Standard State electrolyte

Were the FlCl in its standard state, AC would equal where is the standard emf for the reaction. In general, for any reversible chemical cell without transference, i.e. one with a single electrolyte solution, not one with any kind of junction between two solutions. 

The standard state of an electrolyte is the hypothetical ideally dilute solution (Henry s law) at a molarity of 1 mol kg (Actually, as will be seen, electrolyte data are conventionally reported as for the fonnation of mdividual ions.) Standard states for non-electrolytes in dilute solution are rarely invoked. 

Electrode Potential (E) the difference in electrical potential between an electrode and the electrolyte with which it is in contact. It is best given with reference to the standard hydrogen electrode (S.H.E.), when it is equal in magnitude to the e.m.f. of a cell consisting of the electrode and the S.H.E. (with any liquid-junction potential eliminated). When in such a cell the electrode is the cathode, its electrode potential is positive when the electrode is the anode, its electrode potential is negative. When the species undergoing the reaction are in their standard states, E =, the stan-... 

The difficulties engendered by a hypothetical liquid standard state can be eliminated by the use of unsymmetrically normalized activity coefficients. These have been used for many years in other areas of solution thermodynamics (e.g., for solutions of electrolytes or polymers in liquid solvents) but they have only recently been employed in high-pressure vapor-liquid equilibria (P7). 

For electrolytes where dissociation is extensive, but not complete, the classification is somewhat arbitrary, and the electrolyte can be considered to be either strong or weak. Thermodynamics does not prevent us from treating an electrolyte either way, but we must be careful to designate our assignment because the choice of standard state is different for a strong electrolyte and a weak electrolyte. Assuming that an electrolyte is weak requires that we have some nonthermodynamic procedure for distinguishing clearly between the dissociated and undissociated species. For example, Raman spectroscopy... 

This equation is the basis of the strong electrolyte standard state. Substitution into equation (6.122) gives ArG° = 0, which when substituted into equation (6.123) gives... 

Comparing this equation with equation (6.125) demonstrates that K = I for the dissociation of an electrolyte when the strong electrolyte standard state is chosen. 

The definition of the strong electrolyte standard state gives a2 = a+a so that... 

With the choice of a pure substance standard state for the solid, and a strong electrolyte standard state for the dissolved AgCl, we get... 

This last example provides a demonstration of the flexibility inherent in the choice of standard states. A strong electrolyte standard state is chosen for NaA(aq) and NaCl(aq) so that... 

However, for HA, we choose a weak electrolyte standard state so that... 

We should keep in mind that a strong electrolyte standard state could have been chosen for HOAc, in which case,... 

Electrolytes are solutes that carry an electrical charge. As charged species typically have negligible vapor pressures, it is convenient to introduce yet another standard state for their description.8,9 In general, the same conditions of concentration, temperature, and pressure are assumed as... 

In Equation 50 the chemical potential of non-electrolyte A depends on the usual choice of standard-state conventions described above, and the chemical potentials of both H2(g) and H+(sod are taken to be zero (this defines e.s.s., the electrolyte standard state). By setting the standard-state free energy of the solvated proton equal to zero, this standard-state convention... 

Note, in using Equations 50 and 53 above, that tabulations of thermodynamic data for electrolytes tend to employ a 1 molar ess concentration for all species in solution. For situations defined to have a standard-state pH value different from 0 (which corresponds to a 1 molar concentration of solvated protons), the standard-state chemical potentials for anions and cations are determined as... 

Debye-Huckel effects are significant in the dilute range and are not considered, and (2) the usual composition scale for the solute standard state is molality rather than mole fraction. Both of these problems have been overcome, and the more complex relationships are being presented elsewhere (17). However, for most purposes, the virial coefficient equations for electrolytes are more convenient and have been widely used. Hence our primary presentation will be in those terms. 

The standard state for the mean ionic activity coefficient is Henry s constant H., f is the standard-state fugacity for the activity coefficient f- and x. is the mole fraction of electrolyte i calculated as though thi electrolytes did not dissociate in solution. The activity coefficient f is normalized such that it becomes unity at some mole fraction xt. For NaCl, xi is conveniently taken as the saturation point. Thus r is unity at 25°C for the saturation molality of 6.05. The activity coefficient of HC1 is normalized to be unity at an HC1 molality of 10.0 for all temperatures. These standard states have been chosen to be close to conditions of interest in phase equilibria. 

Vera and co-workers (7,W,lj ) have extended the thermodynamic correlation and made two additions. First, they have developed a semi-empirical expression for the excess Gibbs energy in place of the simple empirical equations originally used (Equations 8 and 9). Also, while they use a standard state of the electrolyte of a saturated solution, they change the standard state of water back to the conventional one of pure water. 

The work of Vera and co-workers nasHed to a semi-empirical expression for the excess Gibbs energy which is consistent with our choice of the saturated solution as the standard state for the electrolyte. Vera has, however, shown that pure water is a more convenient standard state for hLO in place of the saturated solution used by Vega and Funk (19). This is particularly convenient for ternary and higher systems since it avoids the complication of having a composition-dependent standard state. 

Concentrations of aqueous electrolyte solutions are conventionally expressed using the aquamolality scale (L = moles salt per 55.508 mol solvent (l,000g for H20)). Some typical solubilities (298.15K) are listed in Table 5.13. Almost all salts are less soluble in D20 than in H20. For those salts whose solubility increases with temperature, which is the ordinary behaviour, the isotope effects decrease with temperature. Writing the standard state partial molar free energy of pure solid salt as Pxsalt) and its standard state in solution as p, (HorD) we have on comparing the saturated solutions in H20 and D20,... 

Fig. 4-10. Electron energy levels in (a) an isolated solid metal and in (b) a metal electrode immersed in an electrolyte solution M = metal S = electrolyte solution e(STD) = gaseous electrons in the standard state e

ACTIVITIES, EXCESS GIBBS FUNCTIONS, AND STANDARD STATES FOR NON ELECTROLYTES... 

When activity data for a strong electrolyte such as HCl are plotted against 1712/m°), as illustrated in Figure 19.1, the initial slope is equal to zero. Thus, an extrapolation to the standard state yields a value of the activity in the standard state equal to zero, which is contrary to the definition of activity in Equations (16.1) and (16.3). Therefore, it is clear that the procedure for determining standard states must be modified for electrolytes. 

Equation (19.19) is consistent with the empirical observation that a nonzero initial slope is obtained when the activity of a ternary electrolyte such as BaCl2 is plotted against the cube of m2/m°). As the activity in the standard state is equal to 1, by definition, the standard state of a ternary electrolyte is that hypothetical state of unit molality ratio with an activity one-fourth of the activity obtained by extrapolation of dilute solution behavior to m2/m° equal to 1, as shown in Eigure 19.4. 

Optical and nuclear magnetic resonance methods apphcable to moderately strong electrolytes have been made increasingly precise (14). By these methods, it has proved feasible to determine concentrations of the undissociated species and hence of the dissociation constants. Thus, for HNO3 in aqueous solution (14) at 25°C, K is 24. However, in dehning this equilibrium constant, we have changed the standard state for aqueous nitric acid, and the activity of the undissociated species is given by the equation... 

---