Rate Law Calculator
Compute rate law using validated scientific equations. See step-by-step derivations, unit analysis, and reference values.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
rate = k [A]^m [B]^n
The rate law relates reaction rate to the rate constant k and reactant concentrations [A] and [B] raised to their respective orders m and n. The overall reaction order is m + n. The rate constant k incorporates temperature dependence via the Arrhenius equation.
Worked Examples
Example 1: First Order Reaction
Problem:A first-order reaction has k = 0.05 per second and [A] = 0.1 M. Find the reaction rate.
Solution:rate = k[A]^1 = 0.05 * (0.1)^1 = 0.005 M/s\nHalf-life = ln(2) / 0.05 = 13.86 s
Result:Rate = 0.005 M/s, Half-life = 13.86 s
Example 2: Second Order Two-Reactant Reaction
Problem:For rate = k[A]^1[B]^1, k = 2.5 L/(mol*s), [A] = 0.2 M, [B] = 0.3 M.
Solution:rate = 2.5 * (0.2)^1 * (0.3)^1 = 2.5 * 0.06 = 0.15 M/s\nOverall order = 1 + 1 = 2
Result:Rate = 0.15 M/s, Overall order = 2
Frequently Asked Questions
What is a rate law in chemistry?
A rate law is a mathematical expression that relates the rate of a chemical reaction to the concentrations of its reactants raised to specific powers called reaction orders. The general form is rate = k[A]^m[B]^n, where k is the rate constant, [A] and [B] are molar concentrations, and m and n are the reaction orders with respect to each reactant. Rate laws must be determined experimentally and cannot be predicted from the balanced equation alone. The overall reaction order is the sum of all individual orders (m + n).
How do you determine the rate constant k?
The rate constant k is determined experimentally by measuring how the reaction rate changes when reactant concentrations are varied. Using the method of initial rates, you run multiple experiments where only one reactant concentration changes at a time. By comparing the ratios of rates to the ratios of concentrations, you can solve for the exponents and then calculate k. The units of k depend on the overall reaction order: for zeroth order k has units of M/s, for first order 1/s, and for second order 1/(M*s).
How does temperature affect the rate law?
Temperature does not change the form of the rate law or the reaction orders, but it significantly affects the rate constant k. According to the Arrhenius equation, k = A * exp(-Ea/RT), where A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is temperature in Kelvin. A 10-degree Celsius increase typically doubles or triples the rate constant. Higher temperatures provide more molecules with sufficient energy to overcome the activation energy barrier.
What is the ideal gas law and when does it apply?
PV = nRT, where P is pressure, V is volume, n is moles, R is the gas constant (0.0821 L-atm/mol-K), and T is temperature in Kelvin. It applies to gases at low pressure and high temperature relative to their boiling point. Real gases deviate at high pressures and low temperatures.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy