Spontaneous process
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A spontaneous process in chemical reaction terms is one which occurs with the system releasing free energy in some form (often, but not always, heat) and moving to a lower energy, hence more thermodynamically stable, state. The sign convention is the same as for exothermic/endothermic reactions, with a release of free energy corresponding to a negative change in G (the Gibbs free energy).
Thus, for a reaction at constant temperature where
ΔG = ΔH -TΔS
a negative ΔG would require a negative change in enthalpy (ie an exothermic reaction) and/or a positive change in the entropy.
This is a direct consequence of the second law of thermodynamics, which states that for 'any' spontaneous process the overall change in entropy of the system must be greater than or equal to zero. Can a spontaneous chemical reaction have a product with a lower entropy than the reactants? Yes it can. This does not contradict the second law however, since such a reaction must have a sufficiently large negative change in enthalpy (heat energy) that the increase in temperature of the reaction surroundings (considered to be part of the system in thermodynamic terms) results in a sufficiently large increase in entropy that overall the change in entropy is positive. Another way to view the fact that some spontaneous chemical reactions can lead to products with lower entropy than its reactants -and how this does not contradict the second law of thermodynamics is to realize that the law states that entropy of a closed system must increase (or remain constant). Since a positive enthalpy means that energy is being released to the surroundings, then the 'closed' system includes the chemical reaction plus its surroundings. This means that the heat release of the chemical reaction sufficiently increases the entropy of the surroundings such that the over-all entropy of the closed system increases -in accordance with the second law of thermodynamics.
This is why so many spontaneous reactions are exothermic. The release of heat energy creates a large increase in entropy. A spontaneous endothermic reaction (one which absorbs heat) must have a sufficiently large increase in the entropy of the products that it offsets the decrease in the entropy of the surroundings.
Many important reactions are not spontaneous, and require the external addition of energy to drive them forward eg aluminium smelting, iron smelting.
In simplified terms a spontaneous reaction means a reaction that can happen or happens without outside intervention. Keep in mind though that just because a chemist may call a reaction “spontaneous” does not mean the reaction happens with great speed. For example the decay of diamonds into graphite is a spontaneous process (A diamond is forever... not!) but this decay is extremely slow and takes millions of years. Thus the rate of a reaction is independent of its spontaneity. A non-spontaneous reaction (or process) on the other hand is a reaction that will never happen unless with outside intervention. For example table salt (NaCl) will not spontaneously separate into Sodium metal and Chlorine gas, unless it is greatly heated or forcibly separated in electrolysis