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Why is an exothermic reaction spontaneous?
Exothermic reactions are not necessarily spontaneous.
Take the combustion of magnesium for example:
##DeltaH## is negative.
Yet a piece of magnesium is quite safe to handle at room temperature.
This is because a very high temperature is needed to make the magnesium burn. The reaction has a very high activation energy.
This is shown in the diagram:
A low activation energy can result in the reaction being spontaneous.
A good example is sodium reacting with water.
The diagram shows two important areas of physical chemistry.
The ##color(red)("red")## arrow relates to thermodynamics and is concerned with initial and final states.
The ##color(purple)("purple")## arrow relates to kinetics and is concerned with how quickly the change from initial to final state is achieved.