Pure substances, standard states

With the choice of a pure substance standard state for the solid, and a strong electrolyte standard state for the dissolved AgCl, we get... 

The relationship between the activity of A relative to the pure substance standard state and the activity of A relative to the infinitely dilute, weight percent standard state is given by... 

For the reference state, lets us choose a pure-component standard state the real (or hypothetical) pure substance at the temperature of the mixture and at some convenient... 

All standard states, both for pure substances and for components in mixtures and solutions, are defined for a pressure of exactly 1 atmosphere. However the temperature must be specified. (There is some movement towards metricating this to a pressure of 1 bar = 100 kPa = 0.986 924 atm. This would make a significant difference only for gases at J= 298 K, this would decrease a p by 32.6 J moT )... 

The values of the thermodynamic properties of the pure substances given in these tables are, for the substances in their standard states, defined as follows For a pure solid or liquid, the standard state is the substance in the condensed phase under a pressure of 1 atm (101 325 Pa). For a gas, the standard state is the hypothetical ideal gas at unit fugacity, in which state the enthalpy is that of the real gas at the same temperature and at zero pressure. 

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. 

Since concentration variations have measurable effects on the cell voltage, a measured voltage cannot be interpreted unless the cell concentrations are specified. Because of this, chemists introduce the idea of standard-state. The standard state for gases is taken as a pressure of one atmosphere at 25°C the standard state for ions is taken as a concentration of 1 M and the standard state of pure substances is taken as the pure substances themselves as they exist at 25°C. The half-cell potential associated with a halfreaction taking place between substances in their standard states is called ° (the superscript zero means standard state). We can rewrite equation (37) to include the specifications of the standard states ... 

In defining the activity through equations (6.83) and (6.84), we have made no restrictions on the choice of a standard state except to note that specification of temperature is not a part of the standard state condition. We are free to choose standard states in whatever manner we desire.p However, choices are usually made that are convenient and simplify calculations involving activities. The usual choices differ for a gas, pure solid or liquid, and solvent or solute in solution. We will now summarize these choices of standard states and indicate the reasons. Before doing so, we note that activities for a substance with different choices of standard states are proportional to one another. This can be seen as follows With a particular choice of standard state... 

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. 

The standard state for liquid water is chosen as the pure substance at 1 bar total pressure. Thus, at this pressure condition, r/H o = 1 and... 

Values correspond to the temperature of the phase change. The superscript ° signifies that the change takes place at 1 bar and that the substance is pure (that is, the values are for standard states see Section 6.15). 

An enthalpy of reaction also depends on the conditions (such as the pressure). All the tables in this book list data for reactions in which each reactant and product is in its standard state, its pure form at exactly 1 bar. The standard state of liquid water is pure water at 1 bar. The standard state of ice is pure ice at 1 bar. A solute in a liquid solution is in its standard state when its concentration is 1 mol-L". The standard value of a property X (that is, the value of X for the standard state of the substance) is denoted X°. 

A note on good practice Recall that the standard state of a pure substance is its pure form at a pressure of 1 bar (Section 6.15). For a solute, the standard state is for a concentration of 1 mol-L 1. Pure solids and liquids may always be regarded as being in their standard states provided the pressure is close to 1 bar. 

At equilibrium, all components of a mixture have the same molar free energy, i.e., the same chemical potential, in any phase in which they are present, and they have the same chemical potential as all other components. However it is not always convenient to use the same standard state for all components or even for the same component in all phases. Just as Equation 6 defines fugacity, Equation 7 or 8 defines activity. Furthermore, Equations 6-8 define / and a for all substances, not just gases. However we should keep in mind that we do not use the same standard state for a substance in all the phases, mixtures, or pure states in which it may occur or for all components of a mixture. 

Thus the free energy of solvation may be calculated from the Henry s law constant or from the vapor pressure of the pure substance and the limiting activity coefficient. Thus, if the deviation of the solution from Raoult s law behavior is known, calculation of the standard state free energy of solvation requires only the vapor pressure of the pure substance (in the standard state... 

The LFER that results when correlating partitioning in the octanol-water system and the humic substances-water system Implies that the thermodynamics of these two systems are related. Hence, much can be learned about humic substances-water partitioning by first considering partitioning In the simpler octanol-water system. The thermodynamic derivation that follows is based largely on the approach developed by Chlou and coworkers (18-20), Miller et al. (21), and of Karickhoff (J, 22). In the subsequent discussion, we will adopt the pure liquid as the standard state and, therefore, use the Lewls-Randall convention for activity coefficients, l.e., y = 1 if the mole fraction x 1. 

Enthalpies of reaction can also be calculated from individual enthalpies of formation (or heats of formation), AHf, for the reactants and products. Because the temperature, pressure, and state of the substance will cause these enthalpies to vary, it is common to use a standard state convention. For gases, the standard state is 1 atm pressure. For a substance in an aqueous solution, the standard state is 1 molar concentration. And for a pure substance (compound or element), the standard state is the most stable form at 1 atm pressure and 25°C. A degree symbol to the right of the H indicates a standard state, AH°. The standard enthalpy of formation of a substance (AHf) is the change in enthalpy when 1 mol of the substance is formed from its elements when all substances are in their standard states. These values are then tabulated and can be used in determining A//°rxn. 

The standard state (and thus any standard thermodynamic property) of a pure solid refers to the pure substance in the solid phase under the pressure p of 1 bar (0.1 MPa). The standard state of a pure liquid refers to the pure substance in the liquid phase at p = 1 bar. When the substance is a pure gas, its standard state is that of an ideal gas at p = 1 bar (or, which is equivalent, that of a real gas at P = o). 

The case of liquid solutions is more complicated because the conventions vary. These are always stated in introductory chapters of the thermochemical databases and deserve a careful reading. In most tables and in the present book, it is agreed that the standard state for the solvent is the pure solvent under the pressure of 1 bar (which corresponds to unit activity). For the solute, the standard state may refer to the substance in a hypothetical ideal solution at unit molality (the amount of substance of solute per kilogram of solvent) or at mole fraction x = 1. 

The problem can be tackledby considering reaction 2.2, where all reactants and products are the pure species in their standard states at 298.15 K, and evaluating Ar//°(2.2) from data, which are easily found in thermochemical compilations. These data are the standard enthalpies of formation of the substances involved. 

The notion of standard enthalpy of formation of pure substances (AfH°) as well as the use of these quantities to evaluate reaction enthalpies are covered in general physical chemistry courses [1]. Nevertheless, for sake of clarity, let us review this matter by using the example under discussion. The standard enthalpies of formation of C2H5OH(l), CH3COOH(l), and H20(1) at 298.15 K are, by definition, the enthalpies of reactions 2.3,2.4, and 2.5, respectively, where all reactants and products are in their standard states at 298.15 K and the elements are in their most stable physical states at that conventional temperature—the so-called reference states at 298.15 K. 

In summary, the standard enthalpy of formation of a pure substance at 298.15 K is the enthalpy of the reaction where 1 mol of that substance in its standard state is formed from its elements in their standard reference states, all at 298.15 K. A standard reaction enthalpy can be calculated from the values of AfH° for reactants and products by using equation 2.7 (Hess s law) ... 

AG°m (pure hquid is the standard state for each substance) is 1194 J tnol at 0°C. In a solution containing only the two isomers, equilibrium is attained when the mole fraction of the 3-methylhexane is 0.372. Is the equihbrium solution ideal Show the computations on which your answer is based. 

Pure Substances. In most problems involving pure substances, it is convenient to choose the pure solid or the pure liquid at each temperature and at a pressure of 1 bar (0.1 MPa) as the standard state. According to this convention, the activity of a pure solid or pure liquid at 1 bar is equal to 1 at any temperature. 

Solvent in Solution. We shall use the pure substance at the same temperature as the solution and at its equilibrium vapor pressure as the reference state for the component of a solution designated as the solvent. This choice of standard state is consistent with the limiting law for the activity of solvent given in Equation (16.2), where the limiting process leads to the solvent at its equilibrium vapor pressure. To relate the standard chemical potential of solvent in solution to the state that we defined for the pure liquid solvent, we need to use the relationship... 

As the mole fraction of A in the mixture iucreases toward uuity, the secoud term iu Eq. (2.17) teuds toward zero, aud the chemical poteutial of A teuds toward the standard chemical potential, Pa = G, the molar Gibbs euergy (or chemical poteutial) of A iu the realizable standard state of pure A, in the sense that pure liquid A is a known chemical substance. A similar equation holds for the component B. 

While changes in internal energy and enthalpy (AC/ and Ai/) may be determined, it is not possible to measure either U or//absolutely. Consequently, an arbitrary datum is defined at which the enthalpy is zero. For this purpose, the enthalpy of all elements in their standard states is taken as zero at the stated reference temperature. The standard state of a pure substance at temperature T is defined as follows ... 

---