The Effect of Temperature on the Rate of Reactions

Chemical reactions, in general, show an increase in the rate of reaction for an increase in temperature. For example, it takes about 6-12 minutes to boil 1 liter of water at 100°. However, when left in the open at room temperature, the same amount of water may take hours to evaporate. This is because water starts turning into vapor quicker as we increase the temperature. Similarly, ice cream melts quicker on a hot day than in winter.

It may be observed then that with a rise in temperature of about 10°, the effect of temperature on the rate of reaction and the rate of a chemical reaction is doubled. The chemical kinetics of a reaction shows that temperature changes result in a change in concentrations of reactants. This helps us look at a chemical reaction at microscopic levels and consider factors like collisions between particles. To understand how the collision model works, first, we need to understand some microscopic factors that influence reaction rates.

Collision Frequency

The number of collisions that a molecule makes with other molecules per unit time, or collision frequency f. When a question like ‘what is the effect of temperature on the rate of reaction’ is asked, it can be answered that a chemical reaction occurs when molecules, atoms, or ions collide. Therefore, the frequency of collisions influences the reaction rate with an increase in the temperature of reactants, and the average kinetic energy of particles increases. Since speed is proportional to the square root of kinetic energy, increasing temperature increases collisions per unit time. The more the collision frequency is, the faster the reaction happens and vice versa.

Activation Energy

The activation energy of a chemical reaction is kind of like that “hump” you have to get over to get yourself out of bed. Even energy-releasing (exergonic) reactions require some amount of energy input to get going, before they can proceed with their energy-releasing steps. This initial energy input, which is later paid back as the reaction proceeds, is called the activation energy 

We will take an example where Nitrous Oxide (NO) reacts to ozone (O3), which plays an integral part in the depletion of the ozone layer:

NO (gas) + O3 (gas) → NO2 (gas) + O2 (gas)

By increasing temperature from 250K to 350K, the rate constant increases by a factor of more than 10, whereas the increase in the frequency of collisions is 30%. This shows that there is something other than the increase in collision frequency.

The experimental rate law gives rate = k[NO][O3]

This helps to explain the effect of temperature on the rate of reaction. Rate constant doesn’t change with temperature; it remains constant. The figure below shows a graph of the rate constant of NO reaction with ozone at varying temperatures. As you can see – the curve is not linear. Not all particles react to form a product, only that fraction of particles with energy more than the activation energy do.

Sterics

Even when the collision energy between two reactant modules is greater than Ea (activation energy), most collisions may not yield a product. This is because the reaction depends not only on collisions but also on the direction of the collision. 

For example, in the reaction of NO with ozone to produce NO2 and O2, terminal oxygen of ozone must collide with the nitrogen of NO at such an angle which allows ozone to give an oxygen atom to NO to produce NO2 compound. Only those orientations lead to reaction and contribute to the Steric factor. The steric factor is the fraction of orientations that lead to a reaction.

The Arrhenius Equation

With the help of the Arrhenius equation, we can easily show the effect of temperature on the reaction rate. Temperature dependence of reaction was first proposed by the Dutch physical chemist J. H. van ‘t Hoff. But Arrhenius gave a physical justification and interpretation. 

k = Ae-(Ea/RT)

Here A is the Arrhenius factor or the frequency factor, also called a pre-exponential factor; it is constant for a particular reaction. R is gas constant. Ea is the activation energy. The above equation gives the rate of reaction as a function of temperature.

Let’s take an example of the formation of hydrogen iodide by reaction of hydrogen and iodine.

H2 (gas) + I2 (gas) → 2HI (gas)

According to Arrhenius, an intermediate forms when reactants hydrogen and iodine react, which exists for a brief period which ultimately breaks up to form hydrogen iodide. And the required energy to do this operation is called activation energy.

Knowing the reaction rate at various temperatures, the Arrhenius equation can be used to calculate the activation energy. We get the following while applying the natural logarithm on both sides of the Arrhenius equation.

ln k = ln A + (-Ea/RT)

       = ln A + [(-Ea/RT)(1/T)]

we here get an equation of a straight line, y =mx + b

where y = ln k and x = 1/T

We only need to measure the reaction rate at two temperatures to measure activation energy. Arrhenius’ equation mathematically shows the effect of temperature on the reaction rate.

Conclusion

Either for an endothermic reaction where products have higher potential energy than reactants or an exothermic reaction where products have lower potential energy than reactants, Activation energy needs to be overcome to form activated complexes and then to form reactants. The activation energy is always positive and needs to be given to the reaction where the total energy changes may be positive, negative, or zero.