Reaction Rate Formula

Quantifying how fast reactant concentrations change over time

Rate Definitions

Average Rate

Rate = -Δ[A] / Δt

Change in concentration over time interval

Instantaneous Rate

Rate = -d[A] / dt

Rate at specific moment (tangent slope)

For Reaction: aA + bB → cC + dD

Rate = -(1/a)d[A]/dt = -(1/b)d[B]/dt = (1/c)d[C]/dt = (1/d)d[D]/dt

Rate Law

Rate = k[A]ᵐ[B]ⁿ

k (Rate Constant)

Temperature-dependent constant

Units depend on overall order

m, n (Reaction Orders)

Determined experimentally

Usually 0, 1, or 2

Overall Order

Sum: m + n

Affects rate constant units

Rate Constant Units by Order

Zero order (0): M/s or mol/(L·s)

First order (1): s⁻¹ or 1/s

Second order (2): M⁻¹s⁻¹ or L/(mol·s)

Third order (3): M⁻²s⁻¹ or L²/(mol²·s)

Reaction Order Effects

Zero Order (m = 0)

Rate = k (independent of [A])

Doubling [A] has NO effect on rate

First Order (m = 1)

Rate = k[A]

Doubling [A] doubles the rate

Second Order (m = 2)

Rate = k[A]²

Doubling [A] quadruples the rate (2² = 4×)

Worked Examples

Example 1: Determining Rate from Data

Problem: [A] changes from 0.100 M to 0.085 M in 30 seconds. Find average rate.

Solution:

Δ[A] = 0.085 - 0.100 = -0.015 M

Δt = 30 s

Rate = -Δ[A]/Δt = -(-0.015)/30

Rate = 5.0 × 10⁻⁴ M/s

Example 2: Using Rate Law

Problem: Rate = k[A]²[B], k = 0.50 M⁻²s⁻¹. Find rate when [A] = 0.20 M, [B] = 0.30 M.

Solution:

Rate = 0.50 × (0.20)² × (0.30)

Rate = 0.50 × 0.04 × 0.30

Rate = 6.0 × 10⁻³ M/s

Example 3: Effect of Concentration Change

Problem: Rate = k[A]²[B]. How does rate change if [A] triples and [B] doubles?

Solution:

Original: Rate₁ = k[A]²[B]

New: Rate₂ = k(3[A])²(2[B]) = k × 9[A]² × 2[B] = 18k[A]²[B]

Rate₂/Rate₁ = 18

Rate increases by factor of 18

Common Mistakes

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Confusing Order with Stoichiometry

For 2A → B, rate law is NOT necessarily Rate = k[A]². Orders are determined experimentally!

⚠️

Wrong Sign for Reactants

Rate = -Δ[A]/Δt (negative because [A] decreases). Make rate positive!

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Initial Rate Method

Compare experiments where only one concentration changes to find orders

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Rate vs Rate Constant

Rate changes with concentration. k only changes with temperature.