Standard states for solutions

In order to compare the thermodynamic parameters of different reactions, it is convenient to define a standard state. For solutes in a solution, the standard state is normally unit activity (often simplified to 1 M concentration). Enthalpy, internal energy, and other thermodynamic quantities are often given or determined for standard-state conditions and are then denoted by a superscript degree sign ( ° ), as in API", AE°, and so on. 

The numerical value of the activity clearly depends upon the standard state, and one often encounters other choices for the standard state for solutes. For example, just as we obtained Equations 29 and 30 from Equation 22, we could have obtained similar looking equations from Equations 23 or Equation 24. However, the derivation requires a mention of... 

Although the standard state pertaining to these equilibria is often referred to as a state of infinite dilution, we stress that there are different standard states for solutes. They are defined as follows (61 Mil). 

In the thermodynamic derivation of the equilibrium constant, each quantity in Equation 6-2 is expressed as the ratio of the concentration of a species to its concentration in its standard state. For solutes, the standard state is 1 M. For gases, the standard state is I bar (= 105 Pa 1 atm = 1.013 25 bar), and for solids and liquids, the standard states are the pure solid or liquid. It is understood (but rarely written) that [A] in Equation 6-2 really means [A]/( 1 M) if A is a solute. If D is a gas, [D] really means (pressure of D in bars)/( 1 bar). To emphasize that [D] means pressure of D, we usually write Pn in place of [D. The terms of Equation 6-2 are actually dimensionless therefore, all equilibrium constants are dimensionless. 

The standard state for solutes in the (HL) reference is therefore the hypothetical state of pure solute (x, = 1), but with solute molecules interacting only with solvent molecules (y, = 1). Practically, chemical potentials in the standard state are obtained by making measurements at very low concentrations and extrapolating them to X,- = 1, assuming that Henry s law continues to hold to this concentration. At nonzero concentration of solutes, activity coefficients in the (HL) reference measure deviations of the solution from ideally dilute behavior. 

Many biological processes involve hydrogen ions the standard state of an H+ solution is (by definition) a 1 mol L"1 solution, which would have a pH of nearly 0, a condition incompatible with most forms of life. Hence, it is convenient to define the biochemical standard state for solutes, in which all components except H+ are at 1 mol L-1, and H+ is present at 10 7mol L (i.e., pH 7). Biochemical standard-state free energy changes are symbolized by AG0, and the other thermodynamic parameters are indicated analogously (AH0, AS0, etc.). 

Both these considerations would be taken into accoimt if the activation process were assumed to occur at a constant pressure, p, such that the partial molar volume of the solvent is independent of the temperature, though this possibility does not appear to have been considered. A full discussion is beyond the scope of this chapter, but the resulting heat capacities of activation are unlikely to differ greatly from those determined at a constant pressme of, say, 1 atm. (see p. 137). Unfortunately, this approach requires the definition of rather clumsy standard states for solutes, e.g., hypothetically ideal, 1 molal, under a pressure such that a given mass of the pure solvent occupies a particular volume. 

Understanding the choice of standard states in a problem is critical to proper treatment. Sometimes the standard state is one which does not exist at all, but can be readily pictured, hypothetically. For example, most gas mixtiu es do not behave in an ideal fashion. The molecules occupy space (they are not point molecules) they will interact to some extent unless they are infinitely far apart Hence, the commonly used standard state for gaseous substances is defined as hypothetical partial pressure of one atmosphere. Hypothetical, that is, because at one atmosphere, real gases will require some correction in their free energy value to compensate for their volumes and interactions. Analogously, the standard state for solutes commonly used is hypothetical one molal cMwcentration i.e., the concentration of an ideal solute in an ideal solution that would result in the value of the standard free energy. In real solutions, a correction would have to be... 

The only state which satisfies these conditions and is equal to 1 molal for all solutes is the ideal (Henryan) one molal solution, and this is universally used as the standard state for solutes. Introducing superscript ° for the standard state, and dropping the now unnecessary superscript", we get... 

The reference point for all enthalpy expressions is called the standard molar enthalpy of formation (AHf) which is defined as the heat change that results when 1 mole of a compound in its standard state is formed from its elements in their standard states. The standard state of a liquid or solid substance is its most thermodynamically stable pure form at 1 bar pressure. The standard state for gases is similar, except that standard state gases are assumed to obey the ideal gas law exactly. The standard state for solutes dissolved in solution will be discussed in Chapter 10. In the notation AHf, the superscript represents standard-state conditions (1 bar), and the subscript f stands for formation. Although the standard state does not specify a temperature, we will assume, unless otherwise stated, AH° values are measured at 25°C. 

Another standard state for solutes that is employed espeeially in the study of galvanic cells is that based on the relationships... 

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. 

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 numerical values of AG and A5 depend upon the choice of standard states in solution kinetics the molar concentration scale is usually used. Notice (Eq. 5-43) that in transition state theory the temperature dependence of the rate constant is accounted for principally by the temperature dependence of an equilibrium constant. 

But that is not all. For dilute solutions, the solvent concentration is high (55 mol kg ) for pure water, and does not vary significantly unless the solute is fairly concentrated. It is therefore common practice and fully justified to use unit mole fraction as the standard state for the solvent. The standard state of a close up pure solid in an electrochemical reaction is similarly treated as unit mole fraction (sometimes referred to as the pure component) this includes metals, solid oxides etc. 

Standard State of a Solvent in a Mixture The usual choice of a standard state for a solvent in a solution is the pure solvent at a pressure of 1 bar, the same convention as for a pure solid or liquid. Thus,u... 

For liquid mixtures (especially when the components are nonelectrolytes) in which we work with solutions over the entire range of composition, we often choose the Raoult s law standard state for both components. Thus, for the second component... 

Standard States of Solutes in Solution For a solute, particularly in situations where only dilute solutions can or will be considered, the usual procedure is to define the standard state in terms of a hypothetical solution that follows Henry s law at either a concentration of. y2 =1 or mi = 1. These standard states are known as Henry s law standard states. The standard state solutions are said to be hypothetical because real solutions at these high concentrations do not follow Henry s law. 

A Raoult s law standard state for the solute is often chosen for nonelectrolyte mixtures that cover the entire concentration range from. v — 0 to. Vi = 1 ... 

E6.6 The partial pressure of Bri above a (. 1CCI4 +. v Bn) solution is 1.369 kPa. The composition of the solution is a = 0.0250. The vapor pressure of pure bromine at the same temperature is 28.4 kPa. Assume a Raoult s law standard state for bromine and calculate the activity coefficient of Br2 in the solution. 

Thus, with a Henry s law standard state, H° is the enthalpy in an infinitely dilute solution. For mixtures, in which we choose a Raoult s law standard state for the solvent and a Henry s law standard state for the solute, we can... 

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. 

This illustrates the statement made earlier that the most convenient choice of standard state may depend on the problem. For gas-phase problems involving A, it is convenient to choose the standard state for A as an ideal gas at 1 atm pressure. But, where the vapor of A is in equilibrium with a solution, it is sometimes convenient to choose the standard state as the pure liquid. Since /a is the same for the pure liquid and the vapor in equilibrium... 

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... 

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