All processes in the universe tend to follow a natural direction without outside help. This tendency for a process to occur without continuous external energy input is known as spontaneity. A spontaneous process continues on its own once started, regardless of speed. The fundamental concept governing this directionality is entropy, which measures the dispersal of energy and matter within a system. This dispersal represents the natural tendency toward greater disorder or randomness.
Defining Entropy and Spontaneity
The Second Law of Thermodynamics governs whether a process is spontaneous. This law states that for any spontaneous process, the total entropy of the universe must increase. The universe is conceptually divided into the system (the process under observation) and the surroundings (everything else). Therefore, the total change in universal entropy (\(\Delta S_{univ}\)) is the sum of the change in the system’s entropy (\(\Delta S_{sys}\)) and the change in the surroundings’ entropy (\(\Delta S_{surr}\)).
A process is spontaneous only if the total universal entropy change is positive. A system’s entropy (\(\Delta S_{sys}\)) can decrease, meaning it becomes more ordered, provided the surroundings become more disordered by a greater amount. For instance, a living organism maintains a highly ordered state by releasing heat and waste products that increase the entropy of its surroundings. The overall spontaneity of any process is determined by the net change across the entire universe, not just within the system.
How Enthalpy Influences the Process
Entropy is not the sole factor determining spontaneity in most real-world scenarios. The heat exchange between the system and its surroundings, measured by the change in enthalpy (\(\Delta H\)), also plays a significant role. Enthalpy change describes whether a process releases heat (exothermic, \(\Delta H\) is negative) or absorbs heat (endothermic, \(\Delta H\) is positive). This heat exchange directly affects the entropy of the surroundings (\(\Delta S_{surr}\)).
When a reaction is exothermic, it releases heat into the surroundings, increasing the random motion of surrounding molecules and thus increasing the surroundings’ entropy (\(\Delta S_{surr}\)). This increase favors a spontaneous process. Conversely, an endothermic reaction absorbs heat from the surroundings, which decreases the random motion of surrounding molecules and decreases the surroundings’ entropy.
To accurately predict spontaneity, the combined influence of enthalpy and entropy must be considered using the Gibbs Free Energy equation. This equation combines the system’s change in enthalpy (\(\Delta H\)) and the system’s change in entropy (\(\Delta S_{sys}\)) with the absolute temperature (\(T\)). A negative value for the change in Gibbs Free Energy (\(\Delta G\)) indicates that a process is spontaneous.
The Four Situations Determining Spontaneity
The interplay between enthalpy (\(\Delta H\)) and system entropy (\(\Delta S\)) results in four distinct scenarios, which reveal when entropy becomes the primary driving force. The first scenario involves a process that releases heat (\(\Delta H\) is negative) and simultaneously increases the system’s disorder (\(\Delta S\) is positive). Because both factors favor spontaneity, this type of process is always spontaneous regardless of the temperature.
The second scenario is the opposite: the process absorbs heat (\(\Delta H\) is positive) and decreases the system’s disorder (\(\Delta S\) is negative). In this case, both factors work against spontaneity, meaning the process will never be spontaneous under any temperature conditions.
In the third scenario, both \(\Delta H\) and \(\Delta S\) are negative; the process releases heat but becomes more ordered. This process is spontaneous only at low temperatures. At low temperatures, the favorable heat release (\(\Delta H\)) is the dominant factor. However, as temperature increases, the unfavorable decrease in entropy eventually overpowers the enthalpy, making the process non-spontaneous.
The fourth scenario is where entropy takes the lead: the process absorbs heat (\(\Delta H\) is positive) but also increases the system’s disorder (\(\Delta S\) is positive). This process is non-spontaneous at low temperatures, becoming spontaneous only when the temperature is high. At higher temperatures, the increasing magnitude of the temperature-scaled entropy term (\(T\Delta S\)) outweighs the positive enthalpy cost, driving the process forward. This is the specific condition under which entropy is the sole driving force for spontaneity.
Real-World Examples of Entropy at Work
Processes that are spontaneous only at high temperatures illustrate entropy as the driving force. A classic example is the melting of ice at standard atmospheric pressure. Ice turning into liquid water is endothermic, meaning it must absorb heat from the surroundings (\(\Delta H\) is positive).
However, the highly ordered crystalline structure of solid ice breaks down into the more random liquid state, resulting in a large increase in system entropy (\(\Delta S\) is positive). Below \(0^\circ\text{C}\) (low \(T\)), the process is non-spontaneous. Above \(0^\circ\text{C}\) (high \(T\)), the favorable entropy increase overcomes the unfavorable enthalpy cost, making the melting spontaneous. Another example is the diffusion of a perfume across a room. The fragrance molecules spontaneously spread out from a concentrated area into the larger volume, maximizing dispersal and increasing the total entropy.