Rate Law Definition
The rate law is the relationship between the concentrations of reactants and their various reaction rates. Reactions rates are often determined by the concentration of some, all, or none of the reactants present, and determines which reaction order the reaction falls into.
Rate law is a measurement which helps scientists understand the kinetics of a reaction, or the energy, speed, and mechanisms of a reaction. Using the rate law, scientists can understand how long a reaction will take to go to completion, the energy required to stimulate a reaction,
Rate Law Equation
For the reaction:
aA + bB → cC
The rate law equation would be the following:
Rate = k[A]Y[B]Z
This equation describes several different aspects of the rate law. The first is the rate constant or “k”, which is specific to every reaction at a specific temperature. This rate constant can change with the temperature, as the temperature will affect the overall speed of the reaction.. [A] is the concentration of substance A, while [B] is the concentration of substance B. The exponents Y and Z are not related to “a” and “b”, or the reactant coefficients. Instead, Y and Z are determined experimentally and are called reaction orders. The sum of these reaction orders determines the overall reaction order.
How to Determine Rate Law
The rate law is most commonly determined by the initial rates method, which measures the initial rates of reactions, the concentration of reactants, and their effects on the overall reaction. Let’s consider the simplest possible example to determine how this works. Consider the following reaction:
A → B + C
In this reaction, reactant A is the only reactant. To determine the rate law, a series of experiments must be done which vary the concentration of the reactant and observe the initial rate. Suppose that you tested the above reaction, and got the following data:
|Initial Concentration A||Reaction Rate|
|1 mole/L||5 moles/sec|
|2 mole/L||10 moles/sec|
|4 mole/L||20 moles/sec|
Given this “experimental data”, we can easily calculate the rate law for this reaction. After we have our experimental data, we can simply input these different values into the rate equation to find the reaction orders of each reactant. Here is the general rate law equation for the reaction:
Rate = [A]Y
Thus, if we are comparing two experiments, we can put them into the same equation to find which exponents will complete the equation. For example:
Rate1/Rate2 = [A1]Y/[A2]Y
If we plug the experimental results into this equation, we find:
5/10 = 1Y/2Y
Rearranged and simplified, this leaves us with the equation:
0.5 = (1/2)Y
Clearly, the exponent in this case must be 1, making the reaction order 1 for substance A. However, with more complex equations you might need to use algebra to solve for Y. If substance A is the only reactant or product which influences the rate of the reaction, the overall reaction order will also be 1. These reaction orders within the rate law describe the change to the rate if changes in the concentration of reactants or products are made.
Rate Law Examples
Creating Nitric Acid
The following reaction describes a step in the production of nitric acid from oxygen and nitrogen monoxide:
O2 + 2NO → 2NO2
In this reaction, the oxygen molecule is split and one oxygen atom is added to the nitrogen monoxide, creating the acidic species nitrogen dioxide. Scientists have determined experimentally that the rate law for this reaction is:
Rate = k[O2][NO]2
But what does this mean for the reaction itself? Well, the rate law tells us too things about the reaction. First, if you notice that the concentration of oxygen does not have an exponent, we must realize this means “1”. Therefore, oxygen has a first order rate compared to its concentration. Simply put, this means that if you double the amount of oxygen present, the rate will also double.
Nitrogen monoxide, on the other hand, has a second order rate. This means that if you double the amount of NO, you will quadruple the rate. In this way, rate law can be used to determine the outcomes of changing different reaction conditions, especially concentration. Scientists can use this to determine things like the efficiency of their reactions, how they can increase or decrease the rate of a reaction, and can even allow them to conduct analyses of how profitable or efficient their process may be.
Formation of Ozone
The formation of ozone is a reaction that takes place high within the atmosphere. Here, gaseous oxygen (O2) turn into ozone (O3), which is an important molecule for blocking dangerous UV radiation from the sun. Below is the general equation:
2O3 ↔ 3O2
Under experimental conditions, scientists have determined that the rate law equation for this reaction is:
Rate = k[O3]2[O2]-1
This rate law tells us some very important things about the rate and type of reaction. Here, the exponent on ozone tells us that every time the concentration of ozone doubles, the reaction rate quadruples. The negative exponent on oxygen tells us that if the concentration of oxygen doubles, the rate will actually be divided by that concentration, reducing the rate of reaction by half. If we consider both of these statements, we can see the true nature of the reaction. This rate law tells us that there is a delicate balance between the reactant and product, which slows to equilibrium as the concentration of ozone drops and is replaced by oxygen.