Difference Between Rate Law and Law of Mass Action

Key Difference – Rate Law vs Law of Mass Action
 

The key difference between rate law and law of mass action is that rate law indicates the relationship between the rate of a chemical reaction and the concentrations of reactants whereas law of mass action states that rate of a chemical reaction is proportional to the masses of the reacting substances.

Rate law is a law in chemistry that is used to explain the behavior of a reaction mixture. The rate law indicates that rate of a reaction is directly proportional to the reaction rate. The proportionality constant is known as the rate constant. The law of mass action indicates that the reaction rate of a chemical reaction is directly proportional to the product of masses of reactants which are raised to a power (it is often equal to their stoichiometric coefficient in the chemical equation) that is determined experimentally.

CONTENTS

1. Overview and Key Difference
2. What is Rate Law 
3. What is Law of Mass Action
4. Side by Side Comparison – Rate Law vs Law of Mass Action in Tabular Form
5. Summary

What is Rate Law?

The rate law indicates the relationship between the rate of a chemical reaction and the concentrations of reactants. According to rate law, the rate of a reaction is directly proportional to the concentrations of reactants that are raised to a power (it is often equal to the stoichiometric relationship in the chemical equation) that is determined experimentally.

Rate law can be found in two types as follows:

1. Differential Rate Law

The differential rate law gives the rate of a reaction as a function of the change in concentration of reactants during a particular time period.

2. Integrated Rate Law

The integrated rate law gives the rate of a reaction as a function of the initial concentration of a reactant at a specific time period.

Let us consider an example to understand this.

aA   +   bB         →       cC  +   dD

Rate = k[A]^a[B]^b

The above equation gives the mathematical expression of the rate law. There, “k” is a proportionality constant. It is known as the rate constant. The exponents “a” and “b” are the orders of reaction with respect to the reactant A and B respectively. The overall order (p) of the reaction is given as the sum of all orders in the rate law equation.

p = a + b

Figure 1: The rate of reaction and the concentration of first-order reactions and second-order reactions.

Based on the overall order of a reaction, the reactions are in three types as:

1. Zero-order reactions – the rate of reaction is independent of the concentration of reactants
2. First-order reactions – the rate of reaction is proportional to the concentration of one reactant.
3. Second-order reactions – the rate of reaction is proportional either to the product of concentrations of two reactants or to the square of the concentration of one reactant.

What is Law of Mass Action?

Law of mass action indicates that the rate of a chemical reaction is proportional to the masses of the reacting substances. It is also known as the mass action law. This law is useful to obtain the accurate equilibrium equation of a particular chemical reaction. The law is also given by activities or concentrations of reactants. According to the law of mass action, the ratio between concentrations of products and reactants is a constant in a reaction mixture that is in an equilibrium state.

The law of mass action is a universal concept, which means, it is applicable to any system under any circumstance. This law can be given in a mathematical expression as below.

For the reaction,

aA   +   bB         ↔       cC  +   dD

The ratio between products and reactants at equilibrium;

Keq = [C]^c[D]^d / [A]^a[B]^b

At a given temperature, the above ratio is a constant for the equilibrium between reactants (A and B) and products (C and D). Here, Keq is known as the equilibrium constant.

What is the Difference Between Rate Law and Law of Mass Action?

Summary – Rate Law vs Law of Mass Action

Rate laws and the law of mass action are used to explain the behavior of a reaction mixture. The key difference between rate law and law of mass action is that the rate law indicates the relationship between the rate of a chemical reaction and the concentrations of reactants whereas law of mass action indicates that the rate of a chemical reaction is proportional to the concentrations of the reacting substances.

Reference:

1. “The Rate Law.” Chemistry LibreTexts,  21 July 2016, Available here.
2. “12.3 Rate Laws.” Chemistry, Available here.
3. Laidler, Keith J. “Law of Mass Action.” Encyclopædia Britannica, Encyclopædia Britannica, Inc., 26 Oct. 2016, Available here.

Image Courtesy:

1. “Rateloglogplot” By Fabiuccio~enwikibooks at English Wikibooks – Transferred from en.wikibooks to Commons., (Public Domain) via Commons Wikimedia

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