What are the Rate Law and Rate Constant?

Kelly Carroll, Amy Meyers
  • Author
    Kelly Carroll

    Kelly earned a PhD in Microbiology and immunology from the University of Louisville. She has experience doing scientific research as well as teaching university biology and chemistry. She is a freelance writer and runs the early education blog Hey Kelly Marie, a passion project.

  • Instructor
    Amy Meyers

    Amy holds a Master of Science. She has taught science at the high school and college levels.

Learn the difference between rate constant and rate law. Explore how to use the rate law equation to find the reaction order for one and two reactants. Updated: 05/10/2022

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Rate Law and Rate Constant: Understanding the Difference

What is rate law? The rate law is the quantitative expression linking the relationship of the concentration of reactants to the rate of a chemical reaction. The rate law measures the pace of a reaction in comparison to the concentrations of the reactants. The reaction rate is the rate or speed at which a chemical reaction occurs. The rate law definition states that the rate of a reaction can depend more on the concentration of one reactant than another reactant. Accordingly, the reactants included in the rate law equation can vary and include one, many, or no reactants.

The rate law can be expressed as the following equation:

rate = k[A]m [B]n [C]o

What is a rate constant? In this equation, k is the rate constant, a constant with a value that is explicit for a given reaction under specific conditions. The rate constant definition explains that k is reflective of the speed of the chemical reaction. Higher rate constant values indicate a faster reaction speed, while lower rate constant values indicate a slower reaction speed. The rate constant is also sometimes called the proportionality constant. The variables A, B, and C represent the concentrations of the three reactants A, B, and C. The exponent variables m, n, and o represent the partial reaction order for each reactant. Exponent m represents the partial reaction order for A, n represents the partial reaction order for B, and o represents the partial reaction order for C.

The rate law for a given equation is determined through carrying out experiments. The rate constant, k, is variable based on the conditions in which the chemical reaction is taking place, like temperature. Accordingly, every chemical reaction has a different rate constant. The rate law can be calculated by carrying out the same chemical reaction using varying reactant concentrations and observing the corresponding reaction rates.

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Order of Reaction: Take One

According to the rate law definition, the order of a reaction is the summation of all the partial reaction orders for the reactants in the equation. The total order of the reaction is calculated by adding up the partial reaction orders for each reactant. The reaction order is usually a whole number, but rarely can be a fraction or a negative number.

In the previously stated rate law equation, the overall reaction order is expressed:

reaction order = m + n + o

If the rate law is stated:

rate = [A]2 [B]0

reaction order = 2 + 0 = 2

In a first-order reaction, the rate of the reaction is determined by the concentration of one reactant. As such, there may be other reactants present in the chemical equation, but their order or exponent is equal to zero. First-order reactions are also called unimolecular reactions. An example of a first-order reaction is:

[A] --> [B] + [C]

The rate is dependent on the concentration of one reactant, A. The rate equation can be expressed as:

rate = k[A]m

If at stable environmental conditions, the following concentrations and rates of reaction are:

Experiment 1:

Concentration of A: 2.0 M

Rate: 10 x 10-3 M/s

Experiment 2:

Concentration of A: 1.0 M

Rate: 5 x 10-3 M/s

To calculate the order of the reaction and find the value of the variable m, the rate law equation can be rearranged to state:

rate 1 / rate 2 = (k[A1]m) / (k[A2]m)

In this equation, rate 1 and A1 correspond to the data from experiment 1. Rate 2 and A2 correspond to the data from experiment 2.

The experimental results for rate and concentration can be plugged into the equation to state:

(10 x 10-3 M/s) / (5 x 10-3 M/s) = (k (2.0 M)m)) / (k (1.0 M)m)

This equation can be further simplified to be stated as:

2 = 2m

m=1

Because m is equal to 1, this is a first-order reaction.

After determining the reaction order as 1, the rate constant k can be calculated. Because the exponent m value is known and m=1, that value along with one of the reactant concentrations and rate from the experimental data can be put into the rate value equation to calculate k.

rate = k[A]1

5 x 10-3 M/s = k (1.0M)

k = 5 x 10-3 s-1

In first-order reactions, the rate of the reaction is directly proportional to the concentration of the reactant. When the concentration of reactant A increases, the rate of the reaction will go up proportionally. When the concentration of A triples, the rate of the reaction will also triple. The units of k in a first-order reaction are s-1.

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Frequently Asked Questions

What is the rate constant k equal to?

The rate constant k is a value that is specific to each chemical reaction under specific conditions. The rate constant is reflective of the speed of a reaction, as a higher rate constant reflects a faster reaction speed.

What is rate constant and rate of reaction?

The rate constant is a specific value for a chemical reaction under defined conditions. The rate of a reaction is the speed at which a chemical reaction takes place.

What is meant by rate law in chemistry?

The rate law is specific for each chemical reaction and quantitatively expresses the relationship between a reaction rate and the concentration of reactants. The rate law is stated rate = k [A]x [B]y [C]z

How does one find rate law?

The rate law is determined through experimentation. Through experimental trials the data of reaction concentration and rate of reaction can be observed. Using this data, the reaction order can be calculated. From the reaction order and experimental trial data, the rate constant, k, can be calculated.

How does one find the rate constant?

The rate constant, k, can be determined using experimental data of reactant concentration and reaction rate. By using a ratio of one experimental trial rate and concentration to another experimental trial rate and concentration, the reaction order can be solved for each reactant. After the reaction order is determined, one trial experimental data set can be plugged into the reaction's rate law and k can be calculated.

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