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Arrhenius equation calculator

Evaluate molar or molecular Arrhenius forms, solve kinetic parameters in linear or exponential notation, and draw an optional Arrhenius plot.

Calculator

Rate constant k
1.000000
Natural logarithm of k
0.000000
Frequency factor A
2.718282
Natural logarithm of A
1.000000
Activation energy (J/mol)
2,494.338785
Activation energy per molecule (J)
0.000000000000000000004142
Temperature
300
Reciprocal temperature (1/K)
0.003333
Arrhenius slope (K)
-300.000000
Arrhenius plot Line chart. The data table follows. 0 -0.2 0.001 -0.1143 0.002 -0.0286 0.003 0.0571 0.004 0.1429 Reciprocal temperature (1/K) Natural logarithm of k
Arrhenius plot data
SeriesReciprocal temperature (1/K)Natural logarithm of k
Arrhenius model0.0028571428571428570.1428571428571428
Arrhenius model0.0028985507246376810.13043478260869557
Arrhenius model0.00294117647058823530.11764705882352933
Arrhenius model0.00298507462686567170.10447761194029848
Arrhenius model0.00303030303030303030.09090909090909083
Arrhenius model0.0030769230769230770.07692307692307687
Arrhenius model0.0031250.0625
Arrhenius model0.00317460317460317460.04761904761904756
Arrhenius model0.00322580645161290320.032258064516129004
Arrhenius model0.0032786885245901640.016393442622950727
Arrhenius model0.00333333333333333350
Arrhenius model0.003389830508474576-0.016949152542372836
Arrhenius model0.0034482758620689655-0.034482758620689724
Arrhenius model0.0035087719298245615-0.05263157894736836
Arrhenius model0.0035714285714285713-0.0714285714285714
Arrhenius model0.0036363636363636364-0.09090909090909105
Arrhenius model0.003703703703703704-0.11111111111111116
Arrhenius model0.0037735849056603774-0.13207547169811318
Arrhenius model0.0038461538461538464-0.15384615384615397
Arrhenius model0.00392156862745098-0.17647058823529416
Arrhenius model0.004-0.19999999999999996

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How this calculator works

Choose a per-mole activation energy with the gas constant or a per-molecule energy with the Boltzmann constant. Exponential forms use A, k and absolute temperature. Logarithmic forms use natural logarithms and reciprocal kelvins; their straight-line slope is -Ea/R or -E/kB. The plot assumes constant A and activation energy across your range. Values too large or small to represent as positive finite A and k are rejected.

Formula

k = A exp(-Ea/RT) = A exp(-E/kBT). ln(k) = ln(A) - (Ea/R)(1/T). R = NA kB; kB = 1.380649 x 10^-23 J/K.

Worked example

At 300 K with A = e and Ea = 2494.338785 J/mol, k = 1. If Ea = 0 and A = 10, k stays 10 at every positive temperature and the Arrhenius plot is horizontal.

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Frequently asked questions

What units does k use?

Use the rate-constant units appropriate to the reaction order; A must use the same units.

Are log and ln interchangeable?

This page uses natural logarithms. Base-10 logarithms would require a factor ln(10).

Why limit the plot size?

Up to 500 points fit the chart engine. Increase the temperature step for a wider range.

Sources

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