Reaction Rates

Reaction rate tells you how quickly reactants turn into products. This subtopic defines rate precisely, introduces the rate law that connects rate to reactant concentration, clears up several common points of confusion, and walks through the method of initial rates — the standard technique for determining reaction order and the rate constant from experimental data.

Key Takeaways

• Rate of reaction is the change in concentration of a reactant or product over time. For aA + bB → cC + dD, the rate expression normalizes each species' rate of change by its stoichiometric coefficient.

• The rate law, rate = k[A]^x[B]^y, is an empirical model determined experimentally — k is the rate constant (specific to the reaction and temperature), and x, y are reaction orders.

• The rate expression defines how fast species appear/disappear relative to each other; the rate law describes how rate depends on concentration. They are not the same statement.

• Common pitfalls: reaction order ≠ stoichiometric coefficient; the rate law ≠ the equilibrium constant expression; k is specific to a given temperature, not universal; equilibrium is a dynamic balance reachable at any point, not just an end state.

• The method of initial rates determines reaction order by comparing pairs of experiments where only one concentration changes, then solves for k using the completed rate law.

Defining Reaction Rate

Rate, in general, is a change in some quantity over a unit of time. For a chemical reaction, the rate of reaction is the change in concentration of a reactant or product over a given time period — how much of a reactant is consumed, or how much of a product is formed, in a specific time frame.

For a general reaction:

aA + bB → cC + dD

Note: the transcript for this subtopic describes the rate expression in words but the actual equation appeared only on-screen and wasn't captured in the source text. The expression below is the standard MCAT-level form, independently verified against Chemistry LibreTexts and the UCalgary Chemistry Textbook, supplied here rather than transcript-quoted.

rate = −(1/a)(Δ[A]/Δt) = −(1/b)(Δ[B]/Δt) = (1/c)(Δ[C]/Δt) = (1/d)(Δ[D]/Δt)

Here, Δ[A], Δ[B], Δ[C], and Δ[D] are the changes in concentration of each species over the time interval Δt, and dividing by each species' stoichiometric coefficient (a, b, c, d) keeps the rate consistent no matter which species you happen to track. The negative signs on the reactant terms reflect that reactant concentrations decrease over time, while product concentrations increase.

Determining the Rate Law Experimentally

Reactions don't come with built-in speedometers. To find out how a reaction's rate actually depends on concentration, chemists run experiments that measure the initial rate of a reaction under different starting concentrations of each reactant.

For nearly all forward, irreversible reactions, rate turns out to be proportional to the concentration of each reactant raised to some experimentally determined exponent. This relationship is the rate law:

rate = k[A]^x[B]^y

• k is the rate constant — specific to the reaction at a given temperature.

• [A] and [B] are the concentrations of the reactants.

• x and y are the reaction orders with respect to each reactant, determined experimentally — not assumed.

Rate Expression vs. Rate Law

It's easy to see two different things labeled "rate =" and assume they're the same statement. They're not:

• Rate expression (Δ[reactant or product]/Δt): the basic definition of how fast a reaction proceeds — how quickly a reactant is used up or a product is formed. It relates the appearance and disappearance rates of the different species to one another.

• Rate law (rate = k[A]^x[B]^y): a mathematical model describing how the rate depends on reactant concentration. It incorporates the rate constant k, which is specific to the reaction at a given temperature, along with the experimentally determined reaction orders x and y.

In short: the rate expression is a definition of speed; the rate law is an empirical model of what controls that speed.

Common Kinetics Pitfalls

A few points trip students up consistently:

• Assuming reaction orders match stoichiometric coefficients. They don't have to. Stoichiometric coefficients describe the relative amounts of reactants and products in the balanced equation; reaction orders describe how rate depends on concentration, and must be determined experimentally. For the reaction 2A + B → C, the rate law might turn out to be rate = k[A][B] — first-order in both A and B — even though A's stoichiometric coefficient is 2.

• Mistaking the equilibrium constant expression for the rate law. The equilibrium constant expression, K = [C][D]/[A][B], relates concentrations of reactants and products at equilibrium. The rate law, rate = k[A]^x[B]^y, describes how rate depends on concentration at any point during the reaction and requires experimentally determined orders. The two expressions look superficially similar but answer completely different questions.

• Assuming k is the same under all conditions. The rate constant k is specific to a given reaction and a given temperature — it changes when temperature (or other conditions) change. There's no single universal k for a reaction.

• Assuming equilibrium principles only apply at the end of a reaction. Equilibrium describes a dynamic balance between forward and reverse reaction rates, and that balance can be reached — and is continuously maintained — at any point where those rates become equal, not only as some final terminal state.

The Method of Initial Rates

When you're given experimental data — initial reactant concentrations paired with initial rates of product formation — you can determine reaction order using the method of initial rates:

• Identify a pair of experiments where the concentration of one reactant changes while the concentrations of all other reactants stay constant.

• Analyze the rate change between that pair. Since only one concentration changed, any change in rate is attributable to that one reactant.

• Determine the reaction order for that reactant by comparing the ratio of the rates to the ratio of the concentrations.

• Calculate the rate constant k once all reaction orders are known, by plugging any trial's data back into the rate law and solving.

Worked Example — Determining a Rate Law from Data

Given the following experimental data for a reaction at 300 K:

Order with respect to B — compare Trials 1 and 2, where [A] is held constant at 1.00 M:

Rate₂/Rate₁ = 8.1/2.0 ≈ 4.05 ≈ 2², while [B]₂/[B]₁ = 2.00/1.00 = 2

Since doubling [B] roughly quadruples the rate (2² = 4), the reaction is second-order in B.

Order with respect to A — compare Trials 2 and 3, where [B] is held constant at 2.00 M:

Rate₃/Rate₂ = 15.9/8.1 ≈ 1.96 ≈ 2¹, while [A]₃/[A]₂ = 2.00/1.00 = 2

Since doubling [A] roughly doubles the rate, the reaction is first-order in A.

Rate law: rate = k[A][B]² — third-order overall (1 + 2 = 3).

Calculating k — solving with Trial 1's data:

k = rate/([A][B]²) = 2.0/((1.00)(1.00)²) = 2.0 M⁻²s⁻¹

Checking against Trials 2 and 3 gives k ≈ 2.025 M⁻²s⁻¹ and k ≈ 1.9875 M⁻²s⁻¹ respectively — consistent with Trial 1 within the rounding of the given data, confirming the rate law: rate = k[A][B]², with k ≈ 2.0 M⁻²s⁻¹.

Common MCAT Mistakes

• Reading a stoichiometric coefficient off the balanced equation and using it as a reaction order. Reaction orders must come from experimental rate data — the method of initial rates — never from the balanced equation itself.

• Mixing up the rate law with the equilibrium constant expression. Both look like a ratio of concentrations, but the rate law (rate = k[A]^x[B]^y) governs rate at any point during the reaction, while K = [products]/[reactants] describes concentrations only at equilibrium.

• Treating the rate constant k as fixed for a reaction regardless of temperature. k is specific to both the reaction and the temperature at which it's measured — changing temperature changes k.

• Trying to determine two reaction orders from a single pair of trials. The method of initial rates requires holding all but one reactant's concentration constant between the two trials being compared; varying two concentrations at once makes the order of either one impossible to isolate.

MCAT-Style Concept Check

Question: In a kinetics experiment, tripling the concentration of reactant B while holding [A] constant causes the initial rate to increase ninefold. What is the reaction order with respect to B?

• A) 0

• B) 1

• C) 2

• D) 3

Answer: C

Explanation: The rate increases by a factor of 3ⁿ when [B] is tripled, where n is the order with respect to B. Since the rate increased ninefold and 3² = 9, the reaction is second-order in B.

FAQ

What is the difference between rate expression and rate law?

The rate expression defines how fast reactant or product concentrations change over time, normalized by stoichiometric coefficients. The rate law (rate = k[A]^x[B]^y) is a separate, experimentally determined model of how that rate depends on reactant concentration.

Why aren't reaction orders always equal to stoichiometric coefficients?

Because stoichiometric coefficients describe the ratio of reactants and products in the balanced overall equation, while reaction orders describe how rate depends on concentration — a property of the reaction's actual mechanism, which must be measured experimentally rather than read off the equation.

What is the method of initial rates used for?

It's the standard technique for determining reaction order: compare pairs of experimental trials where only one reactant's concentration changes, use the resulting rate change to find that reactant's order, then solve for the rate constant k.

Is the rate constant k the same at every temperature?

No. The rate constant k is specific to a given reaction at a given temperature — it changes if the temperature changes, which is why kinetics experiments always report k alongside the temperature at which it was measured.