Solutes, thermodynamic standard state

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. 

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 of a substance is a reference state that allows us to obtain relative values of such thermodynamic quantities as free energy, activity, enthalpy, and entropy. All substances are assigned unit activity in their standard state. For gases, the standard state has the properties of an ideal gas, but at one atmosphere pressure. It is thus said to be a hypothetical state. For pure liquids and solvents, the standard states are real states and are the pure substances at a specified temperature and pressure. For solutes In dilute solution, the standard state is a hypothetical state that has the properties of an infinitely dilute solute, but at unit concentration (molarity, molality, or mole fraction). The standard state of a solid is a real state and is the pure solid in its most stable crystalline form. 

Standard electrode potentials, designated refer to standard-state conditions. These standard-state conditions are one molar solutions for ions, one atmosphere pressure for gases, and all solids and liquids in their standard states at 25°C. (Remember that we refer to thermodynamic standard-state conditions, and not standard temperature and pressure as in gas law calculations.) As any of the standard cells described earlier operates, and concentrations or pressures of reactants change, the observed cell voltage drops. Similarly, cells constructed with solution concentrations different from one molar, or gas pressures different from one atmosphere, cause the corresponding potentials to deviate from standard electrode potentials. 

Standard cell A cell in which all reactants and products are in their thermodynamic standard states (1 M for solution species and 1 atm partial pressure for gases). 

A Word about Units for Q and K In this text (and most others), the values of Q and K are shown as unitless numbers. This is because each term in the reaction quotient represents the ratio of the measured quantity of the substance (molar concentration or pressure) to the thermodynamic standard-state quantity of the substance. Recall from Section 6.6 that these standard states are 1 Mfora substance in solution, 1 atm for gases, and the pure substance for a liquid or solid. Thus, a... 

Because reactions are carried out under a variety of conditions, it is convenient to define a standard state for substances and experimental conditions. The standard state is the form (solid, liquid, or gas) assumed by the pure substance at 1 atm pressure. For substances in aqueous solution, the standard-state concentration is 1 M. Standard-state values are designated by a superscript ° following the thermodynamic symbol as in AG°. 

Standard Gibbs free energy change (AG°) (10.7) Free energy change for a reaction in which all participating substances are present in their thermodynamic standard state (gases at 1 atm, solutions at 1 M, T= 25°C). See... 

Standard state n. A reference state for specifying thermodynamic quantities, usually defined as the most stable form of the substance at 1 atm pressure. For a solute the standard state is the ideal, 1M solution. 

Thermodynamic standard states are (1) pure solids or pure liquids at 1 atm, (2) solutions of one-molar concentrations, and (3) gases at partial pressures of 1 atm. 

The emf of a voltaic cell depends on the concentrations of substances and the temperature of the cell. For purposes of tabulating electrochemical data, it is usual to choose thermodynamic standard-state conditions for voltaic cells. The standard emf, eii> is the emf of a voltaic cell operating under standard-state conditions (solute concentrations are each 1 M, gas pressures are each 1 atm, and the temperature has a specified value—usually 25°C). Note the superscript degree sign (°), which signifies standard-state conditions. ... 

We saw in Section 4.2 that in biochemical work it is common to adopt the biological standard state (pH = 7, corresponding to neutral solution), rather than the thermodynamic standard state (pH = 0). To convert standard potentials to biological standard potentials, , we must first consider the variation of potential with pH. The two potentials differ when hydrogen ions are involved in the half-reaction, as in the fumaric acid/succinic acid couple fum/suc with fum = HOOCCH=CHCOOH and sue = HOOCCH2CH2COOH, which plays a role in the citric acid cycle (Case study 4.3) ... 

This important relation establishes the link between emf measurements and chemical thermodynamics. The above chemical potential will now be specified in terms of the hybrid system adopted in Eq. (3.4.4). (i) The standard state for pure solids or liquids participating in the electrochemical processes is that of the isolated material at temperature T under a pressure of 1 bar. (ii) For materials in homogeneous solid or liquid solution the standard state is chosen for each constituent at unit activity at 1 bar at the prevailing temperature, (iii) For gases participating in the chemical reaction the standard state is that of the ideal gas. Then, according to Eq. (3.4.4) and Eq. (4.5.1) we write... 

The values of thermodynamic properties are usually specified with reference to a standard state. We have already defined the standard state of gases and pure liquids and solids to correspond to a pressure of P° (exactly 1 bar). We now choose the standard state for a component of an ideal liquid solution to be the pure liquid substance at pressure P°. For a component of an ideal solid solution the standard state is the pure solid at pressure P°. We will define all of our standard states to correspond to a pressure P°. Since we assume that the chemical potential of a pure liquid or solid substance is nearly pressure-independent, Eq. (6.1-1) becomes, to a good approximation,... 

It is strictly for convenience that certain conventions have been adopted in the choice of a standard-state fugacity. These conventions, in turn, result from two important considerations (a) the necessity for an unambiguous thermodynamic treatment of noncondensable components in liquid solutions, and (b) the relation between activity coefficients given by the Gibbs-Duhem equation. The first of these considerations leads to a normalization for activity coefficients for nonoondensable components which is different from that used for condensable components, and the second leads to the definition and use of adjusted or pressure-independent activity coefficients. These considerations and their consequences are discussed in the following paragraphs. 

The standard-state fugacity of any component must be evaluated at the same temperature as that of the solution, regardless of whether the symmetric or unsymmetric convention is used for activity-coefficient normalization. But what about the pressure At low pressures, the effect of pressure on the thermodynamic properties of condensed phases is negligible and under such con-... 

Krypton Difluoride. Krypton difluoride [13773-81 -4] KrF is a colorless crystalline solid which can be sublimed under vacuum at 0°C but is thermodynamically unstable and slowly decomposes to the elements at ambient temperatures (Table 1). It can, however, be stored for indefinite periods of time at —78° C. The KrF molecule has been shown, like XeF2, to be linear in the gas phase, in the sofld state, and in solution. The standard enthalpy of... 

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. 

The difficulties engendered by a hypothetical liquid standard state can be eliminated by the use of unsymmetrically normalized activity coefficients. These have been used for many years in other areas of solution thermodynamics (e.g., for solutions of electrolytes or polymers in liquid solvents) but they have only recently been employed in high-pressure vapor-liquid equilibria (P7). 

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. 

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