Spontaneous processes chemical potential

Under most conditions, the process is spontaneous/ A chemical potential difference drives the reaction and AG < 0. When the reactants are separated as shown in Figure 9.3, the chemical potential difference can be converted to an electrical potential E. When the electrodes are connected through an external circuit, the electrical potential causes an electric current to flow. Because the electrical potential is the driving force for electrons to flow, it is sometimes... 

In Chapter 5, we considered systems in which composition becomes a variable, and defined and described the chemical potential. We showed that the chemical potential provides the condition for spontaneity or equilibrium. It is the potential that drives the flow of mass in a chemical process, A useful quantity related to the chemical potential is the fugacity. It can also be thought of as a measure of the flow of mass in a chemical process, and can be used to determine the point of equilibrium. It is often known as the escaping tendency since it can be used to describe the ease with which mass flows from one phase to another, particularly the flow from a solid or liquid phase to a gas phase. 

We now have the foundation for applying thermodynamics to chemical processes. We have defined the potential that moves mass in a chemical process and have developed the criteria for spontaneity and for equilibrium in terms of this chemical potential. We have defined fugacity and activity in terms of the chemical potential and have derived the equations for determining the effect of pressure and temperature on the fugacity and activity. Finally, we have introduced the concept of a standard state, have described the usual choices of standard states for pure substances (solids, liquids, or gases) and for components in solution, and have seen how these choices of standard states reduce the activity to pressure in gaseous systems in the limits of low pressure, to concentration (mole fraction or molality) in solutions in the limit of low concentration of solute, and to a value near unity for pure solids or pure liquids at pressures near ambient. 

The chemical potential is defined as the increase in free energy of a system on adding an infinitesimal amount of a component (per unit number of molecules of that component added) when T, p and the composition of all other components are held constant. Clearly, from this definition, if a component i in phase A has a higher chemical potential than in phase B (that is, xf > pf) then the total free energy will be lowered if molecules are transferred from phase A to B and this will occur in a spontaneous process until the chemical potentials equalize, at equilibrium. It is easy to see from this why the chemical potential is... 

Equilibria and rates should be clearly distinguished. Equilibrium is the end point of any spontaneous process, whether chemical or physical, in which the driving forces (potentials) for changes are balanced and there is no further tendency to... 

Let s look more closely at spontaneous processes and at the thermodynamic driving forces that cause them to occur. We saw in Chapter 8 that most spontaneous chemical reactions are accompanied by the conversion of potential energy to heat. For example, when methane burns in air, the potential energy stored in the chemical bonds of CH4 and 02 is partly converted to heat, which flows from the system (reactants plus products) to the surroundings ... 

Further insight regarding the concept of the chemical potential may be obtained as follows Consider a two-phase, one—component system at fixed temperature and pressure for which G - niPi + n p, and suppose that at some instant > px. The system can then not be at equilibrium instead, some spontaneous process must occur which ultimately results in the equalization of and. At constant T and P this can occur only by a transfer of matter from one phase to the other. Let there be a transfer of - dnx - + dn > 0 moles from phase 1 to phase 2 then dG — (p — p1)dn1, where we have set dnx = dnx. Since we assumed p > the preceding relation shows that dG < 0 for this case i.e., the transfer of matter from the phase of higher chemical potential to the phase of lower chemical potential occurs spontaneously. Thus, a difference in chemical potential represents a driving force for transfer of chemical... 

The second law of thermodynamics then states that the entropy of an isolated system (a system with constant U and constant V) increases (d5 > 0) for a spontaneous processes or stays constant (d5 = 0) at equilibrium. In Eq. 11.9, no internal processes ate considered S is normally regarded as an external variable even though it is not possible to control its value externally without knowledge of the properties of the system). If internal processes are considered, an internal variable must be included, namely, /a, the chemical potential (to be discussed shortly). 

We wiU treat the spontaneous transformation of R to Pi as the main process route (process Zl). This transformation is possible when chemical potential ip (and, consequendy, thermodynamic rush R = exp(dR/RT)) of compound R is higher than potential (correspondingly, higher than the thermodynamic rush Pi = exp(ppj/RT)) of compound Pr An analogous relation between Pr and Pp is necessary for the transformation of compound R to the by product P2 (Figure 2.4A). 

We have only discussed two of the sixteen fields given in the figure, the prediction of the direction in which a reaction can proceed spontaneously by means of the chemical potential and the temperature and pressure dependence of p and its application. A next step would be to go over to mass action, i.e., the concentration dependence of p. This leads directly to the deduction of the mass action law, calculation of equilibrium constants, solubilities, and many other data. An expansion of the concept to colligative phenomena, diffusion processes, surface effects, electrochemical processes, etc., is easily possible. Furthermore, the same tools allow solving problems even at the atomic and molecular level that are usually treated by quantum statistical methods. 

A motorcycle is powered by the combustion of fuel, a spontaneous c chemical process. The fuel in the -tanK is at a higher chemical 1 potential than the combustion products (primarily carbon dioxide and water) leaving the exhaust. 

Equilibria and rates should be clearly distinguished. Equilibrium is the end point of any spontaneous process, whether chemical or physical, in which the driving forces (potentials) for changes are balanced and there is no further tendency to change. Chemical equilibrium is the final state of a reaction at which no further changes in compositions occur at a given temperature and pressure. As an example of a physical process, let us consider the absorption of a gas into a liquid. 

It is readily seen from Fig. 3.6 that for each value of x abovethere are two different values of (f>2 at which the chemical potential of the solvent in the two phases is the same. This means that solutions with concentrations represented by these two values of thermodynamic equilibrium fox x >Xc- It also implies that a solution which has an intermediate value of (p2 wiU spontaneously separate into two stable liquid phases with these two concentrations and a concomitant decrease in the free energy. Thus, if is increased by decreasing the temperature, a fully miscible system at higher temperatures is transformed to one of limited miscibility at the lower temperature. At some critical temperature Tc, during this process, incipient phase separation (as indicated by the onset of an... 

As in the case of fluid interfaces, the question of whether the adsorption of proteins onto solids is reversible or irreversible is very important for correct estimation of physicochemical characteristics of the process. In a reversible process, dilution of sorbate in the bulk phase should lead to spontaneous desorption of some portion of adsorbed molecules up to elimination of a transient difference in the chemical potential of the sorbate at the interface and in the solution the ascending and descending branches of the isotherm must overlap at all values of Cb. Only in this case the isotherm represents thermodynamic equilibrium, and the equilibrium constant Kads and the standard Gibbs energy of adsorption AG°ads = A/7°ads - rAS°ads can be determined. 

Gibbs free energy is a potential for reversible work in constant T-P processes, and always decreases in spontaneous processes. By comparison with (5.26) it is clear that G is a measure of the net work or non-PAV work. This function therefore contrasts with the Helmholtz work function, which measures total work, including mechanical PY work. The Gibbs free energy is a particularly useful measure of the electrical or chemical work attainable from a process and is used a great deal with chemical systems where PY work is often unimportant. 

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