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What activation energy
Minimum energy particles must have in order to start a reaction by breaking chemical bonds.
The enthalpy different between reactants and transition state

Whats the transition state
Represents an unstable moment where old bonds are actively breaking and new bonds are forming.
What do catalysts do
Speed up reaction by allowing reaction to take place via an alternative pathway with a lower activation energy than the uncatalysed reaction
How does using catalysts help
They are not used up in reactions and are reusable
Reduces amount of energy needed by chemical industry, reduces need to burn fossil fuels to provide this energy, saves money providing economic benefit.
Reduces CO2 emissions, making chemical industry more sustainable.