Gibbs function, decrease

The negative sign on the right-hand side occurs because the Gibbs function decreases as r increases that is, work would have to be performed on the sedimenting particle to bring it back from an axial position at large r to a position at small r. 

Equation (8.67) shows that the Gibbs function decreases as the reaction proceeds. The affinity is related to the Gibbs function... 

Note that Gibbs function decreases with increase in temperature. Thus, the reversible work and thermod5mamic efficiency of a fuel cell decrease wifh increase in temperafure. This is in contrast to the reversible thermodynamic efficiency of a Carnot heat engine where the efficiency or reversible work increases with increase in temperature. 

If this electrostatic treatment of the substituent effect of poles is sound, the effect of a pole upon the Gibbs function of activation at a particular position should be inversely proportional to the effective dielectric constant, and the longer the methylene chain the more closely should the effective dielectric constant approach the dielectric constant of the medium. Surprisingly, competitive nitrations of phenpropyl trimethyl ammonium perchlorate and benzene in acetic anhydride and tri-fluoroacetic acid showed the relative rate not to decrease markedly with the dielectric constant of the solvent. It was suggested that the expected decrease in reactivity of the cation was obscured by the faster nitration of ion pairs. 

The values of these functions change when thermodynamic processes take place. Processes in which the Gibbs energy decreases (i.e., for which AG<0), will take place spontaneously without specific external action. The Gibbs energy is minimal in the state of equilibrium, and the condition for equilibrium are given as... 

Figure 4.6 The value of the Gibbs function AG decreases as the extent of reaction until, at (eq), there is no longer any energy available for reaction, and AG = 0. =0 represents no reaction and = 1 mol represents complete reaction...

The value of pi - the molar Gibbs function of the contaminant -decreases as xt decreases. In fact, the chemical potential p, of the contaminant is a function of its mole fraction within the host, according to Equation (5.11) ... 

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. 

Interestingly, the standard entropies (and in turn heat capacities) of both phases were found to be rather similar [69,70]. Considering the difference in standard entropy between F2(gas) and the mixture 02(gas) + H2(gas) taken in their standard states (which can be extracted from general thermodynamic tables), the difference between the entropy terms of the Gibbs function relative to HA and FA, around room temperature, is about 6.5 times lower than the difference between enthalpy terms (close to 125 kJ/mol as estimated from Tacker and Stormer [69]). This indicates that FA higher stability is mostly due to the lower enthalpy of formation of FA (more exothermic than for HA), and that it is not greatly affected by entropic factors. Jemal et al. [71] have studied some of the thermodynamic properties of FA and HA with varying cationic substitutions, and these authors linked the lower enthalpy of formation of FA compared to HA to the decrease in lattice volume in FA. 

The theoretical emf for this cell, calculated from the Gibbs function for the decomposition of water, is E° = 1,229 Vat 298 K, but this decreases with temperature to about 1 V at 500 K. A compromise in cell design is therefore always needed between the voltage generated and an operating temperature high enough to maintain a fast reaction. 

Decrease in the Gibbs Function as a Condition for Spontaneous Reaction ... 

Since Ecell is defined to be positive for a spontaneous reaction, this equation correctly expresses a decrease in Gibbs function, which is the thermodynamic criterion for a spontaneous reaction at constant T and P. It is evident that if AGreact can be calculated from AG j- data, the potential of a cell arranged for reversible operation can be determined conversely, experimental measurements of Ecen permit calculation of AGreact. Both types of calculations are useful in electrochemical work and, thus, in the analysis of corrosion. 

The relation (3G/BT)p = — S shows that the Gibbs function of a system decreases with T at constant P in proportion to the magnitude of its entropy. This makes good sense when one considers the definition of G, which is G = U + pV — TS. Hence, G is expected to decrease with T in proportion to S when p is constant. Furthermore, an increase in temperature causes entropy to increase according to... 

Under such conditions the Gibbs function can only decrease or remain constant. The criterion of equilibrium of a system which is held at constant temperature and pressure is therefore that 0 has reached its minimum value. It is, of course, precisely these conditions of constancy of temperature and pressure which are of the greatest practical interest in the laboratory, and it is for this reason that O is so important in the theory of phase equilibrium and reaction equilibrium. 

Thus, between initial and final states which are at the same temperature, and with a heat reservoir which is also at this temperature, the maximum useful work which may be obtained during the steady flow of a fluid is equal to the decrease of its Gibbs function. 

The fugacity is a useful function in the study of phase and reaction equilibrium, as will be shown in later chapters. It may also be used in the computation of the work of expansion or compression of a gas in a flow process. As discussed in 2 4, the maximum shaft work which may be obtainedf during the steady isothermal flow of a gas is equal to the decrease of its Gibbs function ... 

The Gibbs function is a measure of the maximum work possible at a given state from a constant temperature and pressure reversible process. It can be shown from a combination of the first and second laws of thermodynamics for a simple compressible system that the Gibbs function of a system will always decrease or remain the same for a spontaneous process. Consider the differential of the Gibbs function ... 

The decrease of protein thermodynamic stability on pH decreasing suggests a preferential binding of protons to the unfolded state. The effect of pH on the standard denaturation Gibbs function, tyfi, has been theoretically analyzed by... 

Thus, adding surfactants to minimize the oil-water and solid-water interfacial tensions causes removal to become spontaneous. On the other hand, a mere decrease in the surface tension of the water-air interface, as evidenced, say, by foam formation, is not a direct indication that the surfactant will function well as a detergent. The decrease in yow or ysw implies, through the Gibb s equation (see Section III-5) adsorption of detergent. 

Metal deposition can occur only if 77 is negative so the Gibbs energy of a cluster as a function of the particle number N first rises, reaches a maximum, and then decreases. This is illustrated in Fig. 10.4 for three different overpotentials. Notice how strongly the curve depends on the applied overpotential. AG reaches its maximum for a critical particle number of ... 

The Helmholtz and Gibbs energies on the other hand involve constant temperature and volume and constant temperature and pressure, respectively. Most experiments are done at constant Tandp, and most simulations at constant Tand V. Thus, we have now defined two functions of great practical use. In a spontaneous process at constant p and T or constant p and V, the Gibbs or Helmholtz energies, respectively, of the system decrease. These are, however, only other measures of the second law and imply that the total entropy of the system and the surroundings increases. 

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