Animated Solution for Chemistry - Chemical Kinetics: For a reaction $A+2B⟶C$, rate is given by $+\frac{d[C]}{dt}=k[A][B]$, hence the order of the reaction is

Have you ever wondered how chemists determine the speed of a reaction? It's not just about mixing chemicals and watching them fizz; there's a deep mathematical rhythm to it. Let's dive into a classic problem that perfectly illustrates the difference between what a reaction looks like and how it actually behaves.

A Deceptive Equation

We are given a chemical reaction:

At first glance, you might think, "Ah, one molecule of A reacts with two molecules of B. That's three molecules colliding together!" In chemistry, the number of reacting species in an elementary step is called its molecularity. So, the molecularity here appears to be 3.

But wait! The problem also gives us the rate law for this reaction:

This equation is the true master of the reaction's speed. It tells us exactly how the rate depends on the concentrations of the reactants.

The general form of a rate law is:

Here, $k$ is the rate constant, and the exponents $x$ and $y$ represent the order of the reaction with respect to each reactant. The overall order of the reaction is simply the sum of these exponents: $x+y$.

Now, let's look closely at our given rate law:

Notice anything missing? There are no numbers written as powers for $[A]$ and $[B]$. In mathematics, when a variable has no explicit exponent, it is implicitly raised to the power of 1. So, we can rewrite our rate law as:

This means the reaction is first-order with respect to A ($x=1$) and first-order with respect to B ($y=1$).

To find the overall order of the reaction, we just add these exponents together:

So, the reaction is a second-order reaction.

This problem highlights a crucial concept in chemical kinetics: The order of a reaction cannot be predicted from the balanced chemical equation.

Even though the balanced equation has a stoichiometric coefficient of 2 for B, the experimental rate law shows that the rate only depends on $[B]$ to the first power. The order is strictly an experimental quantity, while molecularity is a theoretical concept derived from the reaction mechanism. Always trust the rate law!