Standard molar entropy

Thermodynamics

If a mole of a solid substance is a perfectly ordered solid at 0K, then if the solid is warmed by its surroundings to 298.15K without melting, its absolute molar entropy would be the sum of a series of N stepwise and reversible entropy changes. The limit of this sum as N \rightarrow \infty becomes an integral: :S^\circ = \sum_{k=1}^N \Delta S_k = \sum_{k=1}^N \frac{dQ_k}{T} \rightarrow \int 0 ^{T_2} \frac{dS}{dT} dT = \int 0 ^{T_2} \frac {C{p_k}}{T} dT In this example, T_2 =298.15 K and C{p_k} is the molar heat capacity at a constant pressure of the substance in the reversible process k. 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 \frac{C_{p_k}}{T} is required to find the total molar entropy. The quantity \frac{dQ_{k}}{T} represents the ratio of a very small exchange of heat energy to the 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:

• The heat capacity of one mole of the solid from 0K 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.

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: :{\Delta S^\circ}{rxn} = S^\circ{products} - S^\circ_{reactants}

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: :(\Delta S_{total} = \Delta S_{system} + \Delta S_{surroundings})0 Molar entropy is not the same for all gases. Under identical conditions, it is greater for a heavier gas.

References

References

1. (1960). "The Nature of the Chemical Bond". Cornell University Press.
2. Kosanke, K.. (2004). "Pyrotechnic chemistry". Journal of Pyrotechnics.
3. (2005). "Chemistry". [[McGraw-Hill Higher Education]].