The **key difference** between rate expression and rate law is that **rate expression gives the rate of appearance or disappearance of products or reactants, whereas rate law gives the relationship between rate and concentration or pressure of reactants. **

When one or more reactants are converted to products, they may go through different modifications and energy changes. The chemical bonds in the reactants break, and new bonds are formed to generate products that are totally different from the reactants. This chemical modification is known as chemical reactions. Rate expression and rate law are important chemical concepts we can describe in chemical reactions.

### CONTENTS

1. Overview and Key Difference

2. What is Rate Expression

3. What is Rate Law

4. Side by Side Comparison – Rate Expression vs Rate Law in Tabular Form

5. Summary

## What is Rate Expression?

The rate expression is the way of representing the change in reactant concentration over the time of reaction. We can give this expression using any of the reactants and products of the reaction. When giving the rate expression with respect to reactants, we should use a minus sign because, during the reaction, the reactant amount decreases with time. When writing the rate expression using products, plus sign is used because the amount of products increase with time.

Moreover, we should consider the stoichiometric relationships when giving the rate expression to equalize all the rate expression given in any manner. For example, let us consider the following chemical reaction and the rate expressions that we can give for it;

2X + 3Y ⟶ 5Z

The following rate expressions are possible for the above reaction:

## What is Rate Law?

The rate law is the mathematical expression of the rate of a reaction which includes the relationship between reactants’ rate and product’s rate. We can determine these mathematical data experimentally, and we can verify the relationship as well. There are two major ways we can write a rate law; differential rate law and integrated rate law.

### Differential Rate Law

The differential rate law is the way of expressing the reaction rate using the change in concentration of one or more reactants. Here, we consider the change of the concentration of the reactant(s) over a specific period of time. We name this time interval as Δt. We can name the change in concentration of reactant “R” as Δ[R]. Let us consider an example to understand how to write a differential rate law. For a reaction in which the reactant “A” decomposes to give the products and k is the rate constant while n is the order of this reaction, then the equation for this rate is as follows:

- A ⟶ products

The differential rate law is as follows:

### Integrated Rate Law

The integrated rate law is the way of expressing the reaction rate as a function of time. We can obtain this expression using differential rate law via the integration of the differential rate law. We can obtain this integrated rate law from an ordinary rate as well.

For example, for the reaction A ⟶ products, the ordinary rate law is as follows:

Rate (r)=k[A]

where k is the rate constant and [A] is the concentration of reactant A. If we consider a small time interval, we can write the above equation as follows:

We use the minus sign (–) here because A is the reactant and with increasing time, the concentration of A decreases. Then we can get a relationship as follows by combining the above two equations;

For a very small change in reactant concentration at a very small time interval, we can write the equation as below;

Or

Then, by integrating this equation, we can obtain the following relationship:

ln[A] = -kt + constant

Therefore, when time is zero or t=0, ln[A] is the initial concentration of A reactant (we can give it as [A]_{0}) since at t=0, –kt=0 so ln[A]_{0}=constant. For a first-order reaction, the integrated rate law is,

ln[A] = ln[A]_{0 }– kt

## What is the Difference Between Rate Expression and Rate Law?

Rate expression and rate aw are two ways of giving details about the rate of a reaction. The key difference between rate expression and rate law is that rate expression gives the rate of appearance or disappearance of products or reactants, whereas rate law gives the relationship between rate and concentration or pressure of reactants.

Below infographic summarizes the difference between rate expression and rate law.

## Summary – Rate Expression vs Rate Law

Rate expression and rate law are two ways of giving details about the rate of a reaction. The key difference between rate expression and rate law is that rate expression gives the rate of appearance or disappearance of products or reactants, whereas rate law gives the relationship between rate and concentration or pressure of reactants.

##### Reference:

1. “Rate Expression and Order of Reaction.” *LinkedIn SlideShare*, 15 Sept. 2013, Available here.

## Leave a Reply