Rate law, order and molecularity

How does the rate depend on concentration? The rate law says:

Rate = k[A]^x[B]^y

k is the rate constant (also called the specific reaction rate): the rate when every concentration is 1 mol L⁻¹. Only reactants appear; products are not in the rate law.

The powers x and y are found by experiment. They are not the numbers in the balanced equation, and guessing them from the equation is a common mistake. The order of the reaction is their sum, x + y. An order can be 0, 1, 2, 3 or even a fraction.

The order tells you how the rate responds. If rate = k[A]², tripling [A] makes the rate 3² = 9 times faster.

To find the orders, use the initial rate method: run the reaction several times, changing one concentration at a time. If doubling [A] doubles the rate, the order in A is 1; if it makes it four times faster, the order is 2; if nothing changes, the order is 0.

The units of k depend on the order n. A general rule: (mol)^(1–n) (L)^(n–1) s⁻¹. Put in n:

• Zero order: mol L⁻¹ s⁻¹
• First order: s⁻¹
• Second order: L mol⁻¹ s⁻¹

So the units of k tell you the order straight away.

Most reactions happen in several small steps. A reaction that takes place in one single step is called elementary. For an elementary step we can count the molecularity: the number of particles that must collide at once for it to happen. It can only be 1, 2 or 3: never zero, never a fraction, and never more than 3, since four particles almost never hit each other at the same instant.

Order and molecularity are different things:

• Order comes from experiment, applies to the whole reaction, and can be zero or a fraction.
• Molecularity is a theoretical count for one elementary step and is always a small whole number.

In a reaction with several steps, the slowest step controls the overall rate, like the narrowest part of a funnel. It is the rate-determining step. For that one step, the rate law can be written straight from its equation.