# Rate Law Equation: Constant & Reaction Order

## What is the Rate Law Equation?

Whether someone is studying a chemical reaction in chemistry, molecular biology, or biochemistry, it is important to understand not just what the starting reactants and ending products are, but how the reaction is advancing over time. Simply knowing that a reaction is occurring is often not very useful for solving problems involving chemical reactions.

For instance, one reaction might be quick and occur in seconds while another could be slower and take hours, days, or months to occur. What if the chemical reaction had some impact on the environment? Knowing how quickly the reaction occurs over time would provide extremely valuable data. In any chemical reaction, rate means how fast the reaction is moving over time. The rate of a reaction will differ based on factors like the identity of the reactants, the concentration of each reactant, and the temperature at which the reaction is occurring.

There is a mathematical formula called the **rate law equation** which allows the rate of a reaction to be calculated. An example of how to write the rate law equation (with reactants A and B) is as follows: {eq}r = k[A]^x[B]^y {/eq} where the equation components are:

**Rate law**, which is the entire equation, with rate represented by*r***Rate law constant**, represented by*k***Order of reaction**, represented by exponents*x*and*y***Molar concentration**of the reactants, represented by the letters A, B, etc., in brackets.

### Rate Law

The terms rate law and rate law equation are synonymous and interchangeable with each other. Rate law, with rate represented by the symbol *r*, represents the speed of a reaction per a set unit of time. The rate of reaction definition is always expressed as some concentration (e.g., molarity, or M, which is mol/L) over a unit of time (e.g., seconds, or s), with the rate of reaction units written as concentration/time, e.g., M/s. How to determine rate law requires knowledge of the identity of the reactants, the order of reactants, and the rate law constant.

### Order of Reaction

In rate law, the order of reaction or reaction order refers to the concentration of reactants, expressed as exponents (e.g., *x* and *y*). How does the order of a reaction impact rate? The concentration for each reactant, A and B, is multiplied by the power of the reaction order.

- For reactants A and B, where
*x*= 1 and*y*= 1, the rate law is expressed as {eq}r = k[A][B] {/eq}

- For reactants A and B, where
*x*= 2 and*y*= 1, the rate law is expressed as {eq}r = k[A]^2[B] {/eq}

- For reactants A and B, where
*x*= 1 and*y*= 2, the rate law is expressed as {eq}r = k[A][B]^2 {/eq}

#### How to Determine Order of Reaction:

The reaction order for a chemical equation is the sum of exponents for every reactant in the chemical equation. So, for {eq}r = k[A][B]^2 {/eq} the reaction order is 3, because *x* = 1 and *y* = 2, with *x* + *y* = 3. In this case, reactant A is first-order, reactant B is second-order, and the entire reaction is third-order. The types of order reactions and their definitions include:

- First-order reactions: happens when the sum of all exponents of the reactants equals 1, e.g., {eq}r = k[A] {/eq}

- Second-order reactions: happens when the sum of all exponents of the reactants equals 2, e.g., {eq}r = k[A][B] {/eq}

- Third-order reactions: Happens when the sum of all exponents of the reactants equals 3, e.g., {eq}r = k[A][B]^2 {/eq}

- Zero-order reactions: This happens only when the concentration of the reactants does not have any impact on the rate of the reaction.
- Pseudo-order reactions: This happens when the concentration of one of the reactants is not included in the reaction order for the equation. Pseudo-order reactions can be pseudo-zero or pseudo-first-order, e.g., where a second-order reaction acts as a first-order reaction, or a first-order reaction acts like a zero-order reaction.
- Complex reactions: Complex reactions are reactions with multiple steps.

### How to Find Rate Constant?

Rate constant is a number that represents the relationship between reactant concentration and reaction rate in a particular chemical reaction at a set temperature. To find the value of the rate constant, *k*, which differs for each chemical reaction, experimental data is required. How to find rate constants for each reaction involves solving for *k* in the rate law equation and then plugging in values from experimental data.

An example of how to find the rate constant equation, where {eq}r = k[A][B]^2 {/eq}, for instance, is to solve for *k*, which gives {eq}k = \frac{r}{[A][B]^2} {/eq} as the rate constant equation. Because the concentrations of A and B are expressed in units of M and the units of *k* are expressed as M/s, the rate constant units for *k* is {eq}\frac{1}{M^2s} {/eq}. An example of how to find values for the order of a reaction, the rate constant, and rate law using experimental data is covered in the next section of this lesson.

## Experimental Data

For the chemical equation A + B {eq}\rightarrow {/eq} products, where the following data was collected at a constant temperature, what is the reaction order, the rate constant, and the rate law?

Experiment No. | Concentration of A (M) | Concentration of B (M) | Initial Rate (M/s) |
---|---|---|---|

1 | 0.05 | 0.02 | 0.00125 |

2 | 0.10 | 0.02 | 0.00500 |

3 | 0.10 | 0.04 | 0.01000 |

#### Finding the Reaction Order

- To solve for
*x*, look at the experimental data where the concentration of A changes but B remains the same. From experiment 1 to experiment 2, the concentration of A doubled from 0.05M to 0.10M, but the concentration of B remained the same at 0.02M. However, the rate increased by 4 times from 0.00125 M/s in experiment 1 to 0.0050 M/s in experiment 2 when the concentration of A increased by 2 times. Therefore, the reaction order for A is represented by the equation {eq}2^x = 4 {/eq}, where solving for*x*= 2.

- To solve for
*y*, look at the experimental data where the concentration of B changes but A remains the same. From experiment 2 to experiment 3, the concentration of B doubled from 0.02M to 0.04M, but the concentration of A remained the same at 0.10M. However, the rate increased by 2 times from 0.00500 in experiment 2 to 0.0100 in experiment 3 when the concentration of B increased by 2 times. Therefore, the reaction order for B is represented by the equation {eq}2^y = 2 {/eq}, where solving for*y*= 1.

- After solving for
*x*and*y*, the rate law equation is {eq}r = k[A]^2[B] {/eq}. This means A is second-order, B is first-order, and the overall reaction is third-order.

#### Solving Rate Constant and Rate Law

- When using the rate law equation {eq}r = k[A]^2[B] {/eq} to solve for
*k*, the rate constant equation is {eq}k = \frac{r}{[A]^2[B]} {/eq}. Now, plug in the values from the experiment, so that r = 0.00125 M/s, A = 0.05M, and B = 0.02M, then solving {eq}k = \frac{0.00125M/s}{[0.05M]^2[0.02M]} {/eq} where {eq}k = 25{(M^2s)}^{-1} {/eq}

- Now that
*y*,*x*, and*k*are known, the rate law can be solved by plugging these values into the rate law equation. Where {eq}r = k[A]^2[B] {/eq}, the solved equation is {eq}r = 25{(M^2s)}^{-1}[0.05M]^2[0.02M] {/eq} = 0.00125 M/s.

## Lesson Summary

In chemistry and related biochemical sciences, the rate of something describes how quickly a chemical reaction is happening over time. Understanding rate is very important for fully comprehending the impacts of chemical reactions. For example, if a chemical in the atmosphere caused ozone to break down, calculating the reaction rate would be critical to understanding its potential environmental impacts. The **rate law equation**, also called **rate law**, is a mathematical formula for calculating the rate of a reaction, expressed as {eq}r = k[A]^x[B]^y {/eq} when the chemical equation is A + B {eq}\rightarrow {/eq} products. In the rate law, the letter *r* represents the calculated rate, the letter *k* represents the **rate law constant**, the letters {eq}[A] {/eq} and {eq}[B] {/eq} represent the **molar concentration** of each reactant, and the exponents *x* and *y* represent the **order of reaction**.

The exponents *x* and *y* are calculated from experimental data. For instance, if the concentration of A is 0.02M in experiment 1 and 0.04M in experiment 2, the concentration of B is unchanged, and the rate increased from 0.125 M/s to 0.250 M/s, this means the concentration of A doubled between experiment 1 and 2 while the rate also doubled. Therefore, to calculate *x*, use the equation {eq}2^x = 2 {/eq}, where solving for *x* = 1. Because *x* is 1, reactant A is a first-order reaction. If the value for *y* was also calculated at 1, then reactant B is also a first-order reaction. So, if *x* = 1 and *y* = 1 based on experimental data for reactants A and B, the entire chemical reaction is second order, because *x* + *y* = 2. Calculating the rate law constant, *k*, also requires experimental data. If it is known from a different set of experimental data, for instance, that *x* = 1 and *y* = 1, {eq}[A] {/eq} = 0.20M, {eq}[B] {/eq} = 0.20M, and the initial rate is 0.126 M/s, *k* can be determined. To solve for *k*, plug these values into the rate law equation {eq}r = k[A][B] {/eq} and solve, where *k* = 3.15{eq}(M^2s)^{-1} {/eq}.

To unlock this lesson you must be a Study.com Member.

Create your account

#### How does one find the rate law?

Solving the rate law equation requires experimental data. First the values for the order of reaction for reactants A and B, represented by exponents *x* and *y*, need to be determined from experimental data. Then, the rate law constant, *k*, needs to be determined. After these values are calculated, the rate law can be determined by plugging in the molar concentration of A and B, the order of reaction for reactants A and B, and the rate law constant, *k*, into the rate law equation and solving for *r*.

#### What is the rate constant or k?

The rate constant, represented by the letter *k*, is a value that represents how the reactant concentration and reaction rate relate to each other in a particular chemical reaction. Rate constant changes with temperature.

#### What is rate law and rate law constant?

Rate law, also known as the rate law equation, is a formula for mathematically calculating the rate of a specific chemical reaction. In this equation, the rate law constant is represented by *k*.

### Register to view this lesson

### Unlock Your Education

#### See for yourself why 30 million people use Study.com

##### Become a Study.com member and start learning now.

Become a MemberAlready a member? Log In

Back### Resources created by teachers for teachers

I would definitely recommend Study.com to my colleagues. Itâ€™s like

**a teacher waved a magic wand and did the work for me.** I feel like itâ€™s a lifeline.