Catalysis
In heterogeneous catalysis, the catalyst is in a different phase from the reactants, most commonly a solid catalyst acting on gaseous or liquid reactants. The process involves four steps: adsorption of reactants onto the catalyst surface, migration or diffusion of reactants along the surface, reaction on the surface, and desorption of products. Catalytic converters in automobiles use platinum, palladium, and rhodium catalysts to convert harmful exhaust gases into less toxic products. The Haber process uses an iron catalyst to facilitate the synthesis of ammonia from nitrogen and hydrogen.
Enzyme Catalysis (Biological Catalysis)
Enzymes are biological catalysts, typically proteins, that catalyze reactions in living organisms with remarkable specificity and efficiency. The substrate binds to the enzyme's active site, described by either the lock-and-key model or the more flexible induced-fit model. Enzyme kinetics follows the Michaelis-Menten equation: Rate = V_max[S] / (K_m + [S]). At low substrate concentrations, the rate is approximately first order in [S]. At high substrate concentrations, the enzyme becomes saturated and the rate approaches V_max, exhibiting zero-order dependence on [S]. The Michaelis constant K_m represents the substrate concentration at which the rate is half of V_max and serves as an indicator of the enzyme's affinity for its substrate.
<image>Panel A: An energy diagram comparing an uncatalyzed reaction (single high activation energy barrier) with a catalyzed reaction (two smaller barriers with an intermediate). Both pathways share the same reactant and product energy levels, but the catalyzed pathway has a significantly lower maximum energy barrier. Labels include "Ea (uncatalyzed)," "Ea (catalyzed)," "Reactants," "Products," and "Intermediate." Panel B: A Michaelis-Menten plot showing reaction rate (v) on the y-axis vs. substrate concentration [S] on the x-axis. The curve rises steeply at low [S], then levels off approaching V_max (shown as a horizontal dashed line). K_m is marked on the x-axis at the point where v = V_max/2.</image>
