Standard States of Pure Substances

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 ... 

Two cases must be considered one in which the state of aggregation is the same in the initial and final state, and the other in which the state of aggregation is different in the two states. In the first case the enthalpy is a continuous function of the temperature and pressure in the interval between (Th P,) and (T, Pj). Equation (4.86) can be used for a closed system and the integration of this equation is discussed in Section 8.1, where the emphasis is on standard states of pure substances. The result of the integration is valid in the present instance with change of the limits of integration and limitation to molar quantities. Equations (8.10) and (8.11) then become... 

The standard free-energy of reaction (AG xn) is the free-energy change for a reaction when it occurs under standard-state conditions, when reactants in their standard states are converted to products in their standard states. Table 18.2 summarizes the conventions used by chemists to define the standard states of pure substances as well as solutions. To calculate AG we start with the equation... 

CHAPTER 7 PURE SUBSTANCES IN SINGLE PHASES 7.7 Standard States of Pure Substances... 

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. 

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°. 

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. 

Remember that the standard state of a substance is its pure form at a pressure of 1 bar. For a solute, it is for a concentration of 1 mol-L-1. The value of AGr refers to any chosen composition of the reaction mixture and represents the difference in molar free energy between the products and reactants at the concentrations present at a specified stage of the reaction. 

Although the choice of standard states is arbitrary, two choices have been established by convention and international agreement. For some systems, when convenient, the pure component is chosen as the substance in the standard state. For other systems, particularly dilute solutions of one or more solutes in a solvent, another state that is not a standard state is chosen as a reference state [19]. This choice determines the standard state, which may or may not be a physically realizable state. The reference state of a component or species is that state to which all measurements are referred. The standard state is that state used to determine and report the differences in the values of the thermodynamic functions for the components or species between some state and the chosen standard state. When pure substances are used in the definition of a standard state, the standard state and the reference state are identical. 

The condition of equilibrium is also applicable to changes of state that involve heterogenous reactions, and the same methods used for homogenous reactions to obtain expressions of the equilibrium constant are used for heterogenous reactions. One difference is that in many heterogenous reactions one or more of the substances taking part in the change of state is a pure phase at equilibrium. In such cases the standard state of the substance is chosen as the pure phase at the experimental temperature and pressure. The chemical potential of the pure substance in its standard state still appears in Y.k vkPk but the activity of the substance is unity and its activity does not appear in the expression for the equilibrium constant. 

As absolute values of free energies and potentials of substances are not known, we can only quote the differences between the values belonging to them in concrete cases and the values related to a certain, so called standard state. Values of other thermodynamic functions, such as internal energy, enthalpy, etc. are quoted in the same way. As the standard state of pure liquid or solid substances we consider their state in stable modification at 1 atm. pressure and at the temperature of the system. As the standard state for gas, either alono or in a mixture, the state of a pure gas in ideal state is taken at 1 atm. pressure and at the temperature of the system. 

In practice it is the International Practical Temperature Scale of1968 (IPTS-68) which is used for calibration of scientific and industrial instruments-t This scale has been so chosen that temperatures measured on it closely approximate ideal-gas temperatures the differences are within the limits of present accuracy of measurement. The IPTS-68 is based on assigned values of temperature for a number of reproducible equilibrium states (defining fixed points) and on standard instruments calibrated at these temperatures. Interpolation between the fixed-point temperatures is provided by formulas that establish the relation between readings of the standard instruments and values of the international practical temperature. The defining fixed points are specified phase-equilibrium states of pure substances, t a given in Table 1.2. 

Standard state of a substance is its pure form at a pressure of exactly 1 bar. 

For a homogeneous reaction in a liquid system the equilibrium constant is conveniently expressed in the form of equation (32.25), the standard state of each substance being the pure liquid at the equilibrium temperature and 1 atm. pressure. Differentiation with respect to temperature then gives [cf. equation (33.16)]... 

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. 

The thermodynamic standard state of a substance is its most stable pure form under standard pressure (one atmosphere) and at some specific temperature (25°C or 298 K unless otherwise specified). Examples of elements in their standard states at 25°C are hydrogen, gaseous diatomic molecules, H2(g) mercury, a silver-colored liquid metal,... 

The standard state for a pure liquid or solid is taken to be the substance in that state of aggregation at a pressure of 1 bar. This same standard state is also used for liquid mixtures of those components that exist as a liquid at the conditions of the mixture. Such substances are sometimes referred to as liquids that may act as a solvent. For substances that exist only as a solid or a gas in the pure component state at the temperature of the mixture, sometimes referred to as substances that can act only as a solute, the situation is more complicated, and standard states based on Henry s law may be used. In this case the pressure is again fixed at 1 bar, and thermal properties such as the standard-state enthalpy and heat capacity are based on the properties of the substance in the solvent at infinite dilution, but the standard-state Gibbs energy and entropy are based on a hypothetical state.of unit concentration (either unit molality or unit mole fraction, depending on the form of Henry s law used), with the standard-state fugacity at these conditions extrapolated from infinite-dilution behavior in the solvent, as shown in Fig. 9.1-3a and b. Therefore just as for a gas where the ideal gas state at 1 bar is a hypothetical state, the standard state of a substance that can only behave as a solute is a hypothetical state. However, one important characteristic of the solute standard state is that the properties depend strongly upon the solvent. used. Therefore, the standard-state properties are a function of the temperature, the solute, and the solvent. This can lead to difficulties when a mixed solvent is used. 

The standard state of a substance is its pure form in a defined state of aggregation at a pressure of 1 bar and a specified temperature. It is denoted by the index e.g. s. A// . The conventional reference temperature for the specification of energy functions (enthalpy) is 298.15 K = 25 C (room temperature). 

Standard state of a substance is referred in terms of the reference conditions. Standard state conditions are 1 atmospheric pressure and specific temperature (K = 298.15 or 25°C), pH 7 and all reactants and products initially at 1 M concentration pure substances at standard state have unit activity. 

The magnitude of any enthalpy change depends on the temperature, pressure, and state (gas, liquid, or solid crystaUine form) of the reactants and products. To compare enthalpies of different reactions, we must define a set of conditions, called a standard suite, at which most enthalpies are tabulated. The standard state of a substance is its pure form at atmospheric pressure (1 atm) and the temperature of interest, which we usually choose to be 298 K (25 °C). The standard enthalpy change of a reaction is defined as the enthalpy change when all reactants and products are in their standard states. We denote a standard enthalpy change as AH°, where the superscript ° indicates standard-state conditions. 

ENTHALPIES OF FORMATION (SECTION 5.7) The enthalpy of formation, AHf, of a substance is the enthalpy change for the reaction in which the substance is formed from its constituent elements. Usually enthalpies are tabulated for reactions where reactants and products are in their staiv dard states. The standard state of a substance is its pure, most stable form at 1 atm and the temperature of interest (usually 298 K). Thus, the standard enthalpy chai of a reaction, A f°, is the enthalpy change when all reactants and products are in their standard states. The standard enthalpy of formation, AHf° of a substance is the change in enthalpy for the reaction that forms one mole of the substance from its elements in their standard states. For any element in its standard state, AHf = 0. 

Hence U2 can be interpreted as the chemical potential of pure solute in a hypothetical liquid state corresponding to extrapolation from infinite dilution (which serves as reference state) to X2 = 1 along a line where Y2 = U that is, along the Henry s law line. In physical terms, it might be regarded as a hypothetical state in which the mole fraction of solute is unity (pure solute), but some thermodynamic properties are those of the solute 2 in the reference state of infinite dilution in solvent 1 (e.g., partial molar heat capacity). Since from the context it should always be clear whether the superscript circle denotes standard state" or "pure substance", no further distinction is introduced. 

The standard state of a substance in a condensed phase (liquid or solid) is the actual pure substance at the standard pressure P° and whatever temperature is of interest. Equation (4.4-13) implies that... 

Previously we have said little about g° other than that it was a function of temperature only and that each species had its own value of g°. We discussed standard states in Chapters 7, 8, and 9. A standard state is some state of matter that we will all agree upon as a suitable basis for constructing tables of properties. For most chemical reaction purposes we choose the standard state of some substance as the pure substance in its normal state (solid, liquid, or gas) at F = 1 atm or 1 bar, and an arbitrarily chosen T, normally = 25°C = 298.15 K for the tables of interest in this chapter. Alas, there are other standard states that are much more convenient for some problems, as discussed previously for vapor-liquid equilibrium calculations. However, if we put off for the moment saying what our standard state is, we can use the symbol ° to indicate a property in the standard state, and then say that, for any pure chemical element or compound (pure species) the partial molar Gibbs energy is the same as the pure species Gibbs energy, and in its standard state... 

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