The question of whether an exothermic reaction will have a positive or negative change in entropy is a common source of confusion when exploring chemical thermodynamics. Chemical reactions are driven by fundamental tendencies, including seeking a state of lower energy and a state of greater molecular disorder. While these two concepts are often related, they are independent. The relationship between energy release and disorder change is central to predicting the ultimate fate of any chemical process.
Defining Exothermic Reactions and Entropy
Exothermic reactions are processes defined by the release of energy, typically as heat, into the surrounding environment. This energy change is quantified by the change in enthalpy, symbolized as Delta H, which is always a negative value for an exothermic reaction. Combustion reactions, such as the burning of natural gas or the oxidation of iron in a hand warmer, are classic examples of this heat-releasing phenomenon.
The concept of entropy, symbolized as Delta S, is a measure of the molecular disorder or randomness within a system. A positive change in entropy (Delta S > 0) means the system has become more disordered, often occurring when phase changes increase molecular freedom or when the number of molecules increases during a reaction. Conversely, a negative change in entropy (Delta S < 0) indicates that the system has become more ordered, such as when a gas condenses or when multiple reactants combine to form a single, complex product. The universe generally favors an increase in disorder.
Entropy is Not Determined by Exothermicity
The change in enthalpy (Delta H) and the change in entropy (Delta S) are independent variables. Knowing a reaction is exothermic does not automatically determine the sign of its entropy change. An exothermic reaction can easily proceed with either an increase or a decrease in molecular disorder, even though the universal tendency favors both lower energy and higher disorder.
A common example of an exothermic reaction with a positive entropy change (Delta S > 0) is the combustion of methane. The reaction releases substantial heat (Delta H < 0). The reaction converts three gas molecules (one methane, two oxygen) into four gas molecules (two carbon dioxide, two water vapor), leading to a net increase in disorder and molecular freedom. Many exothermic processes result in a negative entropy change (Delta S < 0), meaning the system becomes more organized. The formation of water from gaseous hydrogen and oxygen is an example, as three reactant molecules combine to form only two product molecules, reducing the total number of gas molecules and decreasing disorder. Similarly, the formation of a highly ordered solid, such as rust (iron oxide), from gas-phase oxygen is an exothermic process that results in a significant decrease in entropy.
Combining the Factors: Gibbs Free Energy
To predict whether a chemical reaction will occur spontaneously, chemists use the Gibbs Free Energy change, symbolized as Delta G. Spontaneity is defined by a negative Delta G value (Delta G < 0), which indicates that the reaction is energetically favorable to proceed on its own. A positive Delta G means the reaction is non-spontaneous and requires continuous energy input. The Gibbs Free Energy equation mathematically combines the two competing factors of energy and disorder: Delta G = Delta H - T Delta S. In this equation, Delta H is the enthalpy change, Delta S is the entropy change, and T is the absolute temperature in Kelvin. The equation shows that the total energy change (Delta G) is a balance between the energy released by the reaction (Delta H) and the energy associated with the change in disorder (T Delta S). The Delta H term represents the drive toward lower energy, while the T Delta S term represents the influence of disorder. The negative sign in front of the T Delta S term means that a positive entropy change (Delta S > 0) contributes to a more negative, and therefore more spontaneous, Delta G. Thus, the universe’s two fundamental preferences—releasing energy and increasing disorder—both work to make a reaction spontaneous.
The Role of Temperature in Spontaneity
Temperature (T) plays a role in determining the spontaneity of an exothermic reaction, especially when the factors of energy and disorder oppose each other. When an exothermic reaction has a positive entropy change (Delta H < 0 and Delta S > 0), both terms in the Gibbs equation are favorable for spontaneity. Since the enthalpy term (Delta H) is negative and the entropy term (-T Delta S) is also negative, Delta G is guaranteed to be negative at all temperatures. This type of reaction is always spontaneous.
The complex situation occurs when an exothermic reaction involves a decrease in entropy (Delta H < 0 and Delta S < 0). Here, the energy release is favorable (Delta H is negative), but the increase in order is unfavorable (-T Delta S becomes a positive value). The spontaneity of the reaction is then a contest between the magnitude of the negative Delta H and the magnitude of the positive T Delta S term. At low temperatures, the T Delta S term is small, allowing the negative Delta H term to dominate the equation, resulting in a negative Delta G. This means the reaction is spontaneous when the energy release outweighs the penalty of creating order. The Haber synthesis, which forms ammonia and creates fewer gas molecules (Delta S < 0), is an example that is spontaneous only at lower temperatures. If the temperature is raised too high, the positive T Delta S term will eventually become larger than the negative Delta H term, causing Delta G to become positive and the reaction to lose spontaneity.