Standard molar entropy

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In chemistry, the standard molar entropy is the entropy content of one mole of substance, under conditions of standard temperature and pressure (SRP). The standard molar entropy is usually given the symbol S^o, and the units J mol⁻¹ K⁻¹ (joules per mole kelvin). Unlike standard enthalpies of formation, the value of S^o is an absolute. That is, an element in its standard state has a nonzero value of S^o at room temperature, because only at 0 K is the entropy of an element 0 J mol⁻¹ K⁻¹, the third law of thermodynamics.

Thus, when a mole of substance at 0 K is warmed by its surroundings to 298 K, the sum of the incremental values of q_rev/T (q_rev being the amount of heat exchanged by the system if the process is reversible) constitute each element's or compound's standard molar entropy, a fundamental physical property and an indicator of the amount of energy stored by a substance at 298 K.<ref name=ctms>Moore, J. W., C. L. Stanistski, P. C. Jurs (2005). Chemistry, The Molecular Science , 2nd edition. Brooks Cole. ISBN 0-534-42201-2.</ref><ref name=Jungermann>Jungermann, A.H. (2006). “Entropy and the Shelf Model: A Quantum Physical Approach to a Physical Property”. Journal of Chemical Education 83: 1686-1694</ref>

The reversible heat depends on the heat capacity of the substance, so, for example the standard molar entropy of a gas at STP would include contributions from:<ref>Kosanke, K. (2004). “Chemical Thermodynamics”, Pyrotechnic chemistry. Journal of Pyrotechnics. ISBN 1889526150.</ref>

The heat capacity of one mole of the solid from 0 K to the melting point (including heat absorbed in any changes between different crystal structures)
The latent heat of fusion of the solid.
The heat capacity of the liquid from the melting point to the boiling point.
The latent heat of vaporization of the liquid.
The heat capacity of the gas from the boiling point to room temperature.

The total molar entropy would be the addition of all N individual contributions: <math>S^o = \sum_{k=1}^N \Delta S_k =\sum_{k=1}^N \int \frac{dq_k}{T} \, dT</math>