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Pressure potential Gibbs free energy

N, Number of particles P, Pressure V, Volume T, Temperature E, Energy fi. Chemical potential A, Helmholtz free energy S, Entropy G, Gibbs free energy. [Pg.377]

The Gibbs free energy change of a system will depend not only on temperature and pressure but upon the chemical potentials of the species involved, and this statement may be expressed in the form of the partial differential... [Pg.1227]

To find the connection between cell potential and Gibbs free energy, recall that ir Section 7.14 (Eq. 21) we saw that the change in Gibbs free energy is the maximum nonexpansion work that a reaction can do at constant pressure and temperature ... [Pg.612]

Here, AS° = AS i + AS n, but since identical vibrational levels have been assumed for the two electronic levels, AS jb = 0. In addition, AS j is related to the electronic degeneracies of the two levels by ASei = K In ( l/ h)- Finally, if the transformation takes place at constant pressure, AH° = NAE where AE is defined as above. Consideration of the Gibbs free energy for an assembly of N molecules thus produces the same relation for the HS fraction Uh as the potential energy for the isolated molecule, if only the interaction between the molecules is neglected. [Pg.56]

The quantity of primary interest in our thermodynamic construction is the partial molar Gibbs free energy or chemical potential of the solute in solution. This chemical potential reflects the conformational degrees of freedom of the solute and the solution conditions (temperature, pressure, and solvent composition) and provides the driving force for solute conformational transitions in solution. For a simple solute with no internal structure (i.e., no intramolecular degrees of freedom), this chemical potential can be expressed as... [Pg.309]

Whether a reaction is spontaneous or not depends on thermodynamics. The cocktail of chemicals and the variety of chemical reactions possible depend on the local environmental conditions temperature, pressure, phase, composition and electrochemical potential. A unified description of all of these conditions of state is provided by thermodynamics and a property called the Gibbs free energy, G. Allowing for the influx of chemicals into the reaction system defines an open system with a change in the internal energy dt/ given by ... [Pg.227]

The local conditions of temperature and pressure, as well as the new energy source in the form of the electrochemical gradient, can all be incorporated into the Gibbs free energy by adding new terms to the chemical potential. Variation of AG and AH with temperature are all standard thermodynamics, although we will resist the temptation to explore them here. [Pg.253]

The tools for calculating the equilibrium point of a chemical reaction arise from the definition of the chemical potential. If temperature and pressure are fixed, the equilibrium point of a reaction is the point at which the Gibbs free energy function G is at its minimum (Fig. 3.1). As with any convex-upward function, finding the minimum G is a matter of determining the point at which its derivative vanishes. [Pg.32]

Second-order phase transitions are those for which the second derivatives of the chemical potential and of Gibbs free energy exhibit discontinuous changes at the transition temperature. During second-order transitions (at constant pressure), there is no latent heat of the phase change, but there is a discontinuity in heat capacity (i.e., heat capacity is different in the two... [Pg.64]

In these equations gv is the change in Gibbs free energy on taking one atom from a normal lattice site to the surface of the crystal and (gt + gv) the change when an atom is taken from a normal lattice site to an interstitial site, both at constant temperature and pressure. cr denotes a site fraction of species r on its sublattice, and is the chemical potential of a normal lattice ion in the defect-free crystal. [Pg.6]

Temperature and Pressure The effect of temperature and pressure on the ideal potential (E) of a fuel cell can be analyzed on the basis of changes in the Gibbs free energy with temperature and pressure. [Pg.63]

Temperature, Heat capacity. Pressure, Dielectric constant. Density, Boiling point. Viscosity, Concentration, Refractive index. Enthalpy, Entropy, Gibbs free energy. Molar enthalpy. Chemical potential. Molality, Volume, Mass, Specific heat. No. of moles. Free energy per mole. [Pg.34]

Before discussing all these biopolymer applications, we first take this opportunity to remind the reader that, in general, any thermodynamic variable can be expressed as the sum of two functions, one of which depends only on the temperature and pressure, and another which depends on the system composition (expressed as the mole fraction xt of the /-component). Therefore, for example, the chemical potential fM of the /-component of the system at constant temperature T and pressure p (the general experimental conditions), /. e., partial molar Gibbs free energy (dG/dn TtP may be expressed as (Prigogine and Defay, 1954) ... [Pg.81]

An extremely useful quantity in the thermodynamic treatment of multicomponent phase equilibria is the chemical potential. The chemical potential for component /, is the partial molal Gibbs free energy with respect to component i at constant pressure and temperature ... [Pg.108]

OSMOTIC PRESSURE THERMODYNAMIC FOUNDATIONS 3.2a Gibbs Free Energy and Chemical Potential... [Pg.108]

The subject of interest is a gel swollen by solvent. Let F be the Gibbs free energy change after mixing of solvent and an initially unstrained polymer network [1]. When the gel is isotropic and is immersed in a pure solvent with a fixed pressure Po, F is a thermodynamic potential dependent on the temperature T, the pressure p inside the gel, and the solvent particle number Ns inside the gel. It satisfies... [Pg.68]

Equation 9.20 gives the pressure dependence of the Gibbs free energy of a pure substance. More generally, for a mixture one should consider the chemical potential /r, which is defined as the partial molar free energy of species k ... [Pg.374]

Since ideal conditions simplify calculations, an ideal gas at 1 atm pressure in the gas phase which is infinitely dilute in solution will be utilized. Then the total standard partial molar Gibbs free energy of solution (chemical potential), AG, can be directly related to KD, the distribution constant, by the expression... [Pg.568]

The exactness statements in Section HI can also be directly translated to the constant pressure case. The arguments above imply directly that the onset of phase coexistence is found exactly from the moment Gibbs free energy All phases are in the family (A3), because one of them (the parent) is, and the requirement of equal chemical potentials is satisfied. Spinodals and (multi-) critical points are also found exactly. Arguing as in Section HI. A and using the vector notation of Eq. (53), the criterion for such points is found as... [Pg.330]

The pressure is assumed to be the same for both the anode and cathode gas channels. The reversible potential at standard state conditions is obtained from the change in the standard Gibbs free energy. [Pg.135]

An electrochemical cell generates a potential difference E. (The symbol E, commonly used in electrochemistry, refers to electromotive force, an archaic term for potential difference.) The electrical work done when n moles of electrons is passed by the cell can be found using Eq. (15-1), w = -nFE. It can be shown that the electrical work done by an electrochemical cell, at constant temperature and pressure, is equal to the change in Gibbs free energy of the cell components,... [Pg.171]

In the definitions of T, two variables in addition to the ion chemical potential must also be specified as constant. In an equilibrium dialysis experiment, these are temperature and the chemical potential of water. This partial derivative is known as the Donnan coefficient. (Note that the hydrostatic pressure is higher in the RNA-containing solution.) In making connections between T and the Gibbs free energy, it is more convenient if temperature... [Pg.439]

This shows that the chemical potential of a component is just its partial molar Gibbs free energy. Note that the definitions of the chemical potential in terms of other thermodynamic variables, given in Chapter 6, Eq. (8), are not partial molar quantities because pressure and temperature are not the variables held constant in these derivatives. [Pg.228]

Partial molar Gibbs free energies (chemical potentials) can most easily be measured by taking advantage of the equality of chemical potentials in different phases at equilibrium. The chemical potential of a component of a solution is its chemical potential in the vapor that is in equilibrium with the solution. Thus, if the component has a measurable vapor pressure, it can be used to determine its chemical potential in the solution. Assuming that the vapor can be considered an ideal gas, its chemical potential is determined by its vapor pressure ... [Pg.232]


See other pages where Pressure potential Gibbs free energy is mentioned: [Pg.706]    [Pg.133]    [Pg.627]    [Pg.2282]    [Pg.612]    [Pg.634]    [Pg.655]    [Pg.227]    [Pg.64]    [Pg.64]    [Pg.70]    [Pg.93]    [Pg.239]    [Pg.242]    [Pg.74]    [Pg.4]    [Pg.100]    [Pg.430]    [Pg.108]    [Pg.177]    [Pg.327]    [Pg.98]    [Pg.498]    [Pg.402]   


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