Catalyst is a substance that increases a reaction rate and decrease the activation energy of the chemical reaction without itself being consumed in the reaction. The energy released or absorbed by a chemical reaction is exactly the same whether a catalyst is present or not. A catalyst only affects the reaction rate.
Three main types of catalysis are Heterogeneous Catalysis, Homogeneous Catalysis and enzyme Catalysis.
Heterogeneous catalyst is a catalyst that is in a separate phase from the reactants.  Heterogeneous catalysis is widely used in industrial manufacture of chemicals. The catalyst is usually in the solid phase and the reactants are either gaseous or liquid. The gas or liquid molecules bond temporarily to the atoms at the surface of the catalyst, which allows their internal bonds to break more rapidly or at a lower temperature.
Heterogeneous catalysis can be devided naturally into two distinct groups, metals and non metals. The advantage of this catalyst: better separation from the product, ease of recovery and recycling, atom utility, and enhanced stability in the oxidation reaction.
The Haber Synthesis of Ammonia 
Probably the most important industrial process converts nitrogen gas and hydrogen to ammonia for use in fertilizer. The reaction is exothermic (energetically favorable) but it is very slow.
H2 (g) + N2(g) → NH3(g)
H2 molecules adhere readily to the surface of an iron metal catalyst and dissociate readily into H atoms which allows them to react rapidly with nitrogen gas. The reaction proceeds much faster at 500 ºC than it would without the catalyst and makes the reaction an economically process.
Homogeneous catalyst are those in the same physical phase as other reactants. Homogeneous implies that the reaction takes place in solution (a homogeneous system), with the soluble catalyst also in solution. 
The classic example is the catalysis of ester hydrolysis by hydrogen ion. 
CH3COC2H5 + H2O → CH3COOH + C2H5OH
Without H+1 the process is very slow and the rate depends only on ester concentration.
Rate = k [CH3COC2H5]
With H+1, it is much more rapid and the catalyzed reaction is second order, that is first order with respect to both ester and hydrogen ion concentration.
Rate = kc [CH3COC2H5] [H+1]
By the definition of catalysis, kc > k
Enzymes are biological catalysts, always or almost always protein in nature that speed up many biological reactions. Enzymes have an active site, where the substrate attaches in order for its bonds to be weakened. Life as we know it would not exist without enzymes to speed up otherwise sluggish reactions. Enzymes are very substrate specific, since their active sites will only accept a substrate of the right size, shape and charge distribution and hydrogen bonding capability. 
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