Rate Constant Calculator
Compute rate constant using validated scientific equations. See step-by-step derivations, unit analysis, and reference values.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
k = A x exp(-Ea / RT)
The rate constant k equals the pre-exponential factor A multiplied by the exponential of negative activation energy divided by RT. R is the gas constant (8.314 J/mol/K) and T is temperature in Kelvin.
Worked Examples
Example 1: First-Order Decomposition
Problem:Calculate k for a reaction with Ea = 75 kJ/mol, A = 1e13 s-1, at 350 K.
Solution:k = 1e13 x exp(-75000 / (8.314 x 350))\nk = 1e13 x exp(-25.75)\nk = 1e13 x 6.54e-12\nk = 0.0654 s-1\nHalf-life = ln(2)/k = 10.6 s
Result:k = 6.54e-2 s-1, half-life = 10.6 s
Example 2: Two-Temperature Comparison
Problem:k1 = 0.01 s-1 at 300 K. Find k2 at 350 K given Ea = 80 kJ/mol.
Solution:ln(k2/k1) = (80000/8.314)(1/300 - 1/350)\nln(k2/k1) = 9621.8 x 4.76e-4 = 4.582\nk2/k1 = 97.7\nk2 = 0.977 s-1
Result:k2 = 0.977 s-1 (97.7x faster)
Frequently Asked Questions
What is the rate constant in chemistry?
The rate constant (k) is a proportionality factor in a rate law that relates the reaction rate to the concentrations of reactants. For a first-order reaction, rate = k[A], where [A] is the concentration. The rate constant depends on temperature and activation energy but not on concentration. Its units vary by reaction order: s-1 for first order, L/(mol*s) for second order. A larger rate constant means a faster reaction. The rate constant is a fundamental property of each reaction at a given temperature.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy