Standard states aqueous solutions

The table specifies thermodynamic standard valnes -fffgg, G gg, S gg, and Cp for selected substances included in cement-chemical calculations. The state of the substances is given by (s) solid, ) liquid, (g) gaseous, and (aq) for ions and gases in aqueous solution. Standard state p = 101325 Pa, and for dissolved substances c = 1 mol/. Reference temperatnre T = 298.15K (25°C). ... 

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 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-... 

In any equilibrium state, both fi, and /t are absolute, finite quantities with a fixed difference between them. If the same standard state is chosen for each of these equations, then fi, — ji° is the same in each equation, and the activity would be the same in all phases at equilibrium. This would be nice, but it would mean using a vapor pressure as the standard state for activity in solids, or an ideal one molal solution standard state for activities in a gas, or perhaps an ideal gas at one bar for an aqueous solute. This would be not only inconvenient, but impossible in many cases. So we accept the small inconvenience of having different activities for the same species in different phases. 

Lanthanide-actinide oxidation-reduction comparisons in aqueous (uncomplexed, standard-state as well as formal ) solutions... 

Equation 10.2.10 predicts that the activity of HCl in aqueous solutions is proportional, in the limit of infinite dilution, to the square of the HCl molality. In contrast, the activity of a nonelectrolyte solute is proportional to the first power of the molality in this limit. This predicted behavior of aqueous HCl is consistent with the data plotted in Fig. 10.1 on page 285, and is confirmed by the data for dilute HCl solurions shown in Fig. 10.2(a). The dashed line in Fig. 10.2(a) is the extrapolation of the ideal-dilute behavior given by o-m,B = (mB/m°). The extension of this line to niB = m° establishes the hypothetical solute reference state based on molality, indicated by a filled circle in Fig. 10.2(b). (Since the data are for solutions at the standard pressure of 1 bar, the solute reference state shown in the figure is also the solute standard state.)... 

Solutions in water are designated as aqueous, and the concentration of the solution is expressed in terms of the number of moles of solvent associated with 1 mol of the solute. If no concentration is indicated, the solution is assumed to be dilute. The standard state for a solute in aqueous solution is taken as the hypothetical ideal solution of unit molality (indicated as std. state or ss). In this state... 

The values given in the following table for the heats and free energies of formation of inorganic compounds are derived from a) Bichowsky and Rossini, Thermochemistry of the Chemical Substances, Reinhold, New York, 1936 (h) Latimer, Oxidation States of the Elements and Their Potentials in Aqueous Solution, Prentice-Hall, New York, 1938 (c) the tables of the American Petroleum Institute Research Project 44 at the National Bureau of Standards and (d) the tables of Selected Values of Chemical Thermodynamic Properties of the National Bureau of Standards. The reader is referred to the preceding books and tables for additional details as to methods of calculation, standard states, and so on. 

II The increment in the free energy, AF, in the reaction of forming the given substance in its standard state from its elements in their standard states. The standard states are for a gas, fugacity (approximately equal to the pressure) of 1 atm for a pure liquid or solid, the substance at a pressure of 1 atm for a substance in aqueous solution, the hyj)othetical solution of unit molahty, which has all the properties of the infinitely dilute solution except the property of concentration. 

ITlie free energy of solution of a given substance from its normal standard state as a sohd, liquid, or gas to the hyj)othetical one molal state in aqueous solution may he calculated in a manner similar to that described in footnote for calculating the heat of solution. 

This procedure can now be repeated with a base D that is slightly weaker than C, using C as the reference. In this stepwise manner, a series of p determinations can be made over the acidity range from dilute aqueous solution to highly concentrated mineral acids. Table 8-18 gives pS bh+ values determined in this way for nitroaniline bases in sulfuric and perchloric acid solutions. This technique of determining weak base acidity constants is called the overlap method, and the series of p kBH+ values is said to be anchored to the first member of the series, which means that all of the members of the series possess the same standard state, namely, the hypothetical ideal 1 M solution in water. 

Figure 11.9 Plot of volt equivalent against oxidation state for various compounds or ions containing N in acidic aqueous solution. Note that values of - AC refer lo N2 as standard (zero) but are quoted per mol of N aloms and per mol of. Nj they refer to reactions in the direction (ox) ne —> (red). Slopes corresponding to some common oxidizing and reducing agents are included for comparison.

In addition to simple dissolution, ionic dissociation and solvolysis, two further classes of reaction are of pre-eminent importance in aqueous solution chemistry, namely acid-base reactions (p. 48) and oxidation-reduction reactions. In water, the oxygen atom is in its lowest oxidation state (—2). Standard reduction potentials (p. 435) of oxygen in acid and alkaline solution are listed in Table 14.10- and shown diagramatically in the scheme opposite. It is important to remember that if or OH appear in the electrode half-reaction, then the electrode potential will change markedly with the pH. Thus for the first reaction in Table 14.10 O2 -I-4H+ -I- 4e 2H2O, although E° = 1.229 V,... 

The theory of titrations between weak acids and strong bases is dealt with in Section 10.13, and is usually applicable to both monoprotic and polyprotic acids (Section 10.16). But for determinations carried out in aqueous solutions it is not normally possible to differentiate easily between the end points for the individual carboxylic acid groups in diprotic acids, such as succinic acid, as the dissociation constants are too close together. In these cases the end points for titrations with sodium hydroxide correspond to neutralisation of all the acidic groups. As some organic acids can be obtained in very high states of purity, sufficiently sharp end points can be obtained to justify their use as standards, e.g. benzoic acid and succinic acid (Section 10.28). The titration procedure described in this section can be used to determine the relative molecular mass (R.M.M.) of a pure carboxylic acid (if the number of acidic groups is known) or the purity of an acid of known R.M.M. 

Potassium bromate is readily available in a high state of purity the product has an assay value of at least 99.9 per cent. The substance can be dried at 120-150 °C, is anhydrous, and the aqueous solution keeps indefinitely. It can therefore be employed as a primary standard. Its only disadvantage is that one-sixth of the relative molecular mass is a comparatively small quantity. 

However, as can be seen in Figure 6.15, which is a graph of the fugacity of HC1 against molality in dilute aqueous solutions of HC1 (near. i = 1), f2 approaches the m axis with zero slope. This behavior would lead to a Henry s law constant, kn.m = 0. given the treatment we have developed so far. Since the activity with a Henry s law standard state is defined as a —fi/kwnu this would yield infinite activities for all solutions. 

Relative partial molar enthalpies can be used to calculate AH for various processes involving the mixing of solute, solvent, and solution. For example, Table 7.2 gives values for L and L2 for aqueous sulfuric acid solutions7 as a function of molality at 298.15 K. Also tabulated is A, the ratio of moles H2O to moles H2S(V We note from the table that L — L2 — 0 in the infinitely dilute solution. Thus, a Raoult s law standard state has been chosen for H20 and a Henry s law standard state is used for H2SO4. The value L2 = 95,281 Tmol-1 is the extrapolated relative partial molar enthalpy of pure H2SO4. It is the value for 77f- 77°. 

---