Activation Energy from Two Temperatures

Calculate activation energy (E_a) using the Arrhenius equation with two temperature-rate constant pairs. For students, researchers, and technicians. Supports K/°C/°F, multiple rate units, and runs entirely offline.

Educational only. Follow your lab SOPs and SDS.

Point 1

Temperature 1

Rate Constant k₁

Enter scientific notation: 1.2e-3

Point 2

Temperature 2

Rate Constant k₂

Precision:

Results

Activation Energy (E_a)

Pre-exponential Factor (A)

Same units as k

Intermediate Values

ln(k₂/k₁): --
1/T₁ - 1/T₂ (K⁻¹): --
Gas constant R used: 8.314462618 J/(mol·K)

Practical Usage and Examples

Activation energy quantifies the temperature sensitivity of a reaction rate. This tool is essential for extrapolating rates to other temperatures, designing thermal processes, and analyzing kinetic data from two-point experiments.

Step‑by‑Step

Enter two measured rate constants (k) and their corresponding temperatures.
Ensure temperatures are in the same unit (default Kelvin).
Click "Calculate E_a". The tool computes ln(k₂/k₁) and 1/T₁ – 1/T₂.
Result shows E_a in your chosen unit and the pre‑exponential factor A.
Use the swap button to reverse points and verify consistency.

Example Calculations

T₁ (K)	k₁ (s⁻¹)	T₂ (K)	k₂ (s⁻¹)	E_a (kJ/mol)	A (s⁻¹)
298	1.2e-3	310	4.8e-3	~86.2	~1.3e10
400	0.05	450	0.25	~47.7	~2.1e5

Common Mistakes Checklist

Using Celsius/Fahrenheit instead of Kelvin in the Arrhenius equation.
Not using consistent units for k₁ and k₂.
Assuming linearity over very wide temperature ranges.
Ignoring experimental error in two‑point estimates.
Forgetting that A has the same units as k.

Temperature Sensitivity Explorer

Adjust the temperature below to see how the rate constant changes with your calculated E_a.

Explore Temperature

250 K 350 K 500 K

Predicted k at T

Fold increase from T₁

Frequently Asked Questions

How accurate is the two‑point method?

It assumes perfect Arrhenius behavior. Real data often have experimental error; use multiple points for better accuracy.

Can I use different units for k₁ and k₂?

No—k₁ and k₂ must be in the same units because only their ratio matters. The tool does not convert rate units.

What if my temperatures are too close?

Small temperature differences amplify errors in E_a. A ΔT of at least 10–15 K is recommended.

Is this valid for non‑elementary reactions?

The apparent E_a may be composite. Interpret results cautiously for complex mechanisms.

Formulas & Assumptions

Arrhenius equation: k = A·exp(–E_a/(R·T))
Two‑point form: E_a = R · ln(k₂/k₁) / (1/T₁ – 1/T₂)
R = 8.314462618 J·mol⁻¹·K⁻¹ (exact CODATA value)
Temperatures are converted to Kelvin internally: K = °C + 273.15; K = (°F + 459.67) × 5/9
All calculations use double‑precision floating point; results rounded to selected decimal places.
Assumes constant E_a over the temperature range.

For informational and educational purposes only. Estimates depend on your inputs and simplifying assumptions. This tool does not replace professional judgment, lab SOPs, or safety procedures. Always follow SDS guidance and institutional policies.

Sources: Common chemistry constants (R, N_A); Arrhenius equation fundamentals; Standard unit conversions and lab measurement best practices; General analytical chemistry and uncertainty concepts.

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Activation Energy from Two Temperatures

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