Chemistry: Atoms First 2e · Kinetics
Chemical Reaction Rates
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In 30 seconds
Thermodynamics tells you whether a reaction can happen; kinetics tells you how fast it happens. The Reaction rate Change in concentration of a reactant or product per unit time Full entry → is the change in concentration of a reactant or product per unit time — typically moles per liter per second, M s-1. Because concentrations change continuously during a reaction, chemists distinguish an Average rate Rate over a finite time interval; secant slope Full entry → (over a time interval, the slope of a Secant line Straight line through two points on a curve Full entry → on a concentration-vs-time graph) from an Instantaneous rate Rate at a single instant; tangent slope Full entry → (at one moment, the slope of the Tangent line Line touching a curve at one point with the curve's local slope Full entry →). A balanced equation also imposes a relationship: reactants disappear and products appear in proportion to their stoichiometric coefficients, so the rate of the overall reaction can be written from the rate of change of any species. This topic builds the language and definitions — rate expressions, the minus sign convention, average vs. instantaneous rates, and the Initial rate Instantaneous rate at t = 0 Full entry → — that the rest of the kinetics chapter (rate laws, integrated rate laws, collision theory) depends on.
Why this matters
- Medicine and pharmacy: How fast a drug is absorbed, distributed, and cleared depends on reaction rates; drug degradation in a vial is a chemical reaction with a measurable rate.
- Safety and industry: Explosives must react quickly when triggered but stay stable in storage; industrial reactors are sized using the rates of the reactions inside them.
- Environment: The breakdown of pollutants in air and water follows rate laws; ozone depletion chemistry is kinetics.
- Food and everyday chemistry: Spoilage, ripening, and cooking are all reactions proceeding at measurable rates.
- Exams: Rate expressions and the ability to read a concentration-vs-time graph are foundational — almost every kinetics problem in this chapter builds on them.
The college version
Core Concepts
What a reaction rate is
A reaction rate is a change in concentration divided by the time over which it occurs:
rate = Δ[species]Δt
Because concentrations are typically in Molarity Concentration in moles per liter (mol L-1) Full entry → (mol L-1) and time in seconds, rates carry units of M s-1 (or mol L-1s-1). Rates are always reported as positive numbers: we say a reactant is consumed or a product is formed, not that a concentration is "decreasing" with a negative rate.
The rate expression from a balanced equation
For the general reaction:
aA + bB → cC + dD
the rate of the reaction is the same no matter which species you monitor:
rate = -1aΔ[A]Δt = -1bΔ[B]Δt = 1cΔ[C]Δt = 1dΔ[D]Δt
The minus signs on the reactant terms make those changes positive (reactant concentrations fall, so Δ[A] < 0); the 1/coefficient factors make every species report the same numerical rate. Without them, H2 would appear to react three times faster than N2 in ammonia synthesis even though they are part of the same reaction.
Average rate vs. instantaneous rate
An average rate is measured over a finite interval: rate = |Δ[A]/Δt| between two times. On a plot of concentration vs. time, it is the slope of the secant line connecting the two points. An instantaneous rate is the slope of the tangent line at a single time — the limit of the average rate as the interval shrinks to zero. The initial rate is the instantaneous rate at t = 0, measured when concentrations are still at their starting values; it is the cleanest measurement because no products have accumulated to interfere, and it is the value used to determine rate laws.
Why rates change as a reaction proceeds
Reactant concentrations fall as the reaction runs, so collisions between reactant particles become less frequent and the rate decreases with time. A concentration-vs-time curve therefore starts steep and flattens as it approaches the equilibrium or completion concentration — the slope of the tangent (the instantaneous rate) decreases continuously. The rate you report must always name its time (or explicitly be the initial rate), because the same reaction has many different instantaneous rates over its lifetime.
Common Confusions
| Do Not Confuse | With | Difference |
|---|---|---|
| Rate of reaction | Rate of change of one species | Coefficients matter: NH3 forms at 0.080 M s⁻¹ while the reaction rate is 0.040 M s⁻¹ in Example 1 |
| A negative Δ[reactant] | A negative rate | Δ[A] is negative for reactants, but the reported rate is positive; the minus sign in the formula fixes the sign |
| Average rate | Instantaneous rate | Average is a secant over an interval; instantaneous is a tangent at one point; they agree only as the interval approaches zero |
| Rate | Rate constant k | Rate changes as concentrations change; k is constant at fixed temperature (topic: Rate Laws) |
| Speed of reaction from coefficients | Rate measured from data | Coefficients set the ratios between species' rates; they do not by themselves tell you the numerical speed |
| Fast reaction | Spontaneous reaction | Thermodynamics (spontaneity) and kinetics (speed) are independent: a spontaneous reaction can be extremely slow (diamond → graphite) |
Eli explains
The same idea, in plain words
Explain it like I’m 10
A reaction rate is just a speed for chemistry — how much of a substance changes each second, like counting how many cookies disappear from the jar per minute. Early on, the jar is full and cookies vanish fast; later, fewer cookies remain and they vanish more slowly. The "rate" at any moment is how fast the pile is changing right then, and if you watch two different ingredients, their changes follow the recipe's numbers.
Worked example
Example 1: Relating rates through the balanced equation
Ammonia forms from nitrogen and hydrogen:
N2 + 3H2 → 2NH3
If hydrogen is consumed at 0.12 M s-1 (Δ[H2]/Δt = -0.12 M s-1), find the rate of the reaction, the rate of N2 consumption, and the rate of NH3 formation.
Step 1 — Write the rate expression:
rate = -Δ[N2]Δt = -13Δ[H2]Δt = 12Δ[NH3]Δt
Step 2 — Compute the reaction rate from the hydrogen data:
rate = -13(-0.12 M s-1) = +0.040 M s-1
Step 3 — Solve for the other species:
-Δ[N2]Δt = 0.040 M s-1 ⇒ Δ[N2]Δt = -0.040 M s-1
12Δ[NH3]Δt = 0.040 M s-1 ⇒ Δ[NH3]Δt = 0.080 M s-1
Check: N2 is consumed one-third as fast as H2 (coefficients 1 vs. 3) and NH3 forms twice as fast as N2 is consumed (coefficients 2 vs. 1) — the numbers match the stoichiometry.
Example 2: Average rate from two data points
A reactant A is at 0.500 M at t = 0 and 0.350 M at t = 120 s. What is the average rate of consumption of A over this interval?
Step 1 — Write the average-rate formula:
average rate = -Δ[A]Δt
Step 2 — Substitute the data:
average rate = -(0.350 - 0.500) M120 s = 0.150 M120 s = 1.25 × 10-3 M s-1
Dimensional check: M/s = M s-1. The minus sign converts the falling concentration into a positive rate. Note this is an average over two minutes — the instantaneous rate at t = 0 would be larger, because the reaction is fastest at the start.
Example 3: Estimating the initial rate from early data
For the same reaction, [A] = 0.500 M at t = 0 and [A] = 0.480 M at t = 5.0 s. Estimate the initial rate.
Step 1 — Use a short early interval as an approximation of the tangent slope:
initial rate ≈ -(0.480 - 0.500) M5.0 s = 0.020 M5.0 s = 4.0 × 10-3 M s-1
This short-interval estimate (about 3× the two-minute average) correctly captures that the reaction is fastest near t = 0. On a graph, this is the slope of the tangent drawn at the origin, while Example 2's value is the slope of the secant between two later points.
Key takeaways
- Rate = change in concentration per unit time; units M s-1.
- Reactants get a minus sign (their concentrations decrease); products get a plus sign.
- Divide each species' rate by its stoichiometric coefficient so all species report one reaction rate.
- Average rate = secant slope over an interval; instantaneous rate = tangent slope at a point; initial rate = instantaneous rate at t = 0.
- Rates slow over time because reactant concentrations (and collision frequencies) fall.
- The initial rate is measured at t = 0 and is the standard tool for determining rate laws.
Check yourself
6 review questions from the chapter. Try each one, then open the answer.
Write the Rate expression The stoichiometrically balanced way of writing a reaction's rate Full entry → for 2NO + O2 → 2NO2 in terms of all three species.
Show answer
rate = -12Δ[NO]Δt = -Δ[O2]Δt = 12Δ[NO2]Δt.
If O2 is consumed at 0.050 M s-1 in the reaction above, how fast does NO2 form?
Show answer
0.100 M s-1 — twice the O2 rate because the coefficient ratio is 2:1.
What is the difference between a secant-line slope and a tangent-line slope on a concentration-vs-time graph?
Show answer
A secant connects two points and gives the average rate over the interval; a tangent touches at one point and gives the instantaneous rate there.
Why does a reaction's instantaneous rate decrease over time?
Show answer
Reactant concentrations fall as the reaction proceeds, so collisions between reactant particles become less frequent and the rate slows.
A reactant falls from 0.800 M to 0.600 M in 100 s. What is the average rate?
Show answer
rate = -(0.600 - 0.800)/100 = 2.0 × 10-3 M s-1.
Why is the initial rate preferred for measuring reaction orders?
Show answer
At t = 0 the concentrations are the known starting values and no products have built up to interfere, so the measured rate can be directly compared with initial concentrations to determine orders.
Study tools & related lessonsKey vocabulary · Related
Key vocabulary
- Reaction rate
- Change in concentration of a reactant or product per unit time
- Average rate
- Rate over a finite time interval; secant slope
- Instantaneous rate
- Rate at a single instant; tangent slope
- Initial rate
- Instantaneous rate at t = 0
- Rate expression
- The stoichiometrically balanced way of writing a reaction's rate
- Molarity
- Concentration in moles per liter (mol L-1)
- Secant line
- Straight line through two points on a curve
- Tangent line
- Line touching a curve at one point with the curve's local slope
Sources & references
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