Unit 5: Kinetics

In this unit, students will explore various methods to observe the changes that occur during a chemical reaction, the factors that influence reaction rate, and how it relates to a series of elementary reactions.

Introduction to Kinetics

Chemical kinetics focuses on how fast a reaction proceeds rather than whether it is thermodynamically favorable. While thermodynamics tells us if a reaction can occur, kinetics examines the pathway and time scale over which it happens. For example, diamond converting to graphite is thermodynamically favorable but kinetically extremely slow, illustrating that favorable ΔG does not guarantee a fast rate.
The reaction rate is defined as the change in concentration of a reactant or product per unit time, typically expressed in units of \( \text{M} \cdot \text{s}^{-1} \). Rates can be expressed as average rates over an interval or instantaneous rates at a specific moment in time. Instantaneous rates are determined from the slope of the tangent to a concentration vs. time graph, while average rates use the slope between two points.
Rates are always positive quantities, but they are measured differently for reactants and products. For reactants, rates are written as the negative of the concentration change over time because concentration decreases; for products, rates are positive because concentration increases. For example, \( \text{Rate} = -\frac{\Delta [\text{A}]}{\Delta t} = \frac{\Delta [\text{B}]}{\Delta t} \) for the reaction \( \text{A} \rightarrow \text{B} \).
The stoichiometry of a reaction determines how rates of change for different species are related. If \(a\) moles of reactant A produce \(b\) moles of product B, the rates follow \( \frac{-1}{a} \frac{\Delta [A]}{\Delta t} = \frac{1}{b} \frac{\Delta [B]}{\Delta t} \). This relationship ensures that rates are consistent across the reaction, regardless of which species is monitored experimentally.

Factors Affecting Reaction Rate

Concentration: Increasing the concentration of reactants increases the number of particles in a given volume, which raises the collision frequency. Because more collisions occur per second, the probability of an effective collision—one that leads to product formation—also increases. This principle applies to both gases (via partial pressure changes) and solutions (via molarity changes).
Temperature: Raising the temperature increases the average kinetic energy of particles, shifting the Maxwell–Boltzmann distribution toward higher energies. This increases the fraction of collisions with energy equal to or greater than the activation energy \(E_a\), which exponentially increases reaction rate according to the Arrhenius equation. This is why even a modest temperature increase can dramatically accelerate some reactions.
Surface Area: In heterogeneous reactions, increasing the surface area of a solid reactant exposes more particles to possible collisions. For example, powdered solids react faster than large chunks because more surface particles are available for interaction. This principle is exploited in catalysis, where catalysts are often finely divided to maximize surface exposure.
Nature of Reactants: Ionic reactions in aqueous solution tend to be faster because they involve fewer bond rearrangements compared to covalent reactions, which may require multiple bonds to break. The phase of reactants (gas, liquid, solid) also influences rate, with reactions between gases and/or liquids generally occurring more rapidly than those involving solids.
Catalysts: Catalysts increase reaction rate by providing an alternative pathway with lower activation energy. They are not consumed in the reaction and can function in either homogeneous (same phase) or heterogeneous (different phase) systems. Catalysts increase the number of effective collisions without altering the equilibrium position of the reaction.

Rate Laws and Reaction Order

A rate law expresses the relationship between the reaction rate and the concentrations of reactants, typically in the form \( \text{Rate} = k[A]^m[B]^n \). The exponents \(m\) and \(n\) are the reaction orders with respect to each reactant and are determined experimentally, not from the balanced equation (unless the step is elementary). The sum \(m + n\) is the overall reaction order, which influences both the units of \(k\) and the mathematical relationship between concentration and time.
Reaction order indicates how sensitive the rate is to changes in concentration. For example, in a first-order reaction, doubling the concentration of a reactant doubles the rate, while in a second-order reaction, doubling the concentration quadruples the rate. Zero-order reactions have rates independent of reactant concentration, often occurring when a catalyst surface is saturated.
The rate constant \(k\) is unique for a given reaction at a specific temperature, but it changes when temperature changes due to the Arrhenius relationship. Its units depend on the overall order of the reaction: for example, \( \text{M} \cdot \text{s}^{-1} \) for zero-order, \( \text{s}^{-1} \) for first-order, and \( \text{M}^{-1} \cdot \text{s}^{-1} \) for second-order. This dependence allows experimental data to be used not only for finding orders but also for identifying reaction type.
Rate laws connect directly to reaction mechanisms because the experimentally determined law must match the predicted rate law from the mechanism’s slow step. Discrepancies between predicted and observed orders indicate that the proposed mechanism may be incorrect, guiding chemists toward more accurate models of the molecular process.

Methods for Determining Rate Laws

Method of Initial Rates: This technique measures the initial reaction rate for several trials with varying reactant concentrations. By observing how the initial rate changes when one reactant’s concentration is altered (while others are held constant), the order with respect to that reactant can be deduced. The process is repeated for each reactant, and the data collectively yield the full rate law.
Integrated Rate Laws: These equations relate reactant concentration to time and are derived from the differential rate laws. Each reaction order (zero, first, second) has a distinct integrated form: zero-order \( [A] = -kt + [A]_0 \), first-order \( \ln[A] = -kt + \ln[A]_0 \), and second-order \( \frac{1}{[A]} = kt + \frac{1}{[A]_0} \). The form that produces a straight line when graphed confirms the reaction order and allows \(k\) to be determined from the slope.
Half-Life Analysis: The half-life (\(t_{1/2}\)) is the time it takes for the concentration of a reactant to decrease by half. For first-order reactions, half-life is constant and given by \( t_{1/2} = \frac{\ln 2}{k} \), independent of initial concentration. For zero- and second-order reactions, half-life depends on the starting concentration, providing another method to distinguish between orders.
Graphical analysis is particularly powerful because plotting experimental data in different integrated rate law formats quickly reveals the reaction order. This approach is commonly used in conjunction with technology such as spectrophotometers or pressure sensors to monitor changes in concentration indirectly over time.

Collision Theory and Activation Energy

Collision theory states that molecules must collide with sufficient energy and proper orientation to result in a reaction. Not all collisions are effective; only those exceeding the activation energy (\(E_a\)) barrier can form products. This explains why increasing concentration or temperature increases the reaction rate—both factors raise the number of effective collisions per unit time.
Activation energy is the minimum kinetic energy required for reactants to reach the transition state, a high-energy configuration in which old bonds are partially broken and new bonds are partially formed. The transition state is short-lived and unstable, existing at the top of the potential energy barrier. Lowering \(E_a\) with a catalyst increases the fraction of molecules that can react at a given temperature.
The Arrhenius equation, \( k = A e^{-E_a/RT} \), quantitatively links temperature and rate constant. Here \(A\) is the frequency factor, \(R\) is the gas constant, and \(T\) is absolute temperature. Taking the natural log of both sides gives a linear form, \( \ln k = -\frac{E_a}{R} \cdot \frac{1}{T} + \ln A \), allowing \(E_a\) to be calculated from the slope of a \(\ln k\) vs. \(1/T\) plot.
The Maxwell–Boltzmann distribution graphically shows how particle energies are distributed at a given temperature. Raising the temperature shifts the curve to the right and flattens it, greatly increasing the proportion of particles with energies above \(E_a\). This explains why even small increases in temperature can cause large increases in reaction rate.

Reaction Mechanisms

A reaction mechanism is the step-by-step sequence of elementary processes that describe how a chemical reaction occurs at the molecular level. Each step in the mechanism is called an elementary reaction, and the sum of these steps gives the overall balanced equation. Mechanisms help chemists understand which bonds are broken and formed, and in what sequence, allowing for more accurate predictions about reaction rates and product distribution.
The experimentally determined rate law must be consistent with the mechanism's slowest step, known as the rate-determining step (RDS). This step acts as a bottleneck, controlling the overall rate of the reaction much like the narrowest point in a funnel limits the flow of liquid. Any changes in concentration that affect the RDS will have a direct effect on the observed rate law, while changes that affect only faster steps typically have little to no effect on the rate.

Elementary Reactions

An elementary reaction occurs in a single collision or rearrangement of atoms or molecules, with no intermediate steps. The molecularity of the reaction describes the number of reactant particles involved in that step: unimolecular (one particle), bimolecular (two particles), or termolecular (three particles). Molecularity can only be assigned to individual elementary steps and not to the overall reaction.
For an elementary step, the rate law can be written directly from the stoichiometric coefficients because the reaction occurs in a single event. For example, in a bimolecular step \(A + B \rightarrow C\), the rate law is \( \text{Rate} = k[A][B] \). This direct relationship is unique to elementary steps and is not valid for overall reactions, which may have complex multi-step pathways.
Elementary reactions provide critical clues about the collision requirements for a reaction. For example, termolecular steps are rare because the probability of three particles colliding simultaneously with proper orientation and sufficient energy is extremely low. Observing an apparent termolecular rate law in experimental data often indicates that the process actually occurs through two or more simpler steps.

Multistep Reaction Energy Profiles

A multistep reaction involves two or more elementary steps, each with its own activation energy and transition state. The overall energy profile displays multiple peaks (transition states) and valleys (intermediates), representing the changes in potential energy as the reaction progresses. The highest peak corresponds to the slowest, rate-determining step, which sets the pace for the entire reaction.
Intermediates are species that are formed in one step and consumed in another, appearing in the valleys between peaks on the energy diagram. They are different from transition states because they are relatively more stable and can sometimes be isolated under certain conditions. Identifying intermediates is key to understanding the mechanism and verifying it experimentally.
The activation energies of individual steps help determine which modifications, such as adding a catalyst, will have the greatest impact on the reaction rate. A catalyst typically lowers the activation energy of the rate-determining step, which can be visualized as lowering the height of the tallest peak in the multistep energy profile. This targeted effect allows chemists to optimize reaction pathways for industrial and laboratory processes.

Catalysis

Catalysts speed up reactions by providing an alternative pathway with a lower activation energy, thereby increasing the fraction of molecules that can react at a given temperature. They are not consumed in the reaction and are regenerated at the end of the process. Because they do not alter the thermodynamic properties (ΔH, ΔG) of a reaction, catalysts cannot make a nonspontaneous reaction spontaneous.
Homogeneous catalysts are in the same phase as the reactants, allowing them to interact uniformly and often form temporary intermediates. Heterogeneous catalysts are in a different phase, typically providing an active surface for reactants to adsorb, orient correctly, and react more efficiently. In both cases, catalysts lower the activation energy for one or more steps in the reaction mechanism.
Enzymes are biological catalysts with highly specific active sites that bind reactants (substrates) in precise orientations, dramatically lowering activation energies. Their activity can be affected by temperature, pH, and inhibitors, which can either compete with the substrate or bind to the enzyme in a way that alters its shape. Understanding enzyme kinetics is essential for fields such as biochemistry, pharmacology, and biotechnology.

Common Misconceptions

Many students mistakenly assume that a faster reaction rate means a reaction is more thermodynamically favorable. In reality, kinetics and thermodynamics are separate concepts: kinetics describes how quickly a reaction proceeds, while thermodynamics describes whether it is energetically favorable. A reaction with a large negative ΔG can still be very slow if it has a high activation energy, and a reaction with a positive ΔG can be fast if it is driven by external energy input.
It is a common error to determine reaction order from the coefficients in the balanced overall equation. Reaction order must be determined experimentally or inferred from an elementary step in a valid mechanism. Using stoichiometric coefficients from the overall equation leads to incorrect rate laws and can misrepresent the actual dependence of rate on reactant concentrations.
Some students believe catalysts change the equilibrium position of a reaction, but this is false. Catalysts speed up both the forward and reverse reactions equally, allowing the system to reach equilibrium faster but without altering the final concentrations of reactants and products. The thermodynamic properties of the reaction, such as ΔH and ΔG, remain unchanged in the presence of a catalyst.
Another misconception is that increasing temperature always benefits a reaction’s desired outcome. While higher temperatures generally increase the reaction rate by providing more particles with energy above \(E_a\), they can also change the equilibrium position for endothermic or exothermic reactions, potentially decreasing product yield in some cases. Thus, temperature adjustments must be balanced between kinetic and thermodynamic considerations.
Students often think all collisions between reactant particles result in product formation, but collision theory emphasizes that only a fraction of collisions are effective. Particles must not only have sufficient kinetic energy but also the correct orientation for bonds to break and form. This explains why increasing concentration or temperature affects rates differently depending on molecular structure and reaction pathway.