Chemical potential of gas

General expressions for the chemical potentials of gases and solids have been derived in chapters X and XII, so that using equations (10.19) and (12.29) and neglecting the effect of pressure on the chemical potential of the soHd, we have... 

Phase Transition The chemical potential of gases therefore decreases especially fast with increase in temperature. Their tendency to transform decreases most strongly so that, by comparison to other states, the gaseous state becomes more and more stable. This simply means that, as a result of temperature increase, all other states must eventually transform into the gaseous state. At high temperatures, gases possess the weakest tendency to transform and therefore represent the most stable form of matter. 

This equation is precise enough to be applied to pressures up to about 10 kPa (1 bar). It also lends itself to estimates up to 10 or even 10" kPa. In anticipation of this, we have applied the equation above to treating the pressure dependence of the chemical potential of gases [cf. Eq. (5.18)]. 

In the next step the chemical potential of gases is snpposed to be described by the state variables pressnre and temperatnre. The chemical potential of a pnre, ideal... 

Mass transfer Irreversible and spontaneous transport of mass of a chemical component in a space with a non-homogeneous field of the chemical potential of the component. The driving force causing the transport can be the difference in concentration (in liquids) or partial pressures ( in gases) of the component. In biological systems. 

In the case of ions in solution, and of gases, the chemical potential will depend upon concentration and pressure, respectively. For ions in solution the standard chemical potential of the hydrogen ion, at the temperature and pressure under consideration, is given an arbitrary value of zero at a specified concentration... 

In the section on chemical equilibrium in gases we introduced a magnitude called the molecular chemical potential of a component ... 

For condensed phases (liquids and solids) the molar volume is much smaller than for gases and also varies much less with pressure. Consequently the effect of pressure on the chemical potential of a condensed phase is much smaller than for a gas and often negligible. This implies that while for gases more attention is given to the volumetric properties than to the variation of the standard chemical potential with temperature, the opposite is the case for condensed phases. 

In mixtures of real gases the ideal gas law does not hold. The chemical potential of A of a mixture of real gases is defined in terms of the fugacity of the gas, fA. The fugacity is, as discussed in Chapter 2, the thermodynamic term used to relate the chemical potential of the real gas to that of the (hypothetical) standard state of the gas at 1 bar where the gas is ideal ... 

With respect to an enzyme, the rate of substrate-to-product conversion catalyzed by an enzyme under a given set of conditions, either measured by the amount of substance (e.g., micromoles) converted per unit time or by concentration change (e.g., millimolarity) per unit time. See Specific Activity Turnover Number. 2. Referring to the measure of a property of a biomolecule, pharmaceutical, procedure, eta, with respect to the response that substance or procedure produces. 3. See Optical Activity. 4. The amount of radioactive substance (or number of atoms) that disintegrates per unit time. See Specific Activity. 5. A unitless thermodynamic parameter which is used in place of concentration to correct for nonideality of gases or of solutions. The absolute activity of a substance B, symbolized by Ab, is related to the chemical potential of B (symbolized by /jlb) by the relationship yu,B = RTln Ab where R is the universal gas constant and Tis the absolute temperature. The ratio of the absolute activity of some substance B to some absolute activity for some reference state, A , is referred to as the relative activity (usually simply called activity ). The relative activity is symbolized by a and is defined by the relationship b = Ab/A = If... 

Here, j al is the total energy of an isolated 02 molecule at T OK. If we neglect zero-point energies, we can obtain this energy from a simple DFT calculation of the isolated molecule. The second term on the right in Eq. (7.6) is the difference in the chemical potential of 02 between T OK and the temperature of interest at the reference pressure. This chemical potential difference can be evaluated for 02 and many other gases using data tabulated in the NIST-JANAF Thermochemical Tables ... 

The first and the second law of thermodynamics allow the description of a reversible fuel cell, whereas in particular the second law of thermodynamics governs the reversibility of the transport processes. The fuel and the air are separated within the fuel cell as non-mixed gases consisting of the different components. The assumption of a reversible operating fuel cell presupposes that the chemical potentials of the fluids at the anode and the cathode are converted into electrical potentials at each specific gas composition. This implies that no diffusion occurs in the gaseous phases. The reactants deliver the total enthalpy J2 ni Hi to the fuel cell and the total enthalpy J2 ni Hj leaves the cell (Figure 2.1). 

The thermodynamic equations for the Gibbs energy, enthalpy, entropy, and chemical potential of pure liquids and solids, and for liquid and solid solutions, are developed in this chapter. The methods used and the equations developed are identical for both pure liquids and solids, and for liquid and solid solutions therefore, no distinction between these two states of aggregation is made. The basic concepts are the same as those for gases, but somewhat different methods are used between no single or common equation of state that is applicable to most liquids and solids has so far been developed. The thermodynamic relations for both single-component and multicomponent systems are developed. 

The number of isomers in an isomer group is represented by Njso. At chemical equilibrium, all of the isomers have the same chemical potential, and this chemical potential is represented by iso. The amount of an isomer group is represented by niso = En . For a group of gaseous isomers at equilibrium, the chemical potential of the isomer group in a mixture of ideal gases is given by... 

Chemical Potentials of Real Gases Fugacity, f, Activity, a and Activity Coefficient, [Pg.122]

Because of the continual revision in pP values, no attempt will be made to present a list of critically compiled data, even for the compounds of principal interest in soils. In this and subsequent chapters, Standard-State chemical potentials for gases, liquids, solids, and solutes usually will be taken from data in the following critical compilations. 

The units used to express solubilities of gases, e.g. Henry s law coefficients, Ostwald coefficients and Bunsen coefficients, have to be converted to the relevant solution standard state (p. 213). Such solubilities (Battino and Clever, 1966 Wilhelm and Battino, 1973) are valuable in the analysis of kinetic data. For example, the solubility of a neutral solute in a range of aqueous mixtures can provide some indication of the variation of the chemical potential of a neutral reactant because, from eqn (11), 8m AGe = 8mnf. Where the pure solute is a liquid or solid, it is often convenient to chose the pure solute as a standard state, represented by the symbol, ° in eqn (12). Similar comments apply to the related thermodynamic quan-... 

It is evident from Eq. 1.41 that the chemical potential of any constituent of a mixture of ideal gases is determined by its partial... 

From various EOSs, it is possible to determine the compressibility and hence the chemical potential of a real gas. For example, using the virial equation, which is valid for gases at low density, we have... 

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