\(\Delta H\) | \(\Delta S\) | \(-T\Delta S\) | \(\Delta G\) | High T | Low T |
---|---|---|---|---|---|

− | + | − | − | Spontaneous | Spontaneous |

− | − | + | ± | Nonspontaneous | Spontaneous |

+ | + | − | ± | Spontaneous | Nonspontaneous |

+ | − | + | + | Nonspontaneous | Nonspontaneous |

^{−1}and provide information on the stability of compounds. For instance, the \(\Delta {G}_{f}^{o}\) values of water in liquid and gas forms are − 237.1 and − 228.6 kJ mol

^{−1}respectively, indicating that liquid water is the stable phase at 25 °C and 1 bar pressure.

_{2}O (\(\Delta {G}_{f}^{o}=-128.7\) kJ mol

^{−1}) we have the following reactions:

_{2}O: − 494 and − 102 kJ. First, both aerobic respiration and sulphate reduction provide enough energy needed for growth and maintenance of the microbes involved (about − 10 kJ per mol). Second, about five times more energy is liberated during aerobic respiration than during sulphate reduction. Where is the missing energy? It is transferred to the reaction products: the hydrogen sulphide produced can react with oxygen:

## 4.1 How Gibbs Free Energy Depends on Conditions

_{i}to P

_{f}.

^{−1}(\(\left[c\right]= \frac{n}{V}\)) is the analogue of pressure and the change in Gibbs free energy is:

^{−1}for an ideal solution. For non-ideal solutions, we use thermodynamic activity a rather than concentration [c]:

## 4.2 Phase Equilibria

_{3}as calcite or aragonite, Al

_{2}SiO

_{5}as the minerals kyanite, sillimanite or andalusite).

^{−1}K

^{−1}and molar volume change during fusion (\(\Delta {V}_{fusion})\)) of ≈ 4 \(\times \) 10

^{–6}m

^{3}mol

^{−1}(i.e., 4 ml per mol), would yield

^{3}for one mol of H

_{2}O), indicating that the P to T slope is negative (Fig. 4.2). Another application is the calculation of freezing point increases with altitude (see Box 3).

_{1}, T

_{1}to P

_{2}, T

_{2}we arrive at the Clausius-Clapeyron equation:

^{−1}, the volume change from ice to liquid is − 1.63 \(\times {10}^{-6}\) m

^{3}for one mol of H

_{2}O and the pressure difference (\(\Delta P)\) is 35 \(\times {10}^{3}-1.013 \times {10}^{5}\)= − 6.63 \(\times {10}^{4}\) Pa.

_{1}= 1 atm =\(1.013 \times {10}^{5}\) Pa and \({T}_{1}=\) 100 °C = 273.15 K and the standard enthalpy of vaporization of water (\(\Delta {H}_{vap}\)) of 40.7 kJ mol

^{−1}:

## 4.3 Phase Diagrams

_{2}O (C=1) (Fig. 4.2). Within fluid water, or within the domain of ice or water vapor, pressure and temperature can be combined in multiple ways because there are two degrees of freedom (F = 1–1 + 2 = 2). At the interface of water–ice, there is only one degree of freedom (F = 1–2 + 2 = 1), i.e., if temperature is chosen, pressure is fixed or the other way around. The boundary lines between mineral phases are therefore called univariant curves in petrology and mineralogy. At the triple point, ice, water and water vapour co-exist (water is freezing and boiling at the same time) and Gibb’s phase rule indicates that there are no degrees of freedom (F = 1–3 + 2 = 0). In other words, the triple point has a fixed pressure and temperature for a component, e.g., for water it is 0.0098 °C and 6 \(\times \) 10

^{–3}atm.