Standard state for aqueous solutes

Concentration Scales For other, more practical, concentration scales for mixtures, similar considerations arise regarding reference and standard states. For aqueous solutions, both the mole fraction scale and the molal scale are used for thermodynamic interpretations. The solvent water is described on the... 

Standard state for aqueous solutes (aq) The standard state of a dissolved solute is defined as a solution at 1 bar that obeys Henry s law at concentration of unit molality, that is, 1 mol of solute per kg of solvent. 

The standard state specifies the pressure (always i bar) and purity of component. With the exception of the standard state for aqueous solutes, components are taken to be pure. Temperature is not specified but is fixed by the user according to the problem at hand. Since pressure and composition (purity) are fixed, all properties of the standard state are functions of temperature only. 

Calculate the activity of oxygen in water at 25 °C, 5 bar, jc, = 3 x 10-5, using the standard state for aqueous solutes. Solution The concentration of oxygen expressed as molality is... 

At this point you should note that we have not used the infinite dilution standard state for aqueous solutes, as we will for other properties in Chapter 10. Having m- 0 in Equation (8.24) would obviously be inconvenient. 

Although theoretically we could choose any value for m°, any choice except m° = 1 would introduce complications, and of course we want 7 = 1 so that the standard state lies on the tangent and refers to properties at infinite dilution. This leads to the adoption of the hypothetical ideal one molal standard state for aqueous solutes. If in Figure 8.4 we change the concentration scale to molality, and focus on the lower left corner of the diagram, we have Figure 8.5. We have assumed that B is a nonelectrolyte with v = l such as sucrose or oxygen, and the conversion is... 

Standard states For aqueous solutions, gases 1 atm, others 1M... 

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... 

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... 

For species at low concentration in aqueous solution, a different procedure has been widely adopted, because in this case the equality of a, and x, is usually far from correct. The method is based on the use of a fictitious or hypothetical standard state for the solute, taken as the state that would exist if the solute obeyed Henry s law up to a molality m of unity. In this application, Henry s law is expressed as... 

According to Technical Note 270 The standard state for a solute in aqueous solution is taken as the hypothetical ideal solution of unit molality. Non-aqueous solutions are treated as mixtures in Technical Note 270. 

Cells metabolize in an aqueous environment and, except for those of the cells, the thermodynamic properties of the reactants and products of growth-processes are those of these substances in aqueous solution. Values for the free energy, enthalpy, and entropy of formation of all substances from the elements at 298.15 K and 1 atm are referred to as thermodynamic properties. These can be found in several compendia [32-34] listed for quantities of one mol in a given standard state. In aqueous solution, all substances are taken to be at a concentration of one mol at unit activity for values of A , and of a hypothetical one mol at infinite dilution for Af//°. Values for Af5" can be calculated using the following form of the Gibbs free energy equation, where the superscript refers to the aqueous standard state. 

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. 

For aqueous solutions of salts, lt, (P, 7) represents the chemical potential of pure ions. This chemical potential cannot be measnred experimentally. Instead of nsing this hypothetical standard state, the activity coefficients of ions often are normalized by introducing the asymmetrical activity coefficient, y,, defined as... 

Neptunium has been characterized from the +3 to +7 oxidation states in aqueous solution. The standard potentials for various Np ions have been determined from measured formal potentials of the various redox couples. These data have been thoroughly reviewed by Martinet [94] and Fahey [95]. Recently the standard potentials for the redox couples Np02 /Np02, Np +/Np +, and Np02 /Np" in acidic aqueous solution have been reevaluated with more detailed consideration of activity coefficients [49,50]. The standard potential accepted here for the Np02 /Np02 couple is 1.161 0.011 V as determined from... 

From the standpoint of the operational definition of the standard state for the above free energy changes, we must remember that, while mole fractions are strongly recommended composition measures (61 Mil), in practice, both molalities, m, and concentrations, c, are widely used. For dilute aqueous solutions at moderate temperatures the numerical values of m and c are only slightly different. This no longer holds for other solvents. 

Table A5.6 is obtained from the extensive tabulation by W. M. Latimer, The Oxidation States of the Elements and their Potentials in Aqueous Solutions, Second Edition, Prentice-Hall, Inc., Engelwood Cliffs, N.J. (1952). His tabulation was published at the time when p = 1 atm was the standard state for gases. His results should be corrected to the p = 1 bar standard state for comparison with other modern standard state thermodynamic data. The correction is given by (RT/F) In (1.01325), which has a value of 0.0003 volts at T = 298.15 K. The correction is small and probably negligible for all except the most precise work. (E° values measured to better than 1(T3 volts are unusual.)...

Many tables of values of standard changes of enthalpy of formation list values for individual ions, particularly in aqueous solutions. In order to do so, an arbitrary definition must be introduced because the properties of individual ions in solution cannot be determined. We consider an electrolyte Mv+Av which is completely ionized in the infinitely dilute solution. We choose this solution to be the standard state for the enthalpy. The enthalpy of this solution per mole of solute, H, is given by... 

The cell reaction for cells without liquid junction can be written as the sum of an oxidation reaction and a reduction reaction, the so-called half-cell reactions. If there are C oxidation reactions, and therefore C reduction reactions, there are C C — 1) possible cells. Not all such cells could be studied because of irreversible phenomena that would take place within the cell. Still, a large number of cells are possible. It is therefore convenient to consider half-cell reactions and to associate a potential with each such reaction or electrode. Because of Equation (12.88), there would be (C - 1) independent potentials. We can thus assign an arbitrary value to the potential associated with one half-cell reaction or electrode. By convention, and for aqueous solutions, the value of zero has been assigned to the hydrogen half-cell when the hydrogen gas and the hydrogen ion are in their standard states, independent both of the temperature and of the pressure on the solution. 

Figure 15.4 Standard state for dilute aqueous solutions.

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... 

Water has an activity of 1 when Nw (see Eq. 2.8) is 1. The concentration of water on a molality basis (number of moles of a substance per kilogram of water for aqueous solutions) is then 1/(0.018016 kg mol-1) or 55.5 molal (m). The accepted convention for a solute, on the other hand, is that aj is 1 when yfj equals 1 m. For example, if yj equals 1, a solution with a 1 -m concentration of solute j has an activity of 1 m for that solute. Thus the standard state for an ideal solute is when its concentration is 1 m, in which case RT In a - is zero.2 A special convention is used for the standard state of a gas such as CO2 or O2 in an aqueous solution—namely, the activity is 1 when the solution is in equilibrium with a gas phase containing that gas at a pressure of 1 atm. (At other pressures, the activity is proportional to the partial pressure of that gas in the gas phase.)... 

This last equation, valid at extremely low concentrations and lacking the troublesome diameter a, is known as the Debye-Hiickel limiting law for ionic activities and has been well verified in aqueous and some non-aqueous systems. The standard state for these electrical activity coefficients is the infinitely dilute solution in which /, = 1. 

However, there are some important differences between the equilibrium constant for Eq. 2 and the usual Kso First, the compound on the left-hand side of Eq. 2 is not a dry solid at standard temperature and pressure, but instead is a homoionic smectite in contact with an aqueous solution. The standard state for MX (s,aq) accordingly is the homoionic clay mineral at standard temperature and pressure in equilibrium with an infin-... 

According to tables of standard potentials, the open-circuit potential of this cell should be 3.58 V. Note, however, that standard potentials are given for aqueous solutions, whereas here the reaction occurs in the solid state, where the free energy of the different species is quite different. 

The standard electrode potentials, E, for such reduction reactions are related to the free energy change for the process by equation 5.3. Since some elements may exist in a number of different oxidation states, it is possible to construct electrode potential diagrams, sometimes called Latimer diagrams, relating the various oxidation states by their redox potentials. Examples are shown in Figure 5.6 for aqueous solutions of some first-row d-block metals and for some actinides in 1 mol dm acid. In cases where the reduction involves oxide or hydroxide ions bound to... 

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