Catalysts and the Maxwell-Boltzmann distribution

​​In a nutshell

Catalysts increase the rate of reaction. This is helpful in industry as faster reactions reduce energy costs and saves time.

Catalysts

A catalyst increases the rate of reaction by providing an alternative reaction pathway with a lower activation energy. It remains unchanged at the end of the reaction. Each catalyst is specific to a reaction. Only a small amount of a catalyst is required to increase the rate of reaction. 

Catalysts do take part in reactions, but they are completely remade by the end of the reaction. Therefore, they remain unchanged. 

Reaction profiles

Heterogeneous catalysis 

A heterogeneous catalyst is a catalyst that is in a different physical state relative to the reactants and products. It's in a different phase. They work by providing an alternative reaction pathway with a lower activation energy. This means the rate of reaction will increase since a higher proportion of molecules will reach the activation energy and will be able to react. 

The red dotted curve is the reaction with the catalyst. The peak is lower because the activation energy is lower. 

1: Reactants, 2: Products.

Catalysts are very specific to which reaction they catalyse. The way heterogeneous catalyst take part in the reaction is by adsorption and desorption.

The adsorption process is when the reactants bind onto the surface of the catalyst. This causes the bonds in the reactants to break, forming radicals. Radicals are molecules with unpaired electrons. The radicals react together and form the products. Then desorption occurs. This is when the products leave the surface of the catalyst.

Example 

​$$N_2(g)+3\>H_2(g)⇌2\>NH_3(g)$$​​

The production of ammonia from nitrogen and hydrogen is catalysed by iron. Iron is a solid and all the reactants and products are gaseous. Therefore, iron is a heterogeneous catalyst in this reaction.

The hydrogen and nitrogen adsorb onto iron. Once ammonia forms, it desorbs. 

Homogeneous catalysis 

A homogeneous catalyst is a catalyst that is in the same physical state relative to the reactants and products. It's in the same phase. They work by reacting with the reactants to form an intermediate species. The activation energy required is lower than the uncatalysed reaction's activation energy. 

The activation energy required for the intermediate species to react to form the product is lower than the uncatalysed reaction's activation energy. The catalyst is remade. Therefore, the catalyst remains unchanged by the end of the reaction. The catalysed reaction is shown by the solid, black curve below. 

The catalysed reaction has two peaks that have a lower activation energy than the uncatalysed reaction. The intermediate species are formed in between the two peaks. 

1: Reactants, 2: Products, 3: Intermediates, 4: Reaction without a catalyst.

Maxwell-Boltzmann distribution

Catalysts provide an alternative reaction pathway with a lower activation energy. This means the molecules requires less energy to react. This can be shown in the Maxwell-Boltzmann distribution by simply putting the activation energy at a lower energy (shifted to the left on the x-axis). 

The activation energy is lowered when a catalyst is added. 

Catalyst's benefits

Catalysts increase the rate of reaction allowing a lower temperature to be used. This lowers the energy costs. For reversible exothermic reactions, lower temperatures will favour the forward reaction. This means the product is formed more and it's less likely to favour the backward reaction. Hence, the product yield will be higher. 

Catalysts can also produce more useful products. They can make the product more rigid and dense with higher melting points. This increases the profit of the product produced as they can sell it. 

Catalysts also benefit the environment. Due to the increased rate of reaction, less fossil fuels are used for the reactions. This means less $$CO_2$$​ is emitted into the air. Therefore, they make lower contributions to global warming.