Describe the meaning of a spontaneous reaction in terms of enthalpy and entropy changes. Define free energy. Determine the spontaneity of a reaction based on the value of its change in free energy at high and low temperatures.

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The change in enthalpy and change in entropy of a reaction are the driving forces behind all soimg.orgical reactions. In this lesson, we will examine a new function called free energy, which combines enthalpy and entropy and can be used to determine whether or not a given reaction will occur spontaneously.

## Spontaneous Reactions

A spontaneous reaction is a reaction that favors the formation of products at the conditions under which the reaction is occurring. A roaring bonfire (see figure below) is an example of a spontaneous reaction. A fire is exothermic, which means a decrease in the energy of the system as energy is released to the surroundings as heat. The products of a fire are composed mostly of gases such as carbon dioxide and water vapor, so the entropy of the system increases during most combustion reactions. This combination of a decrease in energy and an increase in entropy means that combustion reactions occur spontaneously.

Figure $$\PageIndex{1}$$: Combustion reactions, such as this fire, are spontaneous reactions. Once the reaction begins, it continues on its own until one of the reactants (fuel or oxygen) is gone.

A nonspontaneous reaction is a reaction that does not favor the formation of products at the given set of conditions. In order for a reaction to be nonspontaneous, one or both of the driving forces must favor the reactants over the products. In other words, the reaction is endothermic, is accompanied by a decrease in entropy, or both. Out atmosphere is composed primarily of a mixture of nitrogen and oxygen gases. One could write an equation showing these gases undergoing a soimg.orgical reaction to form nitrogen monoxide.

\<\ce{N_2} \left( g \right) + \ce{O_2} \left( g \right) \rightarrow 2 \ce{NO} \left( g \right)\>

Fortunately, this reaction is nonspontaneous at normal temperatures and pressures. It is a highly endothermic reaction with a slightly positive entropy change $$\left( \Delta S \right)$$. However, nitrogen monoxide is capable of being produced at very high temperatures, and this reaction has been observed to occur as a result of lightning strikes.

One must be careful not to confuse the term spontaneous with the notion that a reaction occurs rapidly. A spontaneous reaction is one in which product formation is favored, even if the reaction is extremely slow. You do not have to worry about a piece of paper on your desk suddenly bursting into flames, although its combustion is a spontaneous reaction. What is missing is the required activation energy to get the reaction started. If the paper were to be heated to a high enough temperature, it would begin to burn, at which point the reaction would proceed spontaneously until completion.

In a reversible reaction, one reaction direction may be favored over the other. Carbonic acid is present in carbonated beverages. It decomposes spontaneously to carbon dioxide and water according to the following reaction.

\<\ce{H_2CO_3} \left( aq \right) \rightleftharpoons \ce{CO_2} \left( g \right) + \ce{H_2O} \left( l \right)\>

If you were to start with pure carbonic acid in water and allow the system to come to equilibrium, more than $$99\%$$ of the carbonic acid would be converted into carbon dioxide and water. The forward reaction is spontaneous because the products of the forward reaction are favored at equilibrium. In the reverse reaction, carbon dioxide and water are the reactants, and carbonic acid is the product. When carbon dioxide is bubbled into water (see figure below), less than $$1\%$$ is converted to carbonic acid when the reaction reaches equilibrium. The reverse of the above reaction is not spontaneous. This illustrates another important point about spontaneity. Just because a reaction is not spontaneous does not mean that it does not occur at all. Rather, it means that the reactants will be favored over the products at equilibrium, even though some products may indeed form.

Figure $$\PageIndex{3}$$: Ice melts spontaneously only when the temperature is above $$0^\text{o} \text{C}$$. The increase in entropy is then able to drive the unfavorable endothermic process.

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When the reaction is exothermic (negative $$\Delta H$$) but undergoes a decrease in entropy (negative $$\Delta S$$), it is the enthalpy term which favors the reaction. In this case, a spontaneous reaction is dependent upon the $$T \Delta S$$ term being small relative to the $$\Delta H$$ term, so that $$\Delta G$$ is negative. The freezing of water is an example of this type of process. It is spontaneous only at a relatively low temperature. Above $$273. \: \text{K}$$, the larger $$T \Delta S$$ value causes the sign of $$\Delta G$$ to be positive, and freezing does not occur.