Equilibrio . Arrangementf átomos

Equilibrio        3

[pic 1]

dG = O

libre de Gibbs

energía

GRAMO

Arrangementof átomos        

Fig. 1.1 Una variación esquemática de energía libre de Gibbs con la disposición de los átomos. Configuración 'A' tiene la menor energía libre y por lo tanto es la disposición cuando el sistema está en equilibrio estable. Configuración 'B' es un equilibrio metaestable.

equilibrio estados para distinguirlos de la equilibrio estable estado. los estados intermedios para que dG 1 = 0 son inestable y sólo alguna vez se realizan momentáneamente en la práctica. Si, como resultado de las fluctuaciones térmicas, los átomos se vuelven dispuestos en un estado intermedio que se reorganizar rápidamente en uno de los mínimos de la energía libre. Si por un cambio de temperatura o presión, por ejemplo, un sistema se traslada de un estable a un estado metaestable que será, con el tiempo, transformar al nuevo estado de equilibrio estable.

Graphite and diamond at room temperature and pressure are examples of stable and metastable equilibrium states. Given time, therefore, aB diamond under these conditions will transform to graphite.

Any transformation that results in a decrease in Gibbs free energy is possible. Therefore a necessary criterion for any phase transformation is

(1.4)

where GI and G2 are the free energies of the initial and final states respec-tively. The transformation need not go directly to the stable equilibrium state but can pass through a whole series of intermediate metastable states.

The answer to the question "How fast does a phase transformation occur?" is not provided by classical thermodynamics. Sometimes metastable states can be very short-lived; at other times they can exist alm ost indefinitely as in the case of diamond at room temperature and pressure. The reason for these differences is the presence of the free energy hump between the metastable and stable states in Fig. 1.1. The study of transformation rates in physical chemistry belongs to the realm of kinetics. In general, higher humps or energy barriers lead to slower transformation rates. Kinetics obviously plays a central

4        Thermodynamics and phase diagrams

role in the study of phase transformations and many examples of kinetic processes will be found throughout this book.

The different thermodynamic functions that have been mentioned in this section can be divided into two types called intensive and extensive prop-erties. The intensive properties are those which are independent of the size of the system such as T and P, whereas the extensive properties are directly proportional to the quantity of material in the system, e.g. V, E, H, Sand G. The usual way of measuring the size of the system is by the number of moles of material it contains. The extensive properties are then molar quantities, i.e. expressed in units per mole. The number of moles of a given component in the system is given by the mass of the component in grams divided by its atomic or molecular weight.

The number of atoms or molecules within I mol of material is given by Avogadro's number (Na) and is 6.023 X 1023 •

1.2        Single Component Systems

Let us begin by dealing with the phase changes that can be induced in a single component by changes in temperature at a fixed pressure, say I atm. A single component system could be one containing a pure element or one type of molecule that does not dissociate over the range of temperature of interest. In order to predict the phases that are stable or mixtures that are in equilibrium at different temperatures it is necessary to be able to calculate the variation of G with T.

1.2.1        Gibbs Free Energy as a Function of Temperature

The specific he at of most substances is easily measured and readily available. In general it varies with temperature as shown in Fig. I.2a. The specific he at is the quantity of heat (in joules) required to raise the temperature of the substance by one degree Kelvin. At constant pressure this is denoted by Cp and is given by

Por lo tanto la variación de H con T puede obtenerse a partir de un conocimiento de la variación de Cp con T. Al considerar las transformaciones de fase o reacciones químicas es sólo cambios en funciones termodinámicas que son de interés. En consecuencia H se puede medir en relación con cualquier nivel de referencia que normalmente se realiza mediante la definición de H = 0 para un elemento puro en su estado más estable a 298 K (25 ° C). La variación de H con T se puede calcular mediante la integración

[pic 2]

(0)        o '. = ------------- ~ T (K)

o

[pic 3]

entalpía

H

o Me ----------- :: ~ ~ T ---- (K)

(B)

[pic 4]

entropía

5

o1 ° C: ....---------- ~ T (K)

(do)        o

Fig. 1.2 (a) Variación de Cpag con la temperatura, Cpag tiende a un límite de ~ 3R. (B) Variación de la entalpía (H)con la temperatura absoluta de un meta pura !. (C) Variación de la entropía(S) con la temperatura absoluta.

6        Termodinámica y diagramas de fase

Ecuación 1.5, es decir,

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