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Inchemistry, thestandard molar entropy is theentropy content of onemole of pure substance at astandard state of pressure and any temperature of interest. These are often (but not necessarily) chosen to be thestandard temperature and pressure.

The standard molar entropy at pressure =${\displaystyle P^0}$ is usually given the symbolS°, and has units ofjoules permole perkelvin (J⋅mol⁻¹⋅K⁻¹). Unlikestandard enthalpies of formation, the value ofS° is absolute. That is, an element in its standard state has a definite, nonzero value ofS atroom temperature. The entropy of a purecrystalline structure can be 0 J⋅mol⁻¹⋅K⁻¹ only at 0 K, according to thethird law of thermodynamics. However, this assumes that the material forms a 'perfect crystal' without anyresidual entropy. This can be due tocrystallographic defects,dislocations, and/or incomplete rotational quenching within the solid, as originally pointed out byLinus Pauling.^[1] These contributions to the entropy are always present, because crystals always grow at a finite rate and at temperature. However, the residual entropy is often quite negligible and can be accounted for when it occurs usingstatistical mechanics.

If amole of a solid substance is a perfectly ordered solid at 0 K, then if the solid is warmed by its surroundings to 298.15 K without melting, its absolute molar entropy would be the sum of a series ofN stepwise and reversible entropy changes. The limit of this sum as${\displaystyle N\to \mathrm{\infty }}$ becomes an integral:

${\displaystyle S^{\circ }=\sum _{k=1}^N\mathrm{\Delta }{S}_k=\sum _{k=1}^N\frac{d{Q}_k}{T}\to {\int }_0^{T_2}\frac{dS}{dT}dT={\int }_0^{T_2}\frac{C_{p_k}}{T}dT}$

In this example,${\displaystyle T_2=298.15K}$ and${\displaystyle C_{p_k}}$ is themolar heat capacity at a constant pressure of the substance in thereversible processk. The molar heat capacity is not constant during the experiment because it changes depending on the (increasing) temperature of the substance. Therefore, a table of values for${\displaystyle \frac{C_{p_k}}{T}}$ is required to find the total molar entropy. The quantity${\displaystyle \frac{d{Q}_k}{T}}$ represents the ratio of a very small exchange of heat energy to the temperatureT. The total molar entropy is the sum of many small changes in molar entropy, where each small change can be considered a reversible process.

The standard molar entropy of a gas atSTP includes contributions from:^[2]

• Theheat capacity of one mole of the solid from 0 K to themelting point (including heat absorbed in any changes between differentcrystal structures).
• Thelatent heat of fusion of the solid.
• The heat capacity of the liquid from the melting point to theboiling point.
• Thelatent heat of vaporization of the liquid.
• The heat capacity of the gas from the boiling point to room temperature.

Changes in entropy are associated withphase transitions andchemical reactions.Chemical equations make use of the standard molar entropy ofreactants andproducts to find the standard entropy of reaction:^[3]

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

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

${\displaystyle (\mathrm{\Delta }{S}_{total}=\mathrm{\Delta }{S}_{system}+\mathrm{\Delta }{S}_{surroundings})>0}$

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

• Entropy
• Heat
• Gibbs free energy
• Helmholtz free energy
• Standard state
• Third law of thermodynamics

• Table of Standard Thermodynamic Properties for Selected Substances

• Chemical properties
• Thermodynamic entropy
• Molar quantities

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