Spontaneity phase changes

The value of the Ising model lies therein that it is the only model of disorder to have produced valid theoretical predictions of spontaneous phase changes. To understand the role of symmetry it is noted that spontaneous magnetization, starting from a random distribution of spins, amounts to a process of ordering that destroys an existing isotropic arrangement. 

CALCULATION OF CHANGE IN THE GIBBS FUNCTION FOR SPONTANEOUS PHASE CHANGE... 

Thermal interactions between the cryogen and water at ambient temperature can induce vapor explosions or so-called rapid phase transitions. A spontaneous phase change occurs due to a sudden improvement of heat transfer between the two liquids. Under certain circumstances, an essential fraction of the thermal energy could be transformed into... 

In Section 8.1 of this chapter, three criteria that determine the spontaneity of a process are given. Review these criteria, and determine which one is involved in each of the following spontaneous phase changes ... 

Unlike melting and the solid-solid phase transitions discussed in the next section, these phase changes are not reversible processes they occur because the crystal stmcture of the nanocrystal is metastable. For example, titania made in the nanophase always adopts the anatase stmcture. At higher temperatures the material spontaneously transfonns to the mtile bulk stable phase [211, 212 and 213]. The role of grain size in these metastable-stable transitions is not well established the issue is complicated by the fact that the transition is accompanied by grain growth which clouds the inteiyDretation of size-dependent data [214, 215 and 216]. In situ TEM studies, however, indicate that the surface chemistry of the nanocrystals play a cmcial role in the transition temperatures [217, 218]. 

On the other hand, this simple rule fails for many familiar phase changes. An example of a spontaneous reaction that is not exothermic is the melting of ice. This takes place spontaneously at 1 atm above 0°C, even though it is endothermic... 

Changing the pressure will have a similar effect. If we increase p by dp, the solid melts. This process can be reversed at any time by decreasing the pressure by dp. Note that at p = 1 atm (101.325 kPa), only at T = 273.15 K can the phase change be made to occur reversibly because this is the temperature where solid and liquid are in equilibrium at this pressure. If we tried to freeze liquid water aip— atm and a lower temperature such as 263.15 K, the process, once started, would proceed spontaneously and could not be reversed by an infinitesimal change in p or T. 

As diagrammed in Figure 14-5. ice melts spontaneously if a mixture of water and ice is placed on a table at 25 °C H2 O (.S 0 ° Table top, 25 C 0 ° C) Recall from Section 11- that a phase change from solid to... 

As described in Section 14-1. when AR and ZlS have the same sign, the spontaneous direction of a process depends on T. For a phase change, enthalpy dominates AG at low temperature, and the formation of the more constrained phase is spontaneous, hi contrast, entropy dominates AG at high temperature, and the formation of the less constrained phase is spontaneous. At one characteristic temperature, A G = 0, and the phase change proceeds in both directions at the same rate. The two phases coexist, and the system is in a state of d Tiamic equilibrium. 

The spontaneous direction of a phase change also depends on pressure, primarily because the molar entropy of a... 

Occasionally we need to be far subtler when we look at reaction spontaneity. The reaction here involves two molecules of diatomic gas reacting to form two molecules of a different diatomic gas. Also, there is no phase change during reaction, nor any change in the numbers of molecules, so any change in the overall entropy is likely to be slight. 

It will be useful to concentrate on the diagram in Figure 5.2 when considering why a phase change occurs spontaneously. We recall from Chapter 4 that one of the simplest tests of whether a thermodynamic event can occur is to ascertain whether the value of AG is negative (in which case the change is indeed spontaneous) or positive (when the change is not spontaneous). 

In the form in which it has been expressed thus far, the second law is not a statement that can be applied conveniently to chemical problems. We wish to use the second law of thermodynamics to establish a criterion by which we can determine whether a chemical reaction or a phase change will proceed spontaneously. Such a criterion would be available if we could obtain a function that had the following two characteristics. 

Thus far we have restricted our attention to phase changes in which equilibrium is maintained. It also is useful, however, to find procedures for calculating the change in the Gibbs function in transformations that are known to be spontaneous, for example, the freezing of supercooled water at —10°C ... 

The entropy, Spontaneous vs non-spontaneous, Reversible and irreversible processes, Calculation of entropy changes (Isothermal, isobaric, isochoric, adiabatic), Phase changes at equilibrium, Trouton s rule, Calculation for irreversible processes... 

Knowing the values of AH and AS for a phase transition makes it possible to calculate the temperature at which the change occurs. Recall from Section 8.14 that AG is negative for a spontaneous process, positive for a nonspontaneous process, and zero for a process at equilibrium. Thus, by setting AG = 0 and solving for T in the free-energy equation, we can calculate the temperature at which two phases are in equilibrium. For the solid — liquid phase change in water, for instance, we have... 

In Fig. 10.13(a) the ball will roll to point B. This diagram is analogous to a phase change. For example, at 25°C ice will spontaneously change com-... 

Calculate the change in Gibbs free energy for reversible and spontaneous phase transformations (Section 13.7, Problems 31-34). 

The chemical potential concept provides a useful way to think about the tendency for spontaneous chemical change in complex environmental systems involving gases, liquids, and solids (cf. Wood and Fraser 1976 Stumm and Morgan 1981). In a particular phase, the chemical potential, /U, of component i is related to the activity of i through the expression... 

However, in many other cases, the sign of AH is no help. An exothermic process occurs spontaneously under certain conditions, whereas the opposite, endothermic, process occurs spontaneously under other conditions. Consider the following examples of phase changes, dissolving salts, and chemical changes. 

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