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
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!
Initial Rate Method
Compare experiments where only one concentration changes to find orders
Rate vs Rate Constant
Rate changes with concentration. k only changes with temperature.
Related Tools
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