# Rate of Reaction

The rate of a reaction depends on many factors such as the concentration of reactants, the temperature at the time of the reaction, the states of reactants, and catalysts. The rate of a reaction is defined as the change of reactant or product concentration in unit time. If we were to define the rate of a reaction in terms of the reactants, we should define the rate as the rate of disappearance of reactants. If we were to define the rate in terms of the products formed, we should define it as the rate of appearance of products.

For further exploration of this concept, let's look at a hypothetical reaction. In the hypothetical representative reaction shown below, the small letters denote the coefficients of the corresponding capital letter reactants or products. In this reaction, A and B are reactants, and a and b their coefficients respectively. X and Y are the products, and x and y their coefficients respectively.

For this reaction, we can represent the rate in terms of the disappearance of each reactant or appearance of each product. The numerators are the concentrations of either the reactant or the product, and Dt represents the elapsed time.

We can also represent it in terms of reactant B. That looks the same as the rate in terms of concentration of A. In order to express it in terms of B's concentration, substitute the numerator with the concentration of B. The minus sign convention indicates that the rate is expressed in terms of the rate of disappearance (decreasing concentration) of the reactants.

Also shown below are the representations of the rate in terms of the products:

# Rate Law

Rate law is an expression that we can find experimentally, which relates the concentration of reactants and the rate of a reaction. Let's consider the same hypothetical equation:

For this reaction, we can write the rate as follows:

Rate = k [A]m [B]n

Here, k is the rate constant,
m and n are the corresponding exponential values, and
[A] and [B] are the concentrations of reactants A and B.

Note that the rate constant and the exponents of a reaction are found experimentally. For questions related to finding the actual rate expression of a reaction, you will be given the relevant experimental data. We will look at some examples to familiarize ourselves with this concept.

We mentioned the exponent values (for this reaction, we represented them as m and n) in the rate law. Those exponents represent the order with respect to a particular reactant, or by adding all the exponents, you will get overall order of the reaction. For our hypothetical reaction, the reaction order with respect to reactant A is m. The order with respect to reactant B is n. The overall order of the reaction is m+n. That is one way to determine the order of a reaction. Chemists categorize them as first order, second order, etc. You may have heard of zero order. In some reactions, even if a reactant appears in the balanced equation of a reaction, it may not appear in the experimentally found rate expression. The reason for this is that the particular reactant that does not appear in the rate expression has an exponent of 0. So the order with respect to that reactant is zero.

Example
From the given experimental data, determine the rate law of the hypothetical reaction indicated below:

Solution

The rate of the reaction will have the general look as shown. Assume that the rate law of the reaction is:

Rate = k [ P ]m [ Q ]n

The plan is to find out the actual values of m and n from the given data. Let's do it step by step.

Look at the given experimental data. If we compare Experiments 1 and 2, we can see that the concentration of Q is doubled in Experiment 2. But the concentration of P is kept constant. With these changes, we see the quadrupling of the rate. That means the exponent of Q is 2. At this point we can rewrite the rate law as follows:

Rate = k [ P ]m [ Q ]2

Now compare Experiments 2 and 3. Here the concentration of Q is kept constant, but the concentration of P is doubled. The rate is doubling because of this change. So the exponent of P is 1. We can now write the completed rate law of the reaction.

Rate = k [ P ] [ Q ]2