Gibbs function pressure

In the following sections, we introduce the concept of a thermodynamic universe (i.e. a system plus its surroundings). For a reaction to occur spontaneously in a system, we require the change in Gibbs function G to be negative. We then explore the thermodynamic behaviour of G as a function of pressure, temperature and reaction composition. 

In a similar way, we say that the value of the Gibbs function changes in response to changes in pressure and temperature. We write this as... 

The change in Gibbs function during gas movement gas molecules move from high pressure to low... 

Gas passes from the flask to the pump where the pressure is lower. The change in Gibbs function associated with these pressure changes is given by... 

Worked Example 4.9 The pressure inside a water pump is the same as the vapour pressure of water (28 mmHg). The pressure of gas inside a flask is the same as atmospheric pressure (760 mmHg). What is the change in Gibbs function per mole of gas that moves Take T = 298 K. 

On opening the drink bottle we hear a hissing sound, which occurs because the pressure of the escaping C02 gas above the liquid is greater than the atmospheric pressure. We saw in Chapter 4 that the molar change in Gibbs function for movement of a gas is given by... 

The relationship between changes in Gibbs function and temperature (at constant pressure p) is defined using Equation (4.38) ... 

As biologic systems operate at constant temperature and pressure, the change in the Gibbs function of a reaction occurring in a biologic system is a measure of the maximum magnimde of the net useful work that can be obtained from the reaction. 

For stretching a him of water at constant pressure and temperature until its area is increased by 1 vA, the change in the Gibbs function AG is given by the equation... 

Hawley [6] has measured the change in the Gibbs function for the transition from native to denatured chymotrypsinogen as a function of temperamre and pressure. The reaction can be described as... 

If the temperature and pressure are changed by amounts dT and dP such that the system reaches a new state of equilibrium, then the molar Gibbs functions of A and B change by amounts of dGA and dG- such that... 

By convention, the standard Gibbs function for formation AfG of graphite is assigned the value of zero. On this basis, AfG gg of diamond is 2900 J mol Entropies and densities also are listed in Table 8.2. Assuming that the entropies and densities are approximately constant, determine the conditions of temperature and pressure under which the manufacture of diamonds from graphite would be thermodynamically and kinetically practical [2]. 

Now that we have considered the calculation of entropy from thermal data, we can obtain values of the change in the Gibbs function for chemical reactions from thermal data alone as well as from equilibrium data. From this function, we can calculate equilibrium constants, as in Equations (10.22) and (10.90.). We shall also consider the results of statistical thermodynamic calculations, although the theory is beyond the scope of this work. We restrict our discussion to the Gibbs function since most chemical reactions are carried out at constant temperature and pressure. 

The values of AG just calculated apply to a system in which all reactants and products are at standard pressure and which is sufficiently large that one mole of reaction does not alter the pressures appreciably. Alternatively, the expression In can be equated to dG/dn)Tp for a finite system, the initial rate of change of the total Gibbs function of the system per mole of reaction when all reactants and products are at standard pressure [2]. 

The condition of Equation (13.7) can be met only if p,j = p,n, which is the condition of transfer equilibrium between phases. Or, to put the argument differently, if the chemical potentials (escaping tendencies) of a substance in two phases differ, spontaneous transfer will occur from the phase of higher chemical potential to the phase of lower chemical potential, with a decrease in the Gibbs function of the system, until the chemical potentials are equal (see Section 10.5). For each component present in aU p phases, (p 1) equations of the form of Equation (13.7) provide constraints at transfer equilibrium. Furthermore, an equation of the form of Equation (13.7) can be written for each one of the C components in the system in transfer equUibrium between any two phases. Thus, C(p — 1) independent relationships among the chemical potentials can be written. As chemical potentials are functions of the mole fractions at constant temperamre and pressure, C(p — 1) relationships exist among the mole fractions. If we sum the independent relationships for temperature. 

EXCESS GIBBS FUNCTION FROM MEASUREMENT OF VAPOR PRESSURE... 

In this chapter, we shall consider the methods by which values of partial molar quantities and excess molar quantities can be obtained from experimental data. Most of the methods are applicable to any thermodynamic property J, but special emphasis will be placed on the partial molar volume and the partial molar enthalpy, which are needed to determine the pressure and temperature coefficients of the chemical potential, and on the excess molar volume and the excess molar enthalpy, which are needed to determine the pressure and temperature coefficients of the excess Gibbs function. Furthermore, the volume is tangible and easy to visualize hence, it serves well in an initial exposition of partial molar quantities and excess molar quantities. 

In our exposition of the properties of the Gibbs function G (Chapter 7), we examined systems with constraints on them in addition to the ambient pressure. We found that changes in Gibbs function are related to the maximum work obtainable from an isothermal transformation. In particular, for a reversible transformation at constant pressure and temperature [Equation (7.79)],... 

Of course, the equahty in Equation (7.79) is symmetric that is, the equation may be read in the mirror-image direction If we perform reversible (non-PV) work DWnei on a system at constant pressure and temperamre, we increase its Gibbs function by the amount dGx,p. For example, if we reversibly change the position x of a body in the gravitational field of the earth [Fig. 21.1(a)], we perform an amount of work given by... 

For a system of constant composition in which fields are absent, we found in Chapter 7 that because the Gibbs function G is a function of pressure and temperature,... 

Standard thermodynamic operations (Prigogine and Defay, 1954) on the Gibbs function, AG, yield expressions for related thermodynamic activation parameters. Thus the dependence of k on T can be used to calculate the enthalpy of activation, A, for processes at constant pressure or the thermodynamic energy of activation, A, for processes at constant volume, which in turn lead to the related entropies of activation, ASp and AS respectively. The dependence of k on pressure can be used to calculate the volume of activation, AV which is related to AHp by eqn (5) where a is the thermal... 

Employing standard states of a single solute in a physical state of infinite dilution in the liquid stationary phase at the temperature and pressure of the system and a single solute in the perfect gas state at unit pressure and the temperature of the system for the solute in the stationary and in the gaseous phase, respectively, we obtain for the standard molar Gibbs function of sorption of solute i, AG°p(/) [19] ... 

The specific Gibbs functions are evaluated at temperature T0 and pressure P() of the environment, and are given by... 

Equivalently (Figure 2.2), dS nw = 0 at equilibrium. The Gibbs function thus expresses the second law as dG < 0 for all possible processes in constant-temperature, constant-pressure systems. (Similarly, the Helmholtz free energy function. A, expresses the second law for isochoric, isothermal systems as dA < 0 for all possible processes.)... 

Structure and orientation of a Me deposit on S in the initial stage of 3D Me bulk phase formation can be either independent of or influenced by the surface structure of S, which can be modified by 2D Meads overlayer formation and/or 2D Me-S surface alloy phase formation in the UPD range. Epitaxial behavior of 2D and 3D Me phases exists if some or all of their lattice parameters coincide with those of the top layer of S. The epitaxy is determined by a minimum of the Gibbs function at constant temperature and pressure. 

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