Learn what the rate law is and how the rate constant relates to it. Learn what reaction order is and how to determine reaction order when given experimental data containing concentration and reaction rate.

## Rate Law and Rate Constant

Pretend you are out camping. You are cold and wet, and you want to build a big fire quickly to dry out and warm up.

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You get a little flame going, but how best do you get a big fire quickly? Do you add oxygen to it? More wood? Lighter fluid? What reactant can you add to make the rate of the reaction happen quicker?The question you are really asking is, ‘What is the reaction mechanism?’ How exactly does the reaction that makes fire work? What reactants must be brought together in what concentrations to make the final product? When studying chemical reactions, the rate law allows scientists to determine factors like these.You have learned that the rate of a reaction is affected by the concentration of the reactants. You know that rate is change over a period of time. For example, a reaction of A + B –> C has a rate of that below:

The delta symbol above means ‘change in.

‘It should come as no surprise after studying chemistry for a while that there is a law for rate. It is called the rate law. The rate law is the relationship between the rate of a reaction and the concentration of the reactants. The equation for the rate law is:Rate = kA^mA is the reactantk is a constant called the rate constantm is the reaction orderIf m = 0, then the reaction is zero order, and the rate is independent of the concentration of A.

If m = 1, then the reaction is first order, and the rate is directly proportional to the concentration of A.If m = 2, then the reaction is second order, and the rate is proportional to the square of the concentration of A.

## Reaction Order for One Reactant

Now you might be wondering what determines the order of a reaction. The order of a reaction is determined by data gathered during experimentation. There is no way to determine the order by just looking at a reaction equation. It must be determined by experiment.

Once you have the experimental data, you can determine the k by comparing the concentration of A and the rate of the reaction. If the concentration of A increases but the rate remains the same, it is a zero order reaction because the reaction rate is independent of the concentration of A. If the concentration of A and the rate increase at the same rate, then the reaction order is one because they are directly proportional. If the rate quadruples for every doubling of A, then the reaction order is two because the rate is proportional to the square of the concentration.

Let me show you a table to try to make this clearer. The table below shows a reaction order of zero. Notice how the rate of the reaction doesn’t change even when the concentration increases.

Concentration of A Rate of Reaction
0.1 0.15
0.

2

0.15
0.4 0.15

The next table shows a reaction order of one.

Notice how the rate of the reaction increases at the same rate as the concentration increases.

Concentration of A Rate of Reaction
0.1 0.15
0.

2

0.30
0.4 0.60

The next table below shows a reaction order of two. The rate of the reaction quadruples for every doubling of the concentration.

Concentration of A Rate of Reaction
0.

1

0.15
0.2 0.60
0.4 2.40

## Reaction Order for Two Reactants

Reaction order can also be determined for reactions with two reactants. For the reaction A + B –> C + D, the rate equation is:Rate = kA^mB^n;where m is the rate order of A and n is the rate order of B.

The rate order of the overall reaction is m + n.

 Concentration of A Concentration of B Rate of Reaction 0.1 0. 1 0.0021 0.2 0.1 0. 0082 0.2 0.2 0.0083 0.4 0. 1 0.0033

The rate of the reaction was determined experimentally, so the numbers are slightly different. Although this will slightly change your final answer, it will not change it significantly.

## Example

Here is an example of a problem when you’d use the rate constant and rate law.How do you use the rate law to find the rate constant for the reaction?The first thing to do is look at the concentration of A and rate of reaction. You can see in the table above that as the concentration of A doubles, the rate quadruples. This suggests that A is a second order reaction.

Now, look at B. As the concentration of B doubles, while the concentration of A remains the same, the rate of reaction remains essentially the same. This suggests that B is a zero order reaction.To determine the rate constant, solve the rate law for k for one of the sets of data in the table. The k will change depending on which set of data you use because the rate law depends on concentrations of reactants, and they were different for each set of data.

Let’s use the third set of data:Rate = kA^2B^0Because B is to the zero power and is a zero order, it can be discarded because the rate does not depend on it. So, the equation simplifies to:Rate = kA^2k = rate / A^2k = 0.0082 / (0.2)^2k= 0.205

## Lesson Summary

The rate law is the relationship between the rate of a reaction and the concentration of the reactants.

The equation for the rate law is:Rate = kA^mA is the reactantk is a constant called the rate constantm is the reaction orderThe order of a reaction is determined by data gathered during experimentation.If m = 0, then the reaction is zero order, and the rate is independent of the concentration of A.If m = 1, then the reaction is first order, and the rate is directly proportional to the concentration of A.If m = 2, then the reaction is second order, and the rate is proportional to the square of the concentration of A.

## Learning Outcomes

After you’ve finished with this lesson, you’ll be able to:

• Discuss rate law and rate constant
• Write the equation for the rate law
• Indicate how the order of a reaction is determined
• Comprehend zero, first and second order
• Solve for the rate constant when given a table of data

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