What is the Difference Between Differential Rate Law and Integrated Rate Law?

The differential rate law and integrated rate law are mathematical expressions that describe the relationship between the reaction rate and the concentrations of reactants in a chemical reaction. The main differences between them are:

Differential Rate Law: This law expresses how the reaction rate depends on the concentration of reactant(s). It is often simply called "the rate law" because it is the most common type of rate law. The differential rate law can be used to determine the rate constant and reaction order for a given reaction.
Integrated Rate Law: This law expresses how the concentration of reactant(s) depends on time. It is derived by using calculus to integrate the differential rate law. The integrated rate law can be used to predict the concentration of reactants at any given time during the reaction.

In summary:

The differential rate law tells you how the rate of a reaction depends on the concentration of reactant(s).
The integrated rate law tells you how the concentration of reactant(s) depends on time.

Both rate laws are essential for understanding the kinetics of a chemical reaction and can be used to determine the rate constant, reaction order, and concentration of reactants at different times during the reaction.

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What is the Difference Between Differential Rate Law and Integrated Rate Law?

Comparative Table: Differential Rate Law vs Integrated Rate Law

Differential Rate Law and Integrated Rate Law are two forms of rate laws that describe the progress of a chemical reaction. Here is a table highlighting the differences between them:

Feature	Differential Rate Law	Integrated Rate Law
Definition	Expresses how the reaction rate depends on the concentration of reactant(s).	Expresses how the reactant(s) concentration depends on time.
Equation	Rate = -d[A]/dt = k[A]^n.	Integrated rate law equations depend on the order of the reaction: - Zero order: [A] = [A]0 + kt - First order: ln[A] - ln[A]0 = -kt - Second order: 1/[A] = 1/[A]0 + kt.
Purpose	Describes the reaction rate in terms of changes in the concentration of one or more reactants over a specific time interval.	Describes the reaction rate in terms of the initial concentration and integrated rate laws are discussed in more detail later.

Both differential and integrated rate laws are essential for understanding the kinetics of a chemical reaction and are used to determine rate constants, reaction orders, and reaction progress.

Guilherme Mazui

Guilherme Mazui is graduated in journalism from the Federal University of Minas Gerais (UFMG) and a master's degree in Communication from the University of São Paulo (USP). In addition, he has experience in advertising writing and has worked as a content editor in several companies.