The third law of thermodynamics states that the entropy of a...

The third law of thermodynamics states that the entropy of a perfect crystal at $0 \mathrm{~K}$ is zero. In Appendix $4, \mathrm{~F}^{-}(a q), \mathrm{OH}^{-}(a q)$, and $\mathrm{S}^{2-}(a q)$ all have negative standard entropy values. How can $S^{\circ}$ values be less than zero?

Key Concepts

Third Law of Thermodynamics

The Third Law of Thermodynamics states that the entropy of a perfect crystalline substance at absolute zero (0 K) is defined to be zero. This law establishes an absolute reference point for the entropy scale, making it possible to determine absolute entropies of substances by integrating heat capacities from 0 K upward. It is important to recognize that this definition applies strictly to perfectly ordered crystals at absolute zero and is a theoretical reference rather than a statement about all substances or conditions.

Standard Entropy vs Absolute Entropy

Absolute entropy is measured from the defined zero point at 0 K as stated by the Third Law, but standard molar entropies (S° values) are determined under standard conditions (typically 1 bar or 1 M, for instance) at a particular temperature (usually 298 K). The standard entropy of a substance may appear negative in certain cases because it is defined relative to a chosen reference state or convention, rather than representing a violation of the Third Law, since the Third Law pertains only to the absolute entropy of a pure, perfectly ordered substance at absolute zero.

Solvation and Hydrogen Bonding Effects

In aqueous solutions, ions such as F?, OH?, and S²? interact with water molecules, often resulting in highly organized hydration shells. This ordering effect decreases the entropy of the system because the water molecules become more structured compared to the bulk liquid. Therefore, the standard molar entropy of these solvated ions can be lower than that of the reference state, leading to negative S° values when measured under standard conditions.

Conventions in Thermodynamic Measurements

The reported standard molar entropies are based on specific conventions and reference states that are used in thermodynamic tables. For instance, the absolute entropy of the proton in aqueous solution is arbitrarily assigned a value (often zero), which subsequently affects the calculated standard entropies of other ions. Thus, negative standard entropy values for aqueous ions reflect the relative nature of the measurement conventions rather than an absolute negative entropy in violation of the Third Law.

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