How To Calculate Rate Of Reaction

A reaction occurs when particles collide. In this collision the particles transfer enough energy to break old bonds and make new ones. But how can you define the rate at which a reaction occurs?

Take a look at a simple reaction like the one below:

\(A\enspace \rightarrow\enspace B\)

In this reaction some reactant A is turned into some product B. The rate of reaction can be represented by a decrease in concentration of A over time or as the increase of B over time. This is written:

\(rate\enspace = -\dfrac{\Delta[A]}{\Delta t} = \dfrac{\Delta[B]}{\Delta t}\)

Since A decreases over time there is a negative sign in front of this rate. The rates expressed here are average rates because they are averaged over some amount of time.

The reaction rate, or the speed that the reaction happens at, is written as the change in concentration of a reactant or product per change in time as shown above.

In order to calculate this experimentally you have to monitor either the concentration of the reactant or product as a function of time. Once you have measurements at different times you can then plot these values and find the instantaneous rate of the reaction or the slope of the line.

Pretend you are looking at the reaction between A and B, which forms C and D. Obviously, the formation of product depends on both A and B. But, by adding an excess of one, say B, you can ensure that the concentration of B remains essentially constant. In this way the change in the amount of B will not affect the measured rate of reaction.

Then, you can plot the rate at different concentrations of A. This will allow you to see whether rate is proportional to the concentration of reactants.

Say that when you plot rate vs. concentration of A it yields a straight line. This means that the rate is directly proportional to the concentration of A. As a result, the higher the concentration of A, the higher the rate.

This can be represented as such:

\(k\enspace =\enspace \dfrac{rate}{[A]}\)

The variable k is known as the rate constant. It is a constant of proportionality between the rate of the reaction and the concentrations of reactants. The variable k is not affected by the concentration of the reactants. It is a ratio of the rate and the reactant concentration. This value k is only affected by temperature.

Since concentration is measured in molarity, the change in concentration is measured in M while the time is measured in seconds. This means that the units for k are usually 1/s or s^-1.

For stoichiometry, simple reactions like the mol to mol ratio between components is equal. For example, when A turns to B, one mol of A is lost for each mol of B made.

Not all reactions are this simple.

Consider the following reaction:

\(3A\enspace \rightarrow\enspace B\)

Each time B is made, 3 moles of A are used. This can be expressed as such:

\(rate\enspace = -\dfrac{1}{3} \dfrac{\Delta[A]}{\Delta t} = \dfrac{\Delta[B]}{\Delta t}\)

In general, for the reaction:

\(aA+bB\rightarrow cC+dD\)

The rate is given as follows:

\(rate\enspace = -\dfrac{1}{a} \dfrac{\Delta[A]}{\Delta t} = -\dfrac{1}{b} \dfrac{\Delta[B]}{\Delta t} = \dfrac{1}{c} \dfrac{\Delta[C]}{\Delta t} = \dfrac{1}{d} \dfrac{\Delta[D]}{\Delta t}\)

The rate law expresses the relationship of the rate of a reaction to the rate constant and the concentrations of reactants raised to some power.

For a general reaction:

\(aA+bB\rightarrow cC+dD\)

The rate law is written as:

\(rate = k[A]^x[B]^y\)

A and B are the reactions. k is the rate constant. x and y are numbers that must be determined experimentally. Once x and y are known, the input of any reactant concentration can be used to find the rate of the reaction.

x and y are important because the give a relationship between the concentrations of reactants A and B and the reaction rate. They also give the reaction order when added together. The reaction order is the sum of the power to which reactant concentrations in the rate law are raised.

As discussed above, the rate law is a mathematical relationship that shows you how changing reactant concentration affects the rate of the reaction. So, how can you find the rate law?

Take a look at the following reaction of hydrogen and nitric acid:

\(2H_2+2NO \rightarrow N_2+2H_2O\)

To find the order, you need to know the exponents of the rate law which would be written:

\(rate = k[H_2]^x[NO]^y\)

This requires use of data that indicates reactant concentration and initial rate.

Consider the following data:

The order of a reaction tells you how rate changes with reactant concentration.

First order reactions are reactions whose rate depends on the reactant concentration raised to the first power. This means that when the concentration of a reactant is doubled so is the rate.

Many decomposition reactions are first order. An example is the decomposition of N₂O₅:

\(N_2O_5 \rightarrow 4NO_2 + O_2\)

Second order reactions are reactions whose rate depends on the concentration of one reactant to the second power or on the concentrations of two reactants each to the first power.

One example of a second order reaction is the combination of iodine to form molecular iodine in the gas phase:

\(I(g)\enspace +\enspace I(g) \rightarrow I_2(g)\)