Intermediate Topic 432 of 1102 Kinetics & Equilibrium
Integrated Rate Laws
Equations giving concentration as a function of time for each reaction order.
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In-depth explanation of Integrated Rate Laws
Integrated rate laws are obtained by solving the differential rate equation to give the concentration of a reactant as an explicit function of time. For zero order the result is [A] = [A]0 - kt, for first order ln[A] = ln[A]0 - kt, and for second order 1/[A] = 1/[A]0 + kt. Each equation is linear when the appropriate quantity is plotted against time, so the graph that gives a straight line identifies the order. This is often more reliable than initial rates alone, because a single run supplies many data points. The integrated forms also allow prediction of how long a reaction takes to reach a given extent of conversion.
Going deeper: Integrated Rate Laws
Key ideas: Memorize the three linear forms and the plots: [A] against t for zero order, ln[A] against t for first order, 1/[A] against t for second order. Slopes give -k, -k and +k respectively. Test several plots on the same data and choose the one that is straight with the lowest scatter; the intercept should equal the initial value.
Common mistakes and connections: A frequent error is choosing a plot by eye from only a few points, or testing only one plot and assuming that a gentle curve still means the right order. Remember each form assumes a single reactant or equal starting amounts. Students also lose the sign of the slope for first order. Integrated laws feed into half-life formulas and into analysis of real experimental data.
Visualization of Integrated Rate Laws
Integrated laws give [A] at any time: [A] linear in t (zero order), ln[A] linear (first), 1/[A] linear (second). The straight plot identifies the order. The interactive lesson shows this as a live animation or chart.
Worked example and use case
If a plot of ln[A] against time is a straight line, the reaction is first order and the slope equals minus k.
Frequently asked questions about Integrated Rate Laws
What is Integrated Rate Laws?
Equations giving concentration as a function of time for each reaction order.
Is Integrated Rate Laws a beginner, intermediate or advanced topic?
Integrated Rate Laws is a intermediate topic in Kinetics & Equilibrium. It builds on the vocabulary of beginner topics in this area.
What should I learn before Integrated Rate Laws?
Study these earlier topics in Kinetics & Equilibrium first: Half-life of Reactions, Pseudo First Order Reaction, Method of Initial Rates.
What comes after Integrated Rate Laws?
The next topics in Kinetics & Equilibrium are Molecularity and Elementary Reactions.
Can I practise Integrated Rate Laws with quizzes?
Yes. The interactive lesson includes a self-check question on Integrated Rate Laws, and the Kinetics & Equilibrium quiz draws on every topic in this area.
Where Integrated Rate Laws fits in Kinetics & Equilibrium
Integrated Rate Laws is topic 13 of 91 in Kinetics & Equilibrium.