Standard state alternative

The standard-state electrochemical potential, E°, provides an alternative way of expressing the equilibrium constant for a redox reaction. Since a reaction at equilibrium has a AG of zero, the electrochemical potential, E, also must be zero. Substituting into equation 6.24 and rearranging shows that... 

The equilibrium eonstant K is independent of pressure with standard states. The effeet of the pressure is shown in Equation 6-6. K. is usually insensitive and may either inerease or deerease slightly with pressure. When (r -i- s) > (a -i- b), the stoiehiometrie eoeffieients, an inerease in pressure P results in a deerease in eonversion of the reaetants to the produets (i.e., A -i- B o R -i- S). Alternatively, when (r -I- s) < (a -I- b), an inerease in pressure P results in an inerease in the equilibrium eonversion. In ammonia synthesis (Nj -i- SHj o 2NH3), the reaetion results in a deerease in the number of moles. Therefore, an inerease in pressure eauses an inerease in equilibrium eonversion due to this faetor. 

Enthalpy changes for biochemical processes can be determined experimentally by measuring the heat absorbed (or given off) by the process in a calorimeter (Figure 3.2). Alternatively, for any process B at equilibrium, the standard-state enthalpy change for the process can be determined from the temperature dependence of the equilibrium constant ... 

Alternative forms of the equilibrium constant can be obtained as we express the relationship between activities, and pressures or concentrations. For example, for a gas phase reaction, the standard state we almost always choose is the ideal gas at a pressure of 1 bar (or 105 Pa). Thus... 

The temperature at which this condition is satisfied may be referred to as the melting point Tm, which will depend, of course, on the composition of the liquid phase. If a diluent is present in the liquid phase, Tm may be regarded alternatively as the temperature at which the specified composition is that of a saturated solution. If the liquid polymer is pure, /Xn —mS where mS represents the chemical potential in the standard state, which, in accordance with custom in the treatment of solutions, we take to be the pure liquid at the same temperature and pressure. At the melting point T of the pure polymer, therefore, /x2 = /xt- To the extent that the polymer contains impurities (e.g., solvents, or copolymerized units), ixu will be less than juJ. Hence fXu after the addition of a diluent to the polymer at the temperature T will be less than and in order to re-establish the condition of equilibrium = a lower temperature Tm is required. 

An alternative, but equivalent, way to define the heat of formation of a species is to define it as the reference enthalpy at the standard state (25 °C, 1 atm). Thus,... 

The standard state for the heat capacity is the same as that for the enthalpy. For a proof of this statement for the solute in a solution, see Exercise 2 in this chapter. This choice of standard state for components of a solution is different fixjm that used by many thermodynamicists. It seems preferable to the choice of a 1-bar standard state, however, because it is more consistent with the extrapolation procedure by which the standard state is determined experimentally, and it leads to a value of the activity coefficient equal to 1 when the solution is ideal or very dilute whatever the pressure. It is also preferable to a choice of the pressure of the solution, because that choice produces a different standard state for each solution. For an alternative point of view, see Ref. 2. 

It must be emphasized that the choice of a particular standard state of reference has no influence on the result of equilibrium calculations and is only a matter of convenience. It is generally convenient to adopt as standard state for solid components the condition of pure component in the pure phase at the P and T of interest or, alternatively, the condition of pure component in the pure phase at P = 1 bar and T = 298.15 K. ... 

However, in practice it is frequently difficult to obtain results at such low surface concentrations either by direct measurement or by extrapolation. Consequently it is convenient to have an alternative definition in terms of surface covered, e.g., Barrer (3) and Foster (4) take 8 = as the standard state. A knowledge of the amount of material required to complete a monolayer is needed to apply this definition. Where such information is not available, one has to fall back on a definition in terms of so much adsorbate per cubic centimeter or per gram of adsorbent, and this makes interpretation more difficult. The accuracy of the determination will be greater when the heat of adsorption is known for adsorption directly to the standard state rather than as an average over the isotherm as a whole. 

Conventional notation for AH(T, P) is often based on a selected standard state (such as T = 298K, P = 1 atm), which is designated by a degree circle (AH°). Alternatively, the T, P values can be explicitly specified by subscript and superscript values (AHj). Because T is often the more important variation, a hybrid notation such as illustrated in (3.101a-c) is common (with, e.g., 1 atm as standard-state pressure) ... 

In general, activity is merely an alternative way to express chemical potential. The general objective is to express fil in a form that emulates the ideal gas expression (6.55), but with the actual vapor pressure PL of component i (rather than that assumed from Dalton s law). The trick will be to choose a standard-state divisor in (6.55) that makes this expression valid for the components of a real solution. 

There s no point in trying to synthesize a substance from its elements under standard-state conditions if the substance has a positive value of AG°f. Such a substance would have to be prepared at other temperatures and /or pressures, or it would have to be made from alternative starting materials using a reaction that has a negative free-energy change. Thus, a knowledge of thermodynamics can save considerable time in chemical synthesis. 

It may be convenient to define the standard state of the system as the state at an arbitrary temperature, T0, and an arbitrary pressure, P0. The enthalpy of the system in any state defined by the temperature T and the pressure P may then be calculated by a combination of Equations (8.5) and (8.8). Two alternate equations, depending on the path we choose, are obtained. These are... 

We use the expression standard change of enthalpy, because we wish to emphasize a standard change of state. The alternate expression, enthalpy of formation relative to a standard state, could also be used. These expressions are frequently shortened to standard enthalpies. ... 

It is sometimes more convenient to use alternative standard states for the species involved in the reaction. When die standard state of liquid A is changed from Raoultian to Henrian standard state, the free energy change of the reaction... 

Standard-State conventions for chemical elements and dissolved solutes are summarized in Table si. 1. Note that the Standard states for gases and for solutes are hypothetical, ideal states and not actual states. For gases, this choice of Standard State is useful because the ideal gas represents a good limiting approximation to the real behavior of gases and possesses equations of state that are mathematically tractable in applications. For solutes, the choice of a hypothetical Standard State is of value because the alternative choice, consisting simply of the pure solute at unit mole fraction, is not very relevant to a solution component whose concentration must always remain small. Moreover, by... 

When liquid and gas phases are both present in an equilibrium mixture of reacting species, Eq. (11.30), a criterion of vapor/liquid equilibrium, must be satisfied along with the equation of chemical-reaction equilibrium. There is considerable choice in the method of treatment of such cases. For example, consider a reaction of gas A and water B to form an aqueous solution C. The reaction may be assumed to occur entirely in the gas phase with simultaneous transfer of material between phases to maintain phase equilibrium. In this case, the equilibrium constant is evaluated from AG° data based on standard states for the species as gases, i.e., the ideal-gas states at 1 bar and the reaction temperature. On the other hand, the reaction may be assumed to occur in the liquid phase, in which case AG° is based on standard states for the species as liquids. Alternatively, the reaction may be written... 

The experimental observations217 of an apparent light intensity threshold for the photocurrent onset have been rationalized218 on the basis that a critical photon flux must be exceeded to counteract the dark current of opposite polarity flowing through the cell. Thus, there appears to be confusion between alternate definitions of a light intensity threshold a threshold for incipient product (say H2) formation and a threshold for product formation in a specific (e.g., standard) state,218... 

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