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.
As a member, you'll also get unlimited access to over 84,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.
Get unlimited access to over 84,000 lessons.
Try it nowAccording 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:
Concentration of A: 2.0 M
Rate: 10 x 10-3 M/s
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.
In a second-order reaction, the value of the reaction order is 2. In second-order reactions, the rate of the reaction is proportional to the square of the reactant concentration. When the concentration of A doubles, the rate of the reaction quadruples. The units of k in a second-order reaction are L Mol-1 s-1.
The reaction order can also be calculated when there are two reactants in a chemical equation. This can be shown through a hypothetical chemical reaction such as:
A + B --> C
Through experimentation, the following data for reaction rates are obtained at varying concentrations of A and B:
Experiment 1:
[A] = 1 ML-1
[B] = 1 ML-1
Rate = 2 x 10-5 M L-1 s-1
Experiment 2:
[A] = 2 ML-1
[B] = 1 ML-1
Rate = 4 x 10-5 M L-1 s-1
Experiment 3:
[A]= 1 ML-1
[B] = 2 ML-1
Rate = 2 x 10-5 M L-1 s-1
The rate law for the chemical reaction is stated:
rate = k [A]m [B]n
Using the rate law, the experimental data can be used to determine the reaction order for reactant A. The order of reactant A is represented by the variable m.
rate 2 / rate 1 = ([A2] / [A1])m
4 x 10-5 M L-1 s-1 / 2 x 10-5 M L-1 s-1 = (2M / 1M)m
2 = 2m
m=1
To find the reaction order for reactant B, the same strategy can be applied. The values for experiments 1 and 3 are used because the concentration for reactant B is doubled and held constant for reactant A.
rate 3 / rate 1 = ([B3] / [B1])n
2 x 10-5 M L-1 s-1 / 2 x 10-5 M L-1 s-1 = (2 M L-1 / ML-1 )n
1 = 2n
n=0
The reaction is zero order with respect to reactant B.
To solve for the rate constant, k, the experimental data from any of the three trials can be plugged into the determined rate law.
rate = k [A]1 [B]0
rate = k [A]1
2 x 10-5 M L-1 s-1 = k (1 ML-1)
k= 2 x L-1 s-1
The rate law is a quantitative expression that relates the concentration of reactants to the rate of a chemical reaction. The reaction rate is the rate or speed at which a chemical reaction takes place. The rate law can include no, one, or many reactants in a chemical reaction. The rate law is expressed rate = k [A]m [B]n [C]o, where k is the rate constant. A, B, and C are reactant concentrations, and m, n, and o are the partial reaction orders for each reactant. The rate constant is specific for a reaction under specific conditions, like temperature. Therefore, every chemical reaction has a variable rate constant. The reaction order is the summation of the partial reaction orders given for each reactant. For the example rate law equation, the reaction order = m + n + o. The rate law and reaction order for a specific chemical reaction is determined through experimentation.
In first-order reactions, the reaction rate is directly proportional to the reactant concentration. When the concentration of a reactant A doubles, the reaction rate also doubles. When the reaction order is two, the effect of doubling the reactant concentrations will be quadruple the reaction rate. When the concentration of reactant A doubles, the reaction rate quadruples.
To unlock this lesson you must be a Study.com Member.
Create your account
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.
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.
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
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.
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.
Already a member? Log In
Back