Reaction Order Calculator (Rate Law Method)
Determine reaction order from concentration and rate data using the integrated rate law method, plus the rate constant.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
n = ln(rate2/rate1) / ln([A]2/[A]1)
The reaction order n is found by comparing rates from two experiments where only one reactant concentration changes. Taking the natural log of the rate ratio divided by the natural log of the concentration ratio gives the order. The rate constant k is then found by substituting back into the rate law.
Worked Examples
Example 1: Determining Order from Two Experiments
Problem:Experiment 1: [A] = 0.10 M, rate = 0.015 M/s. Experiment 2: [A] = 0.20 M, rate = 0.060 M/s. Find the reaction order.
Solution:Rate ratio = 0.060 / 0.015 = 4.0\nConc ratio = 0.20 / 0.10 = 2.0\nn = ln(4.0) / ln(2.0) = 1.386 / 0.693 = 2\nk = 0.015 / (0.10)^2 = 1.5 M^-1 s^-1
Result:Order = 2 (second order), k = 1.5 M^-1 s^-1
Example 2: First Order Reaction Identification
Problem:Experiment 1: [A] = 0.50 M, rate = 0.010 M/s. Experiment 2: [A] = 1.50 M, rate = 0.030 M/s.
Solution:Rate ratio = 0.030 / 0.010 = 3.0\nConc ratio = 1.50 / 0.50 = 3.0\nn = ln(3.0) / ln(3.0) = 1\nk = 0.010 / 0.50 = 0.02 s^-1
Result:Order = 1 (first order), k = 0.02 s^-1
Frequently Asked Questions
What is reaction order in chemistry?
Reaction order describes how the rate of a chemical reaction depends on the concentration of a particular reactant. A first-order reaction rate doubles when the reactant concentration doubles, a second-order reaction rate quadruples when concentration doubles, and a zero-order reaction rate is independent of concentration. The overall reaction order is the sum of all individual orders. Reaction orders are determined experimentally using the method of initial rates or integrated rate law analysis.
How does the method of initial rates work?
The method of initial rates involves running a reaction multiple times with different initial concentrations while measuring the initial rate each time. By changing only one reactant concentration between experiments and keeping others constant, you can isolate the effect of that reactant. The reaction order is found by taking the ratio of rates and concentrations: n = ln(rate2/rate1) / ln([A]2/[A]1). This method requires at least two experiments per reactant to determine each individual order.
Can reaction order be a fraction or negative?
Yes, reaction orders can be fractional, zero, or even negative. Fractional orders (like 0.5 or 1.5) often indicate complex reaction mechanisms with multiple elementary steps. Negative orders mean that increasing the concentration of a reactant actually slows the reaction, which can occur when a reactant inhibits a catalytic surface or competes for active sites. Zero-order reactions proceed at a constant rate regardless of concentration, commonly seen in enzyme-catalyzed reactions at saturation.
What are integrated rate laws and how do they relate to reaction order?
Integrated rate laws describe how concentration changes over time for each reaction order. For zero order: [A] = [A]0 - kt (linear in [A] vs t). For first order: ln[A] = ln[A]0 - kt (linear in ln[A] vs t). For second order: 1/[A] = 1/[A]0 + kt (linear in 1/[A] vs t). By plotting experimental data in these forms, the one that gives a straight line reveals the reaction order. The slope of the straight line gives the rate constant k.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy