The previous section described the various contributions of matter and energy dispersal that contribute to the entropy of a system. With these contributions in mind, consider the entropy of a pure, perfectly crystalline solid possessing no kinetic energy (that is, at a temperature of absolute zero, 0 K). This system may be described by a single microstate, as its purity, perfect crystallinity and complete lack of motion means there is but one possible location for each identical atom or molecule comprising the crystal (*W* = 1). According to the Boltzmann equation, the entropy of this system is zero.

This limiting condition for a system’s entropy represents the third law of thermodynamics: *the entropy of a pure, perfect crystalline substance at 0 K is zero.*

Careful calorimetric measurements can be made to determine the temperature dependence of a substance’s entropy and to derive absolute entropy values under specific conditions. Standard entropies (*S*°) are for one mole of substance under standard conditions (a pressure of 1 bar and a temperature of 298.15 K; see details regarding standard conditions in the thermochemistry chapter of this text). The standard entropy change (Δ*S*°) for a reaction may be computed using standard entropies as shown below:

where ν represents stoichiometric coefficients in the balanced equation representing the process. For example, Δ*S*° for the following reaction at room temperature

is computed as:

A partial listing of standard entropies is provided in the table below, and additional values are provided in the Appendices. The example exercises that follow demonstrate the use of *S*° values in calculating standard entropy changes for physical and chemical processes.

Substance |
$S^°$ (J mol
^{−1} K^{−1}) |

carbon | |

C(s, graphite) |
5.740 |

C(s, diamond) |
2.38 |

CO(g) |
197.7 |

CO_{2}(g) |
213.8 |

CH_{4}(g) |
186.3 |

C_{2}H_{4}(g) |
219.5 |

C_{2}H_{6}(g) |
229.5 |

CH_{3}OH(l) |
126.8 |

C_{2}H_{5}OH(l) |
160.7 |

hydrogen | |

H_{2}(g) |
130.57 |

H(g) |
114.6 |

H_{2}O(g) |
188.71 |

H_{2}O(l) |
69.91 |

HCI(g) |
186.8 |

H_{2}S(g) |
205.7 |

oxygen | |

O_{2}(g) |
205.03 |

Determination of Δ*S*°

Calculate the standard entropy change for the following process:

Solution

Calculate the entropy change using standard entropies as shown above:

The value for Δ*S*° is negative, as expected for this phase transition (condensation), which the previous section discussed.

Check Your Learning

Calculate the standard entropy change for the following process:

## Answer:

−120.6 J K^{–1} mol^{–1}

Determination of Δ*S*°

Calculate the standard entropy change for the combustion of methanol, CH_{3}OH:

Solution

Calculate the entropy change using standard entropies as shown above:

Check Your Learning

Calculate the standard entropy change for the following reaction:

## Answer:

24.7 J K^{–1} mol^{–1}