AP Chemistry: Chemical Kinetics

Chemical kinetics is the study of how fast chemical reactions occur and why their rates change. In AP Chemistry, kinetics connects observable lab data to molecular-level events: collisions, energy barriers, and multi-step mechanisms. Mastering this unit means you can interpret rate experiments, write and use rate laws, and explain how activation energy and catalysis shape reaction speed.

What a Reaction Rate Really Measures

A reaction rate describes how quickly reactants are consumed or products form. It is usually expressed as a change in concentration per unit time, such as ${\text{molcdotpL}}^{-1}{\text{s}}^{-1}$.

For a general reaction $$aA+bB\to cC+dD$$ the rate can be written consistently using stoichiometry: $$\text{Rate}=-\frac{1}{a}\frac{\Delta [A]}{\Delta t}=-\frac{1}{b}\frac{\Delta [B]}{\Delta t}=\frac{1}{c}\frac{\Delta [C]}{\Delta t}=\frac{1}{d}\frac{\Delta [D]}{\Delta t}$$

The negative signs for reactants reflect that their concentrations decrease. This definition matters because experimental data may track only one species, and you must convert it into the reaction rate using coefficients.

Average vs. Instantaneous Rate

• Average rate is computed over a time interval using a secant line on a concentration vs. time graph.
• Instantaneous rate is the slope of the tangent line at a specific moment.

Many AP problems treat rates as “initial rates,” which are effectively instantaneous rates at $t\approx 0$ and are especially useful for determining rate laws.

The Rate Law: An Experimental Relationship

A rate law relates reaction rate to reactant concentrations: $$\text{Rate}=k[A{]}^m[B{]}^n$$ Here, $k$ is the rate constant, and the exponents $m$ and $n$ are the reaction orders with respect to each reactant. The overall order is $m+n$.

Two crucial rules for AP Chemistry:

1. Rate laws are determined experimentally, not from the balanced overall equation.
2. Exponents in a rate law describe how the rate changes when a concentration changes, holding other conditions constant.

Determining a Rate Law Using the Method of Initial Rates

In the method of initial rates, you compare experiments where initial concentrations differ but other conditions (temperature, catalyst, solvent) are constant.

Example logic (no invented data required):

• If doubling $[A]$ while keeping $[B]$ constant doubles the rate, then the reaction is first order in __MATH_INLINE_13__: $m=1$.
• If doubling $[B]$ causes the rate to quadruple, then it is second order in __MATH_INLINE_16__: $n=2$.
• If changing $[A]$ does not change the rate, it is zero order in __MATH_INLINE_19__: $m=0$.

Once the orders are known, plug a single experiment into the rate law to solve for $k$.

Units of the Rate Constant

Because rate has units of concentration over time, the units of $k$ depend on overall order. For an overall order of:

• 0: $k$ has units ${\text{Mcdotps}}^{-1}$
• 1: $k$ has units ${\text{s}}^{-1}$
• 2: $k$ has units ${\text{M}}^{-1}{\text{s}}^{-1}$

A quick check of units is a practical way to catch algebra mistakes on free-response questions.

Integrated Rate Laws and Reaction Order (Big Picture)

AP Chemistry often emphasizes identifying reaction order from concentration vs. time behavior.

Common integrated rate law patterns:

• Zero order: $[A{]}_t=[A{]}_0-kt$

A plot of $[A]$ vs. $t$ is linear.

• First order: $\ln [A{]}_t=\ln [A{]}_0-kt$

A plot of $\ln [A]$ vs. $t$ is linear. First-order reactions also have a constant half-life: $$t_{1/2}=\frac{0.693}{k}$$

• Second order: $\frac{1}{[A{]}_t}=\frac{1}{[A{]}_0}+kt$

A plot of $\frac{1}{[A]}$ vs. $t$ is linear.

In practice, the exam may give you a graph or a table and ask which transformation produces a straight line, or it may ask you to interpret a constant half-life as evidence of first-order kinetics.

Reaction Mechanisms and the Rate-Determining Step

A reaction mechanism is a sequence of elementary steps that add up to the overall reaction. Kinetics becomes especially powerful here because mechanisms must be consistent with experimentally determined rate laws.

Elementary Steps vs. Overall Reactions

An elementary step occurs in a single molecular event. Its rate law can be written directly from its molecularity:

• Unimolecular: $\text{Rate}=k[A]$
• Bimolecular: $\text{Rate}=k[A][B]$ or $k[A{]}^2$
• Termolecular (rare): $\text{Rate}=k[A][B][C]$

In contrast, the overall reaction might be balanced correctly but still provide no direct information about the rate law.

The Rate-Determining Step

Many mechanisms contain one slow step that limits the overall rate. If the slow step is elementary, its rate law often matches the experimentally observed rate law, sometimes after substituting for intermediates.

Intermediates are produced in one step and consumed in another; they do not appear in the net equation. A valid mechanism must:

• Sum to the overall balanced equation
• Include only physically reasonable elementary steps
• Produce a rate law consistent with experiment

This is why a proposed mechanism is not accepted just because it adds up correctly. The kinetics has to agree.

Activation Energy and the Energy Profile

Reaction rate is strongly influenced by activation energy, $E_a$, the energy barrier that reactants must overcome to form products. Even exothermic reactions can be slow if their activation barriers are large.

Collision Theory in Plain Terms

For a reaction to occur, collisions must be:

• Energetic enough (meeting or exceeding $E_a$)
• Oriented properly (the geometry matters)

Increasing temperature increases the fraction of collisions with sufficient energy, which is why many reactions speed up dramatically as temperature rises.

The Arrhenius Equation

The Arrhenius equation connects $k$ to temperature: $$k=A{e}^{-E_a/(RT)}$$ where $A$ is the frequency factor, $R$ is the gas constant, and $T$ is temperature in kelvin.

A key interpretation: increasing $T$ makes the exponent less negative, so $k$ increases. Because of the exponential relationship, even modest temperature changes can noticeably affect reaction rate.

Catalysis: Speeding Up Without Changing the Destination

A catalyst increases reaction rate without being consumed in the net reaction. Catalysts work by providing an alternative pathway with a lower activation energy.

Important AP takeaways:

• A catalyst changes the mechanism, not the overall thermodynamics.
• Catalysts do not change $\Delta G$, $\Delta H$, or the equilibrium constant $K$.
• Catalysts increase the rates of both the forward and reverse reactions, helping the system reach equilibrium faster but not shifting the equilibrium position.

Homogeneous vs. Heterogeneous Catalysis

• Homogeneous catalysis: catalyst is in the same phase as reactants (often all aqueous). Mechanisms commonly involve formation of intermediate complexes.
• Heterogeneous catalysis: catalyst is in a different phase (often a solid surface). Reactants adsorb onto the surface, react, then desorb as products.

Surface catalysis explains why powdered solids can be more effective catalysts than larger chunks: more surface area means more active sites.

Practical Strategy for AP Kinetics Questions

1. Start with what is measured: concentration, pressure, color change, gas volume, or time to reach a threshold.
2. Use comparisons cleanly: change one concentration at a time when using initial rates.
3. Check consistency: mechanism must match both the balanced overall reaction and the experimental rate law.
4. Connect temperature to __MATH_INLINE_53__: if $T$ increases, $k$ increases; the rate typically increases unless concentrations change in a compensating way.
5. Remember what catalysts do not change: equilibrium constants and thermodynamic favorability.

Chemical kinetics is where AP Chemistry moves from “what happens” to “how it happens.” When you can translate data into a rate law and then judge whether a mechanism makes sense, you are thinking like a chemist, not just solving a worksheet.