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Chemistry 2e · Kinetics

Chemical Reaction Rates

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On this page 9 sections
  1. In 30 seconds
  2. Why this matters
  3. The college version
  4. Eli explains
  5. Worked example
  6. Key takeaway
  7. Check yourself
  8. Study tools
  9. Sources & references

In 30 seconds

Chemical kinetics asks not whether a reaction is favorable, but how quickly it occurs. A is the change in amount or concentration of a reactant or product during a stated time interval.

For solution reactions, chemists usually track molar concentration. Reactant concentrations fall, product concentrations rise, and rate units are concentration per time, commonly mol L⁻¹ s⁻¹ (M s⁻¹). By convention rates are positive, so a minus sign is placed before a reactant’s concentration change.

Why this matters

Rates help chemists decide whether a process is useful, safe, or controllable. Drug stability, industrial production, and pollutant modeling all depend on them. Rate data also underpin later kinetic ideas: rate laws, temperature effects, and reaction mechanisms.

The college version

Core Concepts

Rate is a change divided by a time interval

For a species A, its of concentration change over a time interval is Δ[A]/Δt. If A is consumed, the positive average rate of disappearance is:

-Δ[A]Δt

If P is produced, its positive average rate of appearance is:

Δ[P]Δt

The word average is essential. It describes the slope of a line joining two points on a concentration-versus-time graph. A reaction often slows as reactants are depleted, so this one number does not necessarily describe what happens at every moment in the interval.

Instantaneous rate comes from the graph at one moment

The is the rate at one particular time: the slope of the tangent line to a concentration-time curve. In calculus notation, the disappearance rate of A is -d[A]/dt. A steep curve has a large rate magnitude; a nearly horizontal curve changes little per second. Estimate it from a tangent line or very close data points.

Concentrations do not always change at equal numerical rates. Consider:

2N2O5 → 4NO2 + O2

Every 2 moles of N₂O₅ consumed yield 4 moles of NO₂ and 1 mole of O₂. In a fixed-volume system, concentration changes reflect those coefficients. Define one reaction rate by dividing each species rate by its coefficient:

rate=-12Δ[N2O5]Δt =14Δ[NO2]Δt =Δ[O2]Δt

This normalization makes every correct description agree. Use coefficients from the balanced equation, not formula subscripts. Concentration may be measured indirectly through color, gas pressure, turbidity, or pH when its quantitative relation to a species is known.

How It Works / Step-by-Step Process

  1. Write the balanced chemical equation and identify the measured species.
  2. Record its concentration (or a measurement calibrated to concentration) at two stated times.
  3. Calculate Δ[species] = [species]final-[species]initial, then divide by Δt.
  4. Add a negative sign for a reactant if reporting a positive disappearance rate.
  5. If the question asks for the reaction rate or another species’ rate, use the balanced coefficients to convert it and retain M s⁻¹ units.

Worked Example: Relating Appearance and Disappearance Rates

For the decomposition of hydrogen peroxide,

2H2O2(aq) → 2H2O(l) + O2(g)

suppose oxygen gas appears at 1.20 × 10-4 M s-1. What is the of H₂O₂?

Write the relationship first. Each species rate is divided by its coefficient, and all are equal:

rate = -12Δ[H2O2]Δt = Δ[O2]Δt

Substitute the known appearance rate. Since the O₂ coefficient is 1, the reaction rate equals 1.20 × 10-4 M s-1. Now solve for the H₂O₂ disappearance rate:

-Δ[H2O2]Δt = 2 × (1.20 × 10-4 M s-1) = 2.40 × 10-4 M s-1

H₂O₂ disappears twice as fast as O₂ appears because two moles of H₂O₂ are consumed for each mole of O₂ formed. The units check: multiplying M s-1 by the dimensionless coefficient ratio (2 mol H₂O₂ / 1 mol O₂) leaves M s-1.

Common Confusions

Common confusionCorrect understanding
“A negative reactant slope means the reaction rate is negative.”It means reactant concentration is falling. The conventional rate of disappearance and the reaction rate are reported as positive.
“All species have the same concentration change per second.”Their changes are proportional to balanced coefficients; only coefficient-normalized expressions are equal.
“A fast reaction must release much energy.”Speed and energy change are different properties. A thermodynamically favorable reaction can still be very slow.
“One average rate describes the entire reaction.”It only describes the selected interval. Use instantaneous rates when behavior at a particular time matters.
Eli, the EliExplains learning guide

Eli explains

The same idea, in plain words

Explain it like I’m 10

A reaction rate tells how fast ingredients are being used up or new substances are being made. If a baking-soda reaction makes bubbles quickly, its gas-making rate is high; if it makes only a few bubbles each minute, the rate is low. The recipe numbers matter: if one reaction event makes two bubbles’ worth of one product for every one of another, their amounts cannot increase at the same speed.

Worked example

For 2N2O5 → 4NO2 + O2, suppose [N₂O₅] drops from 0.100 M to 0.070 M in 20.0 s. Its concentration change is -0.030 M, so its average disappearance rate is 1.5 × 10-3 M s-1.

This is not yet the normalized reaction rate: divide by N₂O₅'s coefficient, 2, to obtain 7.5 × 10-4 M s-1. O₂ has coefficient 1, so it appears at that rate. NO₂ has coefficient 4 and appears at 3.0 × 10-3 M s-1, twice the N₂O₅ disappearance rate, as the equation requires.

Key takeaways

  • Rate means change per unit time, not simply how much product is present.
  • Reactant concentration decreases, so include a minus sign when reporting its positive disappearance rate.
  • Average rate uses two times; instantaneous rate is the slope at one time.
  • Use stoichiometric coefficients to convert an individual species rate into the common reaction rate.
  • Concentration-time data describe kinetics; they do not by themselves reveal the molecular pathway.

Check yourself

5 review questions from the chapter. Try each one, then open the answer.

  1. What does the unit M s⁻¹ communicate about a reaction rate?

    Show answer

    It reports how many moles per liter change each second.

  2. Why is a minus sign used in -Δ[A]/Δt for a reactant A?

    Show answer

    Because Δ[A] is negative as A is consumed; the minus sign makes the disappearance rate positive.

  3. For 3A → 2B, if A disappears at 0.060 M s-1, what are the reaction rate and B appearance rate?

    Show answer

    The reaction rate is (1/3)(0.060)=0.020 M s-1. B appears at 2(0.020)=0.040 M s-1.

  4. How can you distinguish an average rate from an instantaneous rate on a graph?

    Show answer

    Average rate is a secant-line slope between two times; instantaneous rate is the tangent-line slope at one time.

  5. Name one measurement other than concentration that can be used to follow a reaction and explain what must be known.

    Show answer

    Gas pressure or volume, color intensity, turbidity, or pH may work, provided it has a known quantitative relationship to the amount of a reacting species.

Keep learning

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Study tools & related lessonsKey vocabulary · Related

Key vocabulary

chemical reaction rate
The change in concentration of a reactant or product per unit time, expressed for a specified reaction or species
average rate
The concentration change over a finite interval divided by the length of that interval
instantaneous rate
The rate at one particular moment; the tangent slope of a concentration-time graph
rate of disappearance
A positive expression for reactant consumption, -Δ[reactant]/Δt
rate of appearance
A positive expression for product formation, Δ[product]/Δt
stoichiometric coefficient
The balanced-equation number that gives the mole ratio among reacting species

Sources & references

  1. openstax.org — Chemistry 2e

This lesson was adapted from the open educational references above; their licenses and attributions are preserved. See Copyright & Licensing.

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