A rate law links a reaction's rate to reactant concentrations using the form $R = k[A]^n[B]^m$ , where $k$ is the rate constant and the exponents are reaction orders. You can only find a rate law from experimental data, often by comparing how the rate changes when one reactant's concentration changes at a time. For AP Chemistry, use initial-rate data to justify each reaction order instead of copying coefficients from the balanced equation.

Rate Law for AP Chemistry

In AP Chemistry, a rate law expresses reaction rate as proportional to reactant concentrations raised to powers, such as R = k[A]^n[B]^m. The powers are the reaction orders, their sum is the overall order, and k is the rate constant.

The most important exam move is that rate laws for overall reactions come from experimental evidence, not from the coefficients in the balanced equation. When you get an initial-rate table, compare trials where only one reactant changes, use the rate change to find that reactant's order, then plug one trial into the rate law to solve for k and its units.

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Why This Matters for the AP Chemistry Exam

Rate laws are a core skill in AP Chemistry kinetics. You need to be comfortable reading initial-rate tables, figuring out the order with respect to each reactant, writing the full rate law, and finding the value and units of the rate constant. This topic also sets up later work in the unit, including concentration versus time graphs, elementary reactions, and reaction mechanisms. Expect to explain how the rate changes when a concentration changes and to back up your rate law with data rather than just guessing from the balanced equation.

Key Takeaways

A rate law has the form R = k[A]^n[B]^m, where k is the rate constant and n and m are reaction orders.
Reaction orders must be found experimentally; you cannot read them off the balanced equation.
The order with respect to a reactant tells you how the rate responds when that reactant's concentration changes.
The overall order is the sum of the individual orders.
The rate constant k depends on temperature, and its units depend on the overall reaction order.
The method of initial rates works by changing one reactant's concentration while holding the others constant.

What is a Rate Law?

When the concentration of a reactant goes up, the rate of the reaction usually goes up too. That makes sense: more reactant particles in the same volume means more chances to react. But how do you describe exactly how much faster the reaction goes? That is the job of a rate law.

A rate law is an equation that relates the rate of a reaction to the concentrations of the reactants:

R = k[A]^n[B]^m...

where:

R is the rate of the reaction (sometimes written as the change in concentration over time, which the next topic covers in more depth),
k is the rate constant,
[A] and [B] are the concentrations of the reactants, and
n and m are the reaction orders for each reactant.

The "..." just means the pattern continues if there are more reactants. A reaction could in theory have three or more reactants, but on the AP exam you usually will not see more than two. Reactions that need three or more particles to collide at the same moment are rare, because getting that many particles to hit each other in just the right way at once does not happen often.

What Does Reaction Order Mean?

The exponents n and m are the reaction orders. The reaction order tells you how the rate changes as the concentration of that reactant changes.

For example, suppose the rate law for A + B yields C is R = k[A]^2[B]^1. With [B] held constant, doubling [A] makes the rate increase by a factor of 4 (2^2), because A is second order. With [A] held constant, doubling [B] makes the rate double, because B is first order. The same logic scales up: a third-order reactant would make the rate go up by 8 when its concentration doubles (2^3).

The overall reaction order is the sum of the individual orders. In the example above, the overall order is 3, since A is second order and B is first order.

Using Experiments to Determine a Rate Law

One key fact about rate laws: they can only be determined experimentally. A chemist runs the reaction many times at different concentrations, measures the rate for each run, and uses that data to figure out the orders. Here is how the math works.

Consider the reaction 2NO + 2H₂ yields N₂ + 2H₂O. Suppose three experiments are run with different starting concentrations and the initial rate is recorded for each.

Compare two experiments where [NO] changes but [H₂] stays constant:

If [NO] doubles and the rate increases from 1.25 x 10⁻⁵ to 5.00 x 10⁻⁵, that is a change by a factor of 4 (5.00 x 10⁻⁵ / 1.25 x 10⁻⁵ = 4).
Doubling the concentration made the rate quadruple, so the reaction is second order with respect to NO. Notice you had to pick two experiments where only [NO] changed.

Now compare two experiments where [H₂] changes but [NO] stays constant:

If [H₂] doubles and the rate increases from 5.00 x 10⁻⁵ to 1.00 x 10⁻⁴, that is a change by a factor of 2 (1.00 x 10⁻⁴ / 5.00 x 10⁻⁵ = 2).
Doubling the concentration doubled the rate, so the reaction is first order with respect to H₂.

Put it together to get the rate law: R = k[NO]²[H₂].

As practice, pick one experiment, plug in its concentrations and rate, and solve for k. You should get k = 250 M⁻²s⁻¹. After reading the next section, check that the units match the overall order.

If you guessed the orders straight from the coefficients in the balanced equation, you would write R = k[NO]²[H₂]². That is wrong here, which is exactly why rate laws must come from experimental data. The correct law is R = k[NO]²[H₂].

Understanding k, the Rate Constant

The rate constant k acts as the proportionality constant that connects rate to concentration. The main things you need to know: k is a constant that sets the rate for a given reaction, and it is temperature dependent. The same reaction at a different temperature has a different k.

The units of k change depending on the overall reaction order. Rate is always in M/s, and concentration is always in M (M = mol/L). Working backward from R = k[concentration]^order gives the units for each case:

Zeroth Order

If the overall reaction order is 0:

R = k[A]⁰ simplifies to R = k
k has units of M/s

First Order

If the overall reaction order is 1:

R = k[A]¹, so M/s = k x M
k has units of s⁻¹ (per second)

Second Order

If the overall reaction order is 2:

R = k[A]², so M/s = k x M²
k has units of M⁻¹s⁻¹ (1/(M·s))

How to Use This on the AP Chemistry Exam

Problem Solving

Read initial-rate tables by comparing pairs of experiments where only one reactant's concentration changes. Hold everything else constant to isolate one order at a time.
Find each order by asking: when this concentration changed by some factor, by what factor did the rate change? If doubling the concentration doubles the rate, the order is 1; if it quadruples the rate, the order is 2; if the rate stays the same, the order is 0.
After you have all the orders, solve for k by plugging one experiment's concentrations and rate into your rate law.
Always attach the correct units to k. Let the overall order tell you the units, and double-check that M/s comes out when you multiply k by the concentration terms.

Free Response

Justify your rate law with specific numbers from the data, not just the balanced equation. State which two experiments you compared and how the rate responded.
When you explain how the rate changes, connect it to the order. For example, "the reaction is second order in NO, so doubling [NO] increases the rate by a factor of four."

Common Trap

Do not assume the exponents in a rate law match the coefficients in the balanced equation. They only match for an elementary step, which is a later topic.

Common Misconceptions

Rate orders come from the balanced equation. They do not, except for elementary reactions. For an overall reaction, orders come from experimental data.
k changes when concentration changes. It does not. k stays the same at a fixed temperature no matter the concentrations; only the rate changes. k does change with temperature.
k always has the same units. Its units depend on the overall reaction order, so a first-order k and a second-order k have different units.
Overall order equals the number of reactants. Overall order is the sum of the exponents in the rate law, which may not match how many reactants there are.
A higher order means a faster reaction. Order describes how sensitive the rate is to concentration changes, not the overall speed. Speed also depends on k and the actual concentrations.

zero order.

Can you get a rate law from the balanced equation?

Not for an overall reaction. Rate laws must be determined experimentally unless the reaction is given as an elementary step, which is covered later in the kinetics unit.

What is the overall order of a reaction?

The overall order is the sum of the exponents in the rate law. For R = k[A]^2[B], the reaction is second order in A, first order in B, and third order overall.

How do you find the rate constant k?

After you know the rate law, plug in the rate and reactant concentrations from one experiment, then solve for k. The units of k depend on the overall reaction order.

What are the units of k in a rate law?

The units of k change so that the rate comes out in M/s. For zeroth order, k has units of M/s; for first order, s^-1; and for second order, M^-1s^-1.

Vocabulary

The following words are mentioned explicitly in the College Board Course and Exam Description for this topic.

Term	Definition
initial rates method	An experimental technique for determining reaction order by comparing the initial rates of a reaction under different initial concentrations of reactants.
overall order	The sum of all the individual reaction orders (powers) for each reactant in the rate law expression.
rate constant	The proportionality constant in a rate law expression that relates reaction rate to reactant concentrations; its value depends on temperature.
rate law	A mathematical expression that relates the reaction rate to the concentrations of reactants, with each concentration raised to a power (order).
reactant concentration	The amount of a reactant present in a given volume of solution, typically expressed in molarity (mol/L).
reaction order	The power to which the concentration of a reactant is raised in the rate law expression; indicates how the reaction rate depends on that reactant's concentration.
reaction rate	The speed at which reactants are converted to products per unit of time in a chemical reaction.

Frequently Asked Questions

What is a rate law in AP Chemistry?

A rate law is an equation that relates reaction rate to reactant concentrations. A common form is R = k[A]^n[B]^m, where k is the rate constant and the exponents are reaction orders.

How do you determine reaction order from initial rates?

Compare two trials where only one reactant concentration changes. If doubling that concentration doubles the rate, the reactant is first order. If doubling it quadruples the rate, it is second order. If the rate does not change, it is zero order.