What you'll be able to do: Express a reaction rate correctly from concentration-time data, including the stoichiometric relationships between species.
Thermodynamics says whether a reaction can happen. Kinetics asks how fast. Rate is nothing more exotic than a change in concentration divided by the time it took, but the sign conventions and the coefficients trip people up before any real calculation begins.
These are recommended, not required. You can start this lesson at any time.
Take the concentration of a species at two times and divide the change by the elapsed time. The result has units of molarity per second. Because a reactant is being used up, its concentration change is negative, so a minus sign is placed in front to make the reported rate positive.
rate = -(1/a) * D[A]/Dt = (1/c) * D[C]/Dt
In 2 N₂O₅ → 4 NO₂ + O₂, nitrogen dioxide appears four times as fast as oxygen. Left alone, each species would report a different number. Dividing each rate by its coefficient collapses all of them onto one unique rate of reaction.
2 N₂O₅ → 4 NO₂ + O₂
An average rate is the slope of a straight line joining two points on a concentration-time curve. An instantaneous rate is the slope of the tangent at a single point. Because a typical curve is steepest at the start and flattens later, the average over a long interval always understates the early rate.
The initial rate is the instantaneous rate the moment mixing finishes. It is the cleanest measurement available because no product has accumulated and no reverse reaction is competing. Every rate law determined by the method of initial rates depends on this.
Anything that tracks concentration works: colour change followed with a spectrophotometer, gas volume or pressure for a reaction producing gas, mass loss on a balance, pH for reactions producing or consuming hydrogen ions, or conductivity when ion counts change.
A concentration-time slope belongs to one species. Divide its magnitude by that species's stoichiometric coefficient to report a single reaction rate, and use a minus sign for disappearing reactants. Products have positive slopes. The normalized rate is the same whichever species is monitored in one reaction under the same conditions.
The change in concentration of a species per unit time, reported as a positive quantity in M/s.
Concentration change divided by the time interval, the slope of a chord on the concentration-time curve.
The slope of the tangent to the concentration-time curve at a single instant.
Divide each species rate by its stoichiometric coefficient and every species gives the same value.
As reactants are consumed, collisions become less frequent, so the curve flattens with time.
rate = -(1/a) D[A]/Dt = -(1/b) D[B]/Dt = (1/c) D[C]/Dt
In the reaction 2 N₂O₅ → 4 NO₂ + O₂, [N₂O₅] falls from 0.100 M to 0.080 M in 50.0 s. Find the average rate of reaction and the rate of formation of NO₂.
Try it first: Write the concentration change, then decide where the coefficient 2 goes.
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For N₂ + 3 H₂ → 2 NH₃, hydrogen is consumed at 0.030 M/s. At what rate is ammonia formed?
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A concentration-time curve for a reactant is steep near t = 0 and nearly flat after 200 s. Explain what this shows about the rate.
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For 3 A → 2 B, [A] is falling at 0.060 M/s. Find reaction rate and B formation rate.
Try it first: Normalize A's disappearance by its coefficient.
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Why it's wrong: The minus sign in the definition exists precisely to make the reported rate positive.
Check instead: Apply the minus sign to reactant terms, then quote a positive number.
Why it's wrong: That inflates the rate of the species with the largest coefficient instead of normalising it.
Check instead: Divide each species rate by its own coefficient to obtain the unique rate.
Why it's wrong: The curve is steepest at t = 0, so the whole-run average is always smaller.
Check instead: Use a tangent at t = 0, or the shortest interval available, for an initial rate.
Why it's wrong: Stoichiometry fixes ratios, not the time dependence.
Check instead: Only a zero-order reaction has a constant rate.
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A reaction rate is a change in concentration per unit time, reported as a positive number. Reactant concentrations fall, so their changes carry a minus sign; product concentrations rise, so theirs do not. Dividing each rate by the species coefficient gives one unique rate of reaction that every species agrees on. Average rate uses two points, instantaneous rate is the slope of the tangent at one moment, and the initial rate is the instantaneous rate at t = 0, which is the value used to build rate laws.
Chemistry 2e, OpenStax, Rice University, licensed CC BY 4.0. License