What Is Delta S in Chemistry? Entropy Change Explained

In chemistry, ΔS (“delta S”) is the change in entropy during a process. It equals the entropy of the final state minus the entropy of the initial state:

[ \Delta S = S_{\text{final}} - S_{\text{initial}} ]

Entropy describes how energy and particles are distributed among a system’s possible arrangements. A positive ΔS means the system’s entropy has increased; a negative ΔS means it has decreased. Entropy is a state function, so ΔS depends on the initial and final states, not the route between them.

The sign gives an initial clue about a process, but it cannot determine on its own whether a reaction will occur spontaneously. Chemists also consider enthalpy and temperature.

What the sign of ΔS means

• ΔS > 0: The system’s entropy increases. This often happens when matter spreads out, such as when a liquid becomes a gas.
• ΔS < 0: The system’s entropy decreases. This often happens when matter becomes more constrained, such as when a liquid freezes.
• ΔS = 0: The initial and final states have the same entropy.

These are general patterns, not substitutes for calculation. The number of gas molecules, for example, can help predict a reaction’s entropy change: producing more gas molecules often increases entropy. The phases and structures of the substances also matter.

Entropy is commonly reported in joules per kelvin (J/K) for a system, or joules per mole per kelvin (J/(mol·K)) for molar quantities. The units depend on how the entropy is reported.

One example: melting ice

When ice melts, its water molecules move from an ordered solid structure to a liquid in which they can move more freely. The water’s entropy increases, so melting has ΔS > 0. Freezing is the reverse process: the water’s entropy decreases, so ΔS < 0.

This example describes the system, which is the water itself. Whether melting or freezing happens under particular conditions also depends on the surroundings and the energy changes involved.

How ΔS relates to spontaneity

At constant temperature and pressure, the Gibbs free energy change helps determine whether a process is spontaneous:

[ \Delta G = \Delta H - T\Delta S ]

Here, ΔG is the change in Gibbs free energy, ΔH is the change in enthalpy, and T is the absolute temperature in kelvin. Under these conditions, a negative ΔG indicates a spontaneous process (Wikipedia — Gibbs free energy).

This relationship shows why the sign of ΔS alone does not settle the question. A process with negative ΔS can still be spontaneous if its enthalpy change is sufficiently favorable. A process with positive ΔS can still be nonspontaneous if its enthalpy change is unfavorable.

Temperature affects the size of the entropy contribution because T multiplies ΔS. The units must also be consistent when using the equation. For example, if ΔH is in kilojoules per mole and ΔS is in joules per mole per kelvin, convert one quantity before calculating ΔG.

How to calculate ΔS

Two common approaches use standard entropy values or heat transferred reversibly.

From standard entropy values

For a reaction, calculate the standard entropy change by adding the standard molar entropies of the products and subtracting those of the reactants:

[ \Delta S^\circ = \sum S^\circ_{\text{products}} - \sum S^\circ_{\text{reactants}} ]

Multiply each substance’s standard entropy by its coefficient in the balanced chemical equation. Use the same standard conditions for all values in the calculation.

Thermodynamic reference data for specific substances are available in the NIST Chemistry WebBook. The IUPAC Gold Book gives a formal definition of entropy.

From reversible heat transfer

For a reversible process at constant temperature, calculate the entropy change as:

[ \Delta S = \frac{q_{\text{rev}}}{T} ]

Here, (q_{\text{rev}}) is the heat transferred reversibly to the system, and T is the temperature in kelvin. Under the usual chemistry sign convention, (q_{\text{rev}}) is positive when heat enters the system and negative when heat leaves.

For a process that occurs over a range of temperatures, or when the temperature is not constant, this simple division is not enough. The calculation must account for how heat transfer varies with temperature.

Both approaches give the entropy change between the same endpoints because entropy is a state function. A conceptual introduction is available in Khan Academy’s entropy material.

System entropy and surroundings

A process can decrease the system’s entropy while increasing the entropy of its surroundings. The second law concerns the total entropy change of the system and surroundings together, not the system’s ΔS alone.

For example, a reaction that releases heat transfers energy to the surroundings. This transfer can increase the surroundings’ entropy. At constant temperature and pressure, the Gibbs free energy equation accounts for this connection: a negative ΔG corresponds to a positive total entropy change for the system and surroundings.

This explains why a negative ΔS for the system does not by itself rule out spontaneity. The entropy change of the surroundings also matters.

Key Takeaways

• ΔS is the change in entropy: (S_{\text{final}} - S_{\text{initial}}).
• A positive ΔS means the system’s entropy increases; a negative ΔS means it decreases.
• Entropy is a state function, so only the initial and final states determine ΔS.
• ΔS can be calculated from standard entropy values or, for a reversible process at constant temperature, from (q_{\text{rev}}/T).
• At constant temperature and pressure, spontaneity depends on Gibbs free energy: (\Delta G = \Delta H - T\Delta S).