# Practical Application: Determining Rate Equation, Rate Law Constant & Reaction Order

Instructor: Amanda Robb

Amanda holds a Masters in Science from Tufts Medical School in Cellular and Molecular Physiology. She has taught high school Biology and Physics for 8 years.

This lesson will help you calculate the rate law constant and figure out the rate equation and reaction order when given experimental data. Here, we'll practice each of these skills and give you tips on how to solve this type of problem.

## What Is Rate Law?

What causes chemical reactions to move faster or slower? How can we describe this property in chemistry? The answer is the rate law, which describes the dependence of a reaction on the concentration of reactants and the reaction constant k, which includes both the activation energy and the temperature of the reaction. Today, we're going to learn how to write rate law equations, determine the rate law constant and the reaction order of a particular reaction.

## Step 1: Determining Rate Equation

The rate equation must be determined from experimental data from a reaction, so if a problem asks you to determine a rate equation the problem will also provide you with a table of data. Let's look at an example of an reaction where substance A is mixed with substance B to form substance C

A + B --> C

The problem provides this data:

Experiment Initial Concentration of Reactant A (M) Initial Concentration of Reactant B (M) Initial rate of formation of C (M/sec)
1 0.1 0.1 2
2 0.1 0.2 8
3 0.2 0.2 16

Start with the first reactant. Choose two experiments where the concentration of A changes, but the concentration of B stays the same, like experiment 2 and 3. Here, A doubles and B stays the same. The rate of reaction also doubles. We can put this into our rate equation:

Rate = k [A]x[B]y[C]z

So, if we fill in our values from the table for the rate and the concentration of A, we can figure out the exponent x.

2 = 2x

Therefore, the exponent for reactant A must be 1.

Now, we repeat the same process for the second reactant, B. Between experiment 1 and 2, the concentration of B doubles, but the concentration of A stays the same. Here, the rate increases by a factor of 4, from two to eight M/second. Using our rate equation we get:

4 = 2y

Therefore, the exponent for reactant B is 2.

Putting this information together, we can come up with our rate equation for the reaction:

Rate = k[A][B]2

You can repeat this process for any additional reactants in the equation as needed.

## Step 2: Determining Reaction Order

Now that you have a complete rate equation, you can find the reaction order. To do this, simply add up the exponents on the reactants.

1 + 2 = 3

So, the reaction is overall third order.

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