Equation and purpose
Temperature dependence of rate constant.
\[k = A e^{-E_a/(RT)}\]
Temperature dependence of rate constant.
REARRANGEMENTS
$ln k = ln A - E_a/RT$
Dimensional check: dimensionless exponent ✓
Variables and units
| Symbol | Quantity | Unit | Notes |
|---|---|---|---|
| k | k | — | — |
| A | A | — | — |
| E_a | E_a | — | — |
| R | R | — | — |
| T | T | — | — |
Conditions and limitations
Two-point form often: ln(k2/k1)=-Ea/R(1/T2-1/T1).
Worked example
Use two T points to solve Ea.
Arrhenius Equation
Temperature dependence of rate constant.
Equation
Inline: $k = A e^{-E_a/(RT)}$$
Variables
| Symbol | Quantity | Unit | Notes |
|---|---|---|---|
| rate constant | varies | — | |
| pre-exponential | same as k | — | |
| activation energy | J·mol⁻¹ | — | |
| gas constant | J·mol⁻¹·K⁻¹ | — | |
| temperature | K | — |
Conditions and limitations
Two-point form often: ln(k2/k1)=-Ea/R(1/T2-1/T1).
Rearrangements
Dimensional check: dimensionless exponent ✓
Worked example
Use two T points to solve Ea.
Steps: write equation → substitute with units → check dimensional consistency → report with correct significant figures.
Common errors
- Using Celsius for T
Related resources
- chemical-kinetics topic
- Calculators — linked only when a real calculator implements this formula.
- Constants — sourced constants with version when values are required.
Sources
- NIST Physical Constants 2022 — CODATA.
Reviewed 2026-08-21 by Editorial Team; due 2027-08-21.
Common errors
- Using Celsius for T
RELATED FORMULAS
C
Chemistry Fundamentals Editorial TeamAuthor
E
Editorial Review BoardReviewer
Editorial Team — transparent review placeholder
Reviewed August 21, 2026
SOURCES
- [nist-2022]NIST Physical Constants 2022 (2022). NISThttps://physics.nist.gov/constants