# Rate Law

Calculating Reaction Rates - Explained

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## Key Questions

A rate law is an expression that enables you to find the rate of a chemical reaction.

#### Explanation:

For the general reaction

$A + B \to C$

the general form of a rate law is

$r \left(t\right) = {k}_{\text{obs}} {\left[A\right]}^{x} {\left[B\right]}^{y}$

These terms tell us the factors that affect the rate:

• The observed rate constant, ${k}_{\text{obs}}$, gives us a general idea of whether the reaction is inherently slower or quicker than others, given the same conditions. The subscript accounts for the fact that many reactions are not single-step reactions, but more often than not, multiple elementary steps.
(For instance, a possible ${k}_{\text{obs}}$ could be $\frac{{k}_{- 1} {k}_{2}}{{k}_{1}}$)

• The concentrations $\left[A\right]$ and $\left[B\right]$ tell us that the reaction rate will depend on the concentrations of the reagents in some way.

• The exponents $x$ and $y$ give us some idea of the order of the reaction with respect to each reactant, and hence give an idea of how the mechanism might progress.

• They're important for two reasons:

• They tell you about how a reaction works. The superscripts above the concentrations in the equation give you information about the mechanism of the reaction, which can help you to understand much more than just the one process.

• They tell you how to speed up the reaction. Fast reactions are usually what we're looking for, so if we can get insight on how to make reactions go quickly, it makes us happy.

OK.

• One way is to use the method of initial rates.

A rate law shows how a change in concentration affects the rate.

The equation for a component A is

"rate" = k["A"]^m, where $m$ is the order of the reaction.

Zero Order

"rate" = k["A"]^0 = k

The rate does not depend on the concentration. Whatever you do to the concentration, the rate will not change.

First Order

"rate" = k["A"]^1 = k["A"]

The rate is directly proportional to the concentration.

If you double the concentration, you double the rate.
If you triple the concentration, you triple the rate.
If you halve the concentration, you halve the rate, and so on.

Second Order

"rate" = k["A"]^2

The rate is proportional to the square of the concentration.

If you double the concentration, you multiply the rate by four.
If you triple the concentration, you multiply the rate by nine.
If you halve the concentration, you divide the rate by four, and so on.

Since concentration changes during an experiment, we must measure the initial rate of the reaction, before the concentration has had a chance to decrease.

We set up an experiment and measure the rate. Then we do another experiment in which we change only the concentration of component A. Let's say we double the concentration of A.

If the rate did not change, the reaction was zero order in A.
If the rate doubles, the reaction is first order in A.
If the rate quadruples, the reaction is second order in A.

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