Molality standard state, chemical

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 quantity /rf is the chemical potential of substance i in its molality standard state. This standard state is component i in a hypothetical solution with mi equal to m° (exactly 1 molkg ) and with Henry s law in the form of Eq. (6.2-11) valid at this molality. Again we specify a pressure of exactly 1 bar for this standard state. Since the standard state is a hypothetical solution, the actual 1-molal solution is not required to obey Henry s law. 

We now have the foundation for applying thermodynamics to chemical processes. We have defined the potential that moves mass in a chemical process and have developed the criteria for spontaneity and for equilibrium in terms of this chemical potential. We have defined fugacity and activity in terms of the chemical potential and have derived the equations for determining the effect of pressure and temperature on the fugacity and activity. Finally, we have introduced the concept of a standard state, have described the usual choices of standard states for pure substances (solids, liquids, or gases) and for components in solution, and have seen how these choices of standard states reduce the activity to pressure in gaseous systems in the limits of low pressure, to concentration (mole fraction or molality) in solutions in the limit of low concentration of solute, and to a value near unity for pure solids or pure liquids at pressures near ambient. 

For solvents, 1, is equal to V because the standard state is the pure solvent, if we neglect the small effect of the difference between the vapor pressure of pure solvent and 1 bar. As the standard state for the solute is the hypothetical unit mole fraction state (Fig. 16.2) or the hypothetical 1-molal solution (Fig. 16.4), the chemical potential of the solute that follows Henry s law is given either by Equation (15.5) or Equation (15.11). In either case, because mole fraction and molality are not pressure dependent. 

At standard state, equation 8.211 obviously concerns standard state stable components—i.e., pure Fe metal at F = 25 °C, P = 1 bar, and a hypothetical one-molal Fe + solution referred to infinite dilution, at the same P and T conditions (cf section 8.4). The chemical potentials of components in reactions Fe2+(aqueous), ae-(aqueous)) SFC thosc of Standard State hence, by defini-tion, the activity of all components in reaction is 1—i.e.,... 

Here, p and m are the standard chemical potential and concentration (molal scale) of the /-component (z = 1 for solvent, z = 2 for biopolymer) A2 is the second virial coefficient (in molal scale units of cm /mol, i.e., taking the polymer molar mass into account) and m° is the standard-state molality for the polymer. 

Here is the chemical potential of i in its standard state and a, is its molal activity. This equation can be recast in the form known as the van t Hoff reaction isotherm ... 

The reference state of the electrolyte can now be defined in terms of thii equation. We use the infinitely dilute solution of the component in the solvent and let the mean activity coefficient go to unity as the molality or mean molality goes to zero. This definition fixes the standard state of the solute on the basis of Equation (8.184). We find later in this section that it is neither profitable nor convenient to express the chemical potential of the component in terms of its molality and activity. Moreover, we are not able to separate the individual quantities, and /i . Consequently, we arbitrarily define the standard chemical potential of the component by... 

Table 9.3. Standard chemical potential jj°, standard partial molar enthalpy h°, and standard partial molar entropy s,° for a few hydrated ions Standard state 101.3 kPa, 298 K, unit activity in molality scale.

Electrolytes pose a special problem in chemical thermodynamics because of their tendency to dissociate in water into ionic species. It proves to be less cumbersome at times to describe an electrolyte solution in thermodynamic-like terms if dissociation into ions is explicitly taken into account. The properties of ionic species in an aqueous solution cannot be thermodynamic properties because ionic species are strictly molecular concepts. Therefore the introduction of ionic components into the description of a solution is an etfrathermodynamic innovation that must be treated with care to avoid errors and inconsistencies in formal manipulations.20 By convention, the Standard State of an ionic solute is that of the solute at unit molality in a solution (at a designated temperature and pressure) in which no interionic forces are operative. This convention implies that an electrolyte solution in its Standard State is an ideal solution,21 as mentioned in Section 1.2. 

It is of advantage to choose as the standard state of the undissociated part of the electrolyte its hypothetical unionized state in an ideal solution with the molality m = 1 (or molarity c = 1), and to consider as the standard state of the dissociated part of the substance its hypothetical completely ionized state in an ideal solution with the ion molality m+ = 1 and m — 1. If the chemical potential j.°ab corresponds to the first mentioned standard state, and the potential iA + + Xb to the second one, the difference in the standard free energy A0° between both states is expressed by the equation ... 

For a solute in solution. For a solute in a liquid or solid solution the standard state is referenced to the ideal dilute behaviour of the solute. It is the (hypothetical) state of solute B at the standard molality m, standard pressure and exhibiting infinitely diluted solution behaviour. The standard chemical potential is defined as... 

Sometimes (amount) concentration c is used as a variable in place of molality m both of the above equations then have c in place of m throughout. Occasionally mole fraction x is used in place of m both of the above equations then have x in place of m throughout, and x = 1. Although the standard state of a solute is always referenced to ideal dilute behaviour, the definition of the standard state and the value of the standard chemical potential g are different depending on whether molality m, concentration c, or mole fraction x is used as a variable. 

In this equation, the following definition of the chemical potential of ion i in the hypothetical state of the pure ions dissolved in pure water to give an ideal solution at unit mean molality, under the standard state pressure has been used ... 

Because of the inconvenient nature of the standard state defined above, the concentration units used to describe the concentration dependence of the chemical potential are usually different. More convenient choices for concentration are molality and molarity. When the solution is dilute the relationship between mole fraction and molality is quite simple (see equation (1.2.3)). In terms of molality, the expression for the concentration dependence of the chemical potential of component B becomes... 

The concentration dependence of y is an important feature involved in the experimental and theoretical evaluation of electrolyte behavior. The chemical potential of the standard state, p x, is that for a hypothetical one-molal solution in which all real interactions are imagined to be absent (y =1.00). Thus, the... 

Many chemical experiments are carried out in aqueous solutions and it is important to be able to define activities in these circumstances. However, the standard state we have used so far—the pure liquid at one atmosphere pressure—is singularly inappropriate. We usually wish to express concentrations in molality (moles per kilogram of solvent) and for an electrolyte, such as sodium chloride, the pure-liquid state at room temperature is not a suitable reference state. 

In solution we may write for the chemical potential p - pf -f Rrina (Section 7.2), where the standard state is one of unit molality which behaves as if it were at infinite dilution. Let us consider the simplified equilibrium... 

This table contains standard state thermodynamic properties of positive and negative ions in aqueous solution. It includes en-thcdpy and Gibbs energy of formation, entropy, and heat capacity, and thus serves as a companion to the preceding table, Standard Thermodynamic Properties of Chemical Substances . The standard state is the hypothetical ideal solution with molality m = 1 mol/kg (mean ionic molality in the case of a species which is assumed to dissociate at infinite dilution). Further details on conventions may be found in Reference 1. 

The pf is the chemical potential the solute would have in a 1 molal solution if that solution behaved according to the ideal dilute rule. This standard state is called the ideal solution of unit molality. It is a hypothetical state of a system. According to Eq. (16.20) the practical activity measures the chemical potential of the substance relative to the chemical potential in this hypothetical ideal solution of unit molality. Equation (16.20) is applicable to either volatile or in volatile solutes. 

We can now attempt to approach the problem of solvent basicity by another route the medium effect on the proton. The chemical potential of the proton in a solvent S can be expressed in two ways, depending on whether we take the standard state to be the hypothetical one-molal solution in S... 

Thus fl is a measure of the difference between the chemical potential of i in some equilibrium state, and the chemical potential of i in its standard state. When i is in its standard state, a = 1 and this difference is zero. As we have seen, the activity can take on several different forms, depending on whether we are using fiigacities, molalities, or mole fractions. Therefore the definition of the standard state will be different in each case, because a, = 1 will imply a different state for i in each case. 

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