Standard molality

Pt, H2 HCl, AgCl, D-glueose, 5wt% Ag (molal standard potential) 0.2195 50Wil... 

We have pointed out that a concentration m2(o of the solute in the real solution may have an activity of 1, which is equal to the activity of the hypothetical 1-molal standard state. Also, Hm2, the partial molar enthalpy of the solute in the standard state, equals the partial molar enthalpy of the solute at infinite dilution. We might inquire whether the partial molar entropy of the solute in the standard state corresponds to the partial molar entropy in either of these two solutions. 

We can summarize our conclusions about the thermodynamic properties of the solute in the hypothetical 1-molal standard state as follows. Such a solute is characterized by values of the thermodynamic functions that are represented by p2. 77m2. and 5m2- Frequently a real solution at some molality m2(j) also exists (Fig. 16.4) for which p.2 = that is, for which the activity has a value of 1. The real solution for which // i2 is equal to H 2 is the one at infinite dilution. Furthermore, 5 n,2 has a value equal to 5 2 for some real solution only at a molahty m2(k) that is neither zero nor m2( j). Thus, three different real concentrations of the solute exist for which the thermodynamic qualities p,2, //mi. and S a respectively, have the same values as in the hypothetical standard state. 

In Chapters 16 and 17, we developed procedures for defining standard states for nonelectrolyte solutes and for determining the numeric values of the corresponding activities and activity coefficients from experimental measurements. The activity of the solute is defined by Equation (16.1) and by either Equation (16.3) or Equation (16.4) for the hypothetical unit mole fraction standard state (X2° = 1) or the hypothetical 1-molal standard state (m = 1), respectively. The activity of the solute is obtained from the activity of the solvent by use of the Gibbs-Duhem equation, as in Section 17.5. When the solute activity is plotted against the appropriate composition variable, the portion of the resulting curve in the dilute region in which the solute follows Henry s law is extrapolated to X2 = 1 or (m2/m°) = 1 to find the standard state. 

B. Aquatic partial pressure of each gas = 1 atm activity of each solute = 1 molal Standard Hydrogen Electrode (SHE) same as classical with additional constraint of... 

To obtain the Gibbs energy of formation in aqueous solution, we must have solubility data as well as activity coefficients of acetic acid at various concentrations. From these data the change in Gibbs energy for solution of the liquid acetic acid in water to give aqueous acetic acid in the hypothetical 1 molal standard state (Eq. 6-39) can be obtained. 

These values refer to the hypothetical one molal standard state for the ions. The difference between these values, 3.1 kcal. mole-1, should represent the difference in free energy of formation of Na+ and K+. The value given by Jolly (20) and Coulter (6, 7) for this difference is + 3.4 kcal. mole-1 in good agreement as is the value of AG° = — 3.14 very accurately determined by Schug and Friedman (47) for the reverse reaction. Russell and Sienko (45) used the cells... 

Activities in aqueous solution are generally based on the 1 molality standard state. 

As the activities in aqueous electrolyte solutions are defined with respect to the 1 molality standard state ( or infinitely dilute solution standard state), the activity of an ionic species becomes equal to its molality as the concentration approaches zero (Henry s Law). 

The advantage of this standard state is that it provides a very simple rel between activity and concentration for cases in which Henry s law is at 1 approximately valid. Its range does not commonly extend to a concentration 1 m. In the rare case where it does, the standard state is a real state of the sol-This standard state is useful only where AG° data are available for the ideal the sense of Henry s law) 1-molal standard state, for otherwise the equilibri constant cannot be evaluated by Eq. (15.14). 

The above explanation of the chelate effect depends on the fact that a unit molal standard state is employed for all solute species. The heat and entropy of the replacement reaction correspond to those that would result from converting the reactants to products in their standard states ... 

In summary, thermodynamic models of natural water systems require manipulation of chemical potential expressions in which three concentration scales may be involved mole fractions, partial pressures, and molalities. For aqueous solution species, we will use the moial scale for most solutes, with an infinite dilution reference state and a unit molality standard state (of unit activity), l or the case of nonpolar organic solutes, the pure liquid reference and standard states are used. Gaseous species will be described on the partial pressure (atm — bar) scale. Solids will be described using the mole fraction scale. Pure solids (and pure liquids) have jc, = 1, and hence p, = pf. 

The activity of Na in liquid NH3 has been obtained from measurements of vapour pressure together with previously published electrochemical data. For the reaction (1) in the hypothetical 1 molal standard state, AH° = 6.10 kJ mo The Tait equation of state has been used to calculate the molar volumes of NH3 at 100—10 000 bar and 50—200 °C. The calculations showed that the equation is valid at 100 bar and 50 °C and at 200 bar and 100—200 °C. Temperature dependences of the constants B and C of the Tait equation and the equation accuracy are discussed. 

Molarity, molality, standard state and activity Solubility product constants... 

Here the standard state for the ionic species is a 1-molal ideal solution the enthalpies and Gibbs energies of formation for some ions in this standard state at 25 C are given in Table 13.1-4. In Eq. 13.1-27 the standard state for the undissodated molecule has also been chosen to be the ideal 1-molal solution (see Eq. 9.7-20), although the pure component state could have been used as well (with appropriate changes in AfG, b aA B ). Finally, we have used the mean molal activity coefficient, y , of Eq. 9.10-11. Also remember that for the 1-molal standard state, y ° 1 as the solution becomes veiy dilute in the component. 

As the apparent equilibrium constant is more easily measured in the laboratory than the thermodynamic equilibrium constant, most reported data on biochemical reactions are apparent equilibrium constants. Since the thermodynamic equilibrium constant here is based on ideal 1-molal standard states, so that the activity coefficients are unity at infinite dilution, we have... 

Changing ideal to mean Raoultian ideality, the ideal one molal standard state would give... 

The real situation is of course that in this type of solution no fugacity data are available for the solute, but activity coefficients indicating the deviation from Henry s Law can be either calculated or measured, and they allow us to calculate exactly the same activities and hence ( — ) values using the ideal one molal standard state. For example at 0.5 and 1.0 molal the activity coefficient (7h) is 1.33 and 1.5 respectively, so the activities of B using the ideal one molal standard state (ub = are 0.67... 

Figure 12.4 corresponds to reality. The lengthy introduction by way of the fictitious Figure 12.3 is simply to emphasize that activities using the ideal one molal standard state are really no different from any other activities. They can be thought of as fugacity ratios, and they are simply another of the wide range of choices available for standard states. 

In summary, a value of 1.0 for 7 allows us to obtain values for the properties of the standard state, which we mentioned earlier is the essential factor in the choice of standard state. As for rn°, any value could be used, but none has any advantage over 1.0. Therefore the hypothetical ideal one molal standard state is in universal use for dilute solution (molality-based) activities. 

Suppose you have the activity of a constituent with respect to a particular standard state, but you need its activity using some other standard state. For example, you might know fcoi in a fluid, which is equivalent to knowing its aco2 using an ideal gaseous CO2 at T, 1 bar standard state, but you want to do speciation calculations so you need acoi using the ideal one molal standard state. 

Let s suppose that a measurement of quartz solubility has been used to obtain the free energy of formation (standard or apparent) of H4Si04 in the ideal one molal standard state. This number can then be used (with A/G° terms for the minerals) to calculate the equilibrium constant of the albite-nepheline reaction (equation (13.11)), giving the equilibrium silica concentration in a solution that may never have been experimentally determined, or perhaps never existed, and in which quartz is not stable. Thus knowing the solubility of quartz, one could in a similar way calculate the silica concentration in fluids in contact with a variety of mineral assemblages. 

As usual, it is best to see the truth of a relationship by nnderstanding it rather than by seeing no fault with its derivation. In this case this can be accomplished by realizing that in the ideal one molal standard state to which ArG° refers, the solute component HCl consists in solution entirely as H and Cl, therefore the G of component HCl has no choice but to be identical to Gh+ + Gci, from which it follows that A G° = 0. 

Criss and co-workers, using data from the literature, calculated the entropies of several alkali metal halides in formamide. It should be observed that their published entropies are based on the mol fraction standard state instead of the more common hypothetical one molal standard state. Entropies of electrolytes in this solvent are generally more negative than in water, but more positive than in other solvents that have been examined. 

C. M. Criss, R. P. Held and E. Luksha, J. Phys. Chem., 72, 2970 (1968). The data have been converted from the mol fraction to the hypothetical one molal standard state. 

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