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Reaction rates

A reaction's rate is not one number stamped on the reaction — it is a slope that changes as the reaction runs, and the different species change at rates locked together by the coefficients.

§1

Rate is a changing slope.

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A reaction rate is how fast a concentration changes with time. As a reaction runs, reactant concentrations fall and product concentrations rise, so the rate is read from the slope of a concentration-versus-time curve.

The instantaneous rate is the slope at a single instant (a tangent); the average rate is the slope over an interval (a secant). Because the curve bends, the rate usually decreases as reactants are used up — it is not one fixed value.

The rates of different species are tied together by stoichiometry. In 2A → B, A disappears twice as fast as B appears, because two A are consumed per B formed.

UNIT 5 TOPIC 5.1 • REACTION RATES RATE BASICS concentration time [A] decreases [B] increases average rate = secant slope instantaneous rate = tangent slope RATE — STOICHIOMETRIC DEFINITION For aA → bB (reactants → products) rate = − 1 a · Δ[A] Δt = + 1 b · Δ[B] Δt reactant [A] ↓ sign flips → rate stays positive product [B] ↑ AVERAGE RATE slope of the secant line between TWO points on the curve over an interval Δt INSTANTANEOUS slope of the tangent line at ONE point on the curve rate at that instant WHAT CHANGES THE RATE Concentration Temperature Surface area Catalyst CED ANCHOR Rate is the slope of a concentration–time graph. It is always reported as a positive quantity. AP Chemistry · Unit 5 · Kinetics
Fig. 5.1.1 Reaction rate is how fast a concentration changes with time. Reactants fall and products rise; the instantaneous rate is the tangent slope at an instant, and the rates of different species are tied together by the reaction's stoichiometry.
§2

Reading rates correctly.

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Distinguish instantaneous from average, and use the coefficients.

  1. Read the instantaneous rate as a tangent. The slope of the tangent line at a point gives the rate at that instant.
  2. Read the average rate as a secant. The slope between two points gives the average rate over that interval — not the instantaneous rate.
  3. Expect the rate to change. The rate usually decreases over time as reactants deplete; it is not a single constant value.
  4. Relate species by stoichiometry. Use the coefficients: a species with a larger coefficient changes proportionally faster.
§3

The pieces you'll meet.

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A few ideas define rate.

rate
Reaction rate
How fast a concentration changes with time — a slope.
instantaneous
Instantaneous rate
The tangent slope at a single instant.
average
Average rate
The secant slope over an interval.
stoich
Stoichiometric link
Coefficients relate how fast each species changes.
decreases
Changing rate
Rate usually decreases as reactants are used up.
tangent
Tangent vs secant
Instantaneous = tangent; average = secant.
§4

Worked example: relate the species rates.

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Question. For N₂ + 3H₂ → 2NH₃, if N₂ is consumed at 0.10 M/s, how fast are H₂ consumed and NH₃ formed?

Hydrogen. The coefficient of H₂ is 3× that of N₂, so H₂ is consumed three times as fast: 0.30 M/s.

Ammonia. The coefficient of NH₃ is 2× that of N₂, so NH₃ forms twice as fast as N₂ is consumed: 0.20 M/s.

Key point. The stoichiometry locks the species' rates together — you cannot read one without the coefficients.

§5

Mistakes that cost real points.

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Pitfall · 01

"A reaction has a single, fixed rate."

The rate changes as the reaction proceeds, usually decreasing as reactants deplete. Reporting one number ignores that the concentration-time curve bends. The instantaneous rate at the start differs from the rate later on.

Fix. Treat rate as a slope that changes over time; specify whether you mean the instantaneous rate (and when) or an average.

Pitfall · 02

"An average rate over an interval is the instantaneous rate."

The average (secant) rate over an interval is generally not equal to the instantaneous (tangent) rate at any single point in it. On a curved graph, the secant slope differs from the tangent slope.

Fix. Use a tangent for the instantaneous rate and a secant for the average; do not swap them.

Pitfall · 03

"All species change concentration at the same rate."

Species change at rates set by their stoichiometric coefficients. In 2A → B, A disappears twice as fast as B forms. Ignoring the coefficients gives the wrong relative rates.

Fix. Scale each species' rate by its coefficient; larger coefficients mean proportionally faster change.

§6

Skill Check.

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