# Standard molar entropy

In chemistry, the standard molar entropy is the entropy content of one mole of pure substance under a standard state (not standard temperature and pressure).

The standard molar entropy is usually given the symbol , and has units of joules per mole kelvin (J⋅mol−1⋅K−1). Unlike standard enthalpies of formation, the value of is absolute. That is, an element in its standard state has a definite, nonzero value of S at room temperature. The entropy of a pure crystalline structure can be 0 J⋅mol−1⋅K−1 only at 0 K, according to the third law of thermodynamics. However, this assumes that the material forms a 'perfect crystal' without any[clarify] frozen in entropy (crystallographic defects, dislocations), which is never completely true because crystals always grow at a finite temperature. However, this residual entropy is often quite negligible.

## Thermodynamics

If a mole of substance were at 0 K, then warmed by its surroundings to 298 K, its total molar entropy would be the addition of all N individual contributions:

${\displaystyle S^{\circ }=\sum _{k=1}^{N}\Delta S_{k}=\int _{T_{1}\approx 0}^{T_{2}}{\frac {dS}{dT}}dT=\sum _{k=1}^{N}{\frac {dQ_{k}}{T}}=\int _{T_{1}\approx 0}^{T_{2}}{\frac {C_{p_{k}}}{T}}dT}$

In this example, ${\displaystyle T_{2}=298K}$  and ${\displaystyle C_{p_{k}}}$  is the specific heat at a constant pressure of the substance in the reversible process k. The specific heat is not constant during the experiment because it changes depending on the temperature of the substance (which is increasing to 298 K in this case). Therefore, a table of values for ${\displaystyle {\frac {C_{p_{k}}}{T}}}$  is required to find the total molar entropy. ${\displaystyle {\frac {dQ_{k}}{T}}}$  represents a very small exchange of heat energy at temperature T. The total molar entropy is the sum of many small changes in molar entropy, where each small change can be considered a reversible process.

## Chemistry

The standard molar entropy of a gas at STP includes contributions from:[1]

Changes in entropy are associated with phase transitions and chemical reactions. Chemical equations make use of the standard molar entropy of reactants and products to find the standard entropy of reaction:[2]

${\displaystyle {\Delta S^{\circ }}_{rxn}=S_{products}^{\circ }-S_{reactants}^{\circ }}$

The standard entropy of reaction helps determine whether the reaction will take place spontaneously. According to the second law of thermodynamics, a spontaneous reaction always results in an increase in total entropy of the system and its surroundings:

${\displaystyle (\Delta S_{total}=\Delta S_{system}+\Delta S_{surroundings})>0}$

Molar entropy is not same for all gases. Under identical conditions, it is greater for a heavier gas.