Thermodynamics studies energy transformations and the natural directionality of processes, determining whether a change can occur by itself—a concept known as spontaneity. A spontaneous process has the intrinsic tendency to proceed without continuous external intervention. It is often assumed that spontaneity results simply from an increase in the system’s disorder. However, this focus on a single variable is misleading. Understanding the true conditions for a reaction requires considering the total energy balance of a process, moving beyond just the system’s internal disorder.
Defining Entropy and Spontaneity
Spontaneity measures a process’s inherent viability under specific conditions, typically constant temperature and pressure. It predicts whether a change can happen, but not how quickly; for instance, the transformation of diamond into graphite is thermodynamically favored but kinetically slow. Entropy, symbolized by \(\Delta S\), is often simplified as disorder.
A more accurate definition is the degree to which energy, particularly thermal energy, is dispersed among a system’s particles. When energy or matter spreads out, the number of possible microscopic arrangements (microstates) increases, resulting in a positive change in entropy (\(\Delta S > 0\)). This dispersal favors spontaneity.
Real-world examples illustrate this preference. When ice melts, the fixed arrangement of water molecules gives way to the greater freedom of motion in the liquid state, increasing energy dispersal and resulting in a positive \(\Delta S\). Similarly, perfume molecules sprayed in a room spontaneously spread out to fill the entire volume. While a positive \(\Delta S\) for the system is favorable, this factor alone does not guarantee spontaneity.
The Universal Rule: The Second Law of Thermodynamics
The limitation of looking only at the system’s entropy arises because the universe consists of the system (the process being studied) and the surroundings (everything else). The ultimate authority on spontaneity is the Second Law of Thermodynamics. This law states that for any process to be spontaneous, the total entropy of the entire universe (\(\Delta S_{universe}\)) must increase.
The total universal entropy change is the sum of the entropy change of the system (\(\Delta S_{system}\)) and the entropy change of the surroundings (\(\Delta S_{surroundings}\)). A process is spontaneous only if \(\Delta S_{universe} > 0\). This distinction explains why a process with a negative \(\Delta S_{system}\) can still be spontaneous.
For example, the freezing of water is spontaneous below \(0^\circ\)C, involving the formation of a more ordered solid (\(\Delta S_{system}\) is negative). However, freezing releases heat into the surroundings. This released heat significantly increases the thermal energy dispersal of the surroundings, leading to a large positive \(\Delta S_{surroundings}\). If the increase in the surroundings’ entropy is greater than the decrease in the system’s entropy, the total \(\Delta S_{universe}\) remains positive, and the process proceeds spontaneously.
Gibbs Free Energy: The True Predictor of Spontaneity
Because calculating \(\Delta S_{universe}\) is impractical, scientists use the Gibbs Free Energy change (\(\Delta G\)) to predict spontaneity under constant temperature and pressure. This quantity combines the system’s entropy change with its enthalpy change (\(\Delta H\)), which is the heat absorbed or released.
The relationship is defined by the equation \(\Delta G = \Delta H – T\Delta S\), where \(T\) is the absolute temperature in Kelvin. The criterion for spontaneity is straightforward: a process is spontaneous only if \(\Delta G\) is negative.
The equation shows that a positive \(\Delta S\) (which favors a negative \(\Delta G\)) is only one part of the calculation. If the process is highly endothermic (absorbs a large amount of heat, large positive \(\Delta H\)), this unfavorable enthalpy term can outweigh the favorable entropy term. For example, if a reaction has a positive \(\Delta S\) but requires significant energy input (\(\Delta H\) is large and positive), the resulting \(\Delta G\) will be positive, and the process will be non-spontaneous.
Positive entropy alone does not guarantee a spontaneous outcome. Spontaneity requires that the favorable entropy contribution (the \(-T\Delta S\) term), combined with the heat change (\(\Delta H\)), results in a net negative value for \(\Delta G\).
Temperature’s Influence on Reaction Outcomes
The absolute temperature (\(T\)) in the Gibbs Free Energy equation acts as a direct weighting factor for the entropy term, profoundly influencing the final outcome. The magnitude of the \(-T\Delta S\) term changes with temperature, which can tip the balance of spontaneity when enthalpy and entropy factors are in opposition.
For processes where enthalpy is unfavorable (\(\Delta H\) is positive) but entropy is favorable (\(\Delta S\) is positive), the process is only spontaneous at high temperatures. Increasing the temperature causes the \(-T\Delta S\) term to become a larger negative number, eventually overpowering the positive \(\Delta H\) and making \(\Delta G\) negative. This explains why melting ice is spontaneous above \(0^\circ\)C.
Conversely, if a process is enthalpy-favorable (\(\Delta H\) is negative) but entropy-unfavorable (\(\Delta S\) is negative), it is only spontaneous at low temperatures. A low temperature minimizes the magnitude of the \(T\Delta S\) term, keeping its positive contribution small so that the favorable negative \(\Delta H\) term dominates, ensuring \(\Delta G\) remains negative.