Standard molar quantity

These quantities (which are standard molar quantities) describe the process initial state transition state... 

The thermodynamic quantities of the reaction are related to standard molar quantities A= Af// (C2H6) + Aff/a(Br) - Aftf e(C2H5) - Aftf (HBr)... 

The solubility data of synthetic NiC03 were thermodynamically analysed to obtain the respective standard molar quantities of formation AjG and A,//". An analogous set of equations was used as described in Section V.3.2.2.3 (Equations (V.41) - (V.44)). Solubility constants were extrapolated to infinite dilution using the Specific Ion-interaction Theory [97GRE/PLY2]. All calculations were based on auxiliary quantities which were either recommended by CODATA (see NEA TDB auxiliary data set) or recently critically evaluated (see Section V.2.1). 

CHAPTER 7 PURE SUBSTANCES IN SINGLE PHASES 7.9 Standard molar Quantities of a Gas... 

A standard molar quantity of a substance is the molar quantity in the standard state at the temperature of interest. We have seen (Sec. 7.7) that the standard state of a pure liquid or solid is a real state, so any standard molar quantity of a pure liquid or solid is simply the molar quantity evaluated at the standard pressure and the temperature of interest. 

Isothermal change of the real gas at pressure / vap to the hypothetical ideal gas at pressure p°. Table 7.5 has the relevant formulas relating molar quantities of a real gas to the corresponding standard molar quantities. 

From Eq. 11.2.15, the relation between a standard molar reaction quantity and the standard molar quantities of the reactants and products at the same temperature is... 

In 1982, the International Union of Pure and Applied Chemistry recommended that the value of the standard pressure p° be changed from 1 atm to 1 bar. This change affects the values of some standard molar quantities of a substance calculated from experimental data. 

CHAPTER 12 EQUILIBRIUM CONDITIONS IN MULTICOMPONENT SYSTEMS 12.10 EVALUATION OF STANDARD MOLAR QUANTITIES... 

The standard molar quantities appearing in Eqs. 12.10.1 and 12.10.2 can be evaluated through a variety of experimental techniques. Reaction calorimetry can be used to evaluate AfH° for a reaction (Sec. 11.5). Calorimetric measurements of heat capacity and phase-transition enthalpies can be used to obtain the value of Sf for a solid or liquid (Sec. 6.2.1). For a gas, spectroscopic measurements can be used to evaluate S° (Sec. 6.2.2). Evaluation of a thermodynanuc equilibrium constant and its temperature derivative, for any of the kinds of equilibria discussed in this chapter (vapor pressure, solubility, chemical reaction, etc.), can provide values of ArG° and AfH° through the relations AfG° = —RTln K and ArH° = -Rd aK/d /T). 

The entropy of a substance, unlike its enthalpy, can be evaluated directly. The details of how this is done are beyond the level of this text, but Figure 17.4 shows the results for one substance, ammonia. From such a plot you can read off the standard molar entropy at 1 atm pressure and any given temperature, most often 25°C. This quantity is given the symbol S° and has the units of joules per mole per kelvin (J/mol-K). From Figure 17.4, it appears that... 

A variety of procedures can be used to determine Z, as a function of composition.2 Care must be taken if reliable values are to be obtained, since the determination of a derivative or a slope is often difficult to do with high accuracy. A number of different techniques are employed, depending upon the accuracy of the data that is used to calculate Z, and the nature of the system. We will now consider several examples involving the determination of V,- and Cpj, since these are the properties for which absolute values for the partial molar quantity can be obtained. Only relative values of //, and can be obtained, since absolute values of H and G are not available. For H, and we determine H, — H° or — n°, where H° and are values for H, and in a reference or standard state. We will delay a discussion of these quantities until we have described standard states. 

To find a numerical value for AHi, we need to know ArH° at one temperature, while evaluation of I requires ArG° at one temperature. The usual choice is to obtain ArH° and ArG° at T = 298.15 K from standard molar enthalpies of formation and standard molar Gibbs free energies of formation. Earlier in this chapter we referred to examples of these quantities. It is now time to define AfH° and AfG° explicitly and describe methods for their measurement. 

In Investigation 5-B, you used the reaction of oxygen with hydrogen to form water. Reactions like this one are known as formation reactions. In a formation reaction, a substance is formed from elements in their standard states. The enthalpy change of a formation reaction is called the standard molar enthalpy of formation, AH°f. The standard molar enthalpy of formation is the quantity of energy that is absorbed or released when one mole of a compound is formed directly from its elements in their standard states. 

Then, the compositions of the essential (> 5 volume %) minerals in the rocks to be classified are defined in a composition matrix (C) and used, in conjunction with a second matrix (7) defining what minerals are employed in classification (the classifying minerals e.g., quartz, plagloclase, alkali feldspar), to obtain a third matrix (1/1/) containing a set of independent vectors containing major element coefficients. When multiplied by the un-standardized molar element quantities, they produce un-standardized molar classifying mineral quantities that are un-affected by the presence of nonclassifying minerals in the rocks. 

Entropy, which has the symbol 5, is a thermodynamic function that is a measure of the disorder of a system. Entropy, like enthalpy, is a state function. State functions are those quantities whose changed values are determined by their initial and final values. The quantity of entropy of a system depends on the temperature and pressure of the system. The units of entropy are commonly J K" mole". If 5 has a ° (5°), then it is referred to as standard molar entropy and represents the entropy at 298K and 1 atm of pressure for solutions, it would be at a concentration of 1 molar. The larger the value of the entropy, the greater the disorder of the system. 

If the concentration of solute 3 Is sufficiently low, relative to Its CMC, the transfer functions become Identical for partial and apparent molar quantities and are said to approach the standard state. 

The relevant quantities are the transfer activity coefficients, wfs related t0 the standard molar transfer Gibbs free energies by ... 

One of them is Gutmann s donor number, DN, (Gutman and Vychera 1966) defined as the negative of the standard molar heat of reaction (expressed in kcal mol 1, 1 cal = 4.184 J) of the solvent with antimony pentachloride to give the 1 1 complex, when both are in dilute solution in the inert diluent 1,2-dichloroethane. This quantity needs to be determined calorimetrically, as was done for a considerable number of solvents at that time (Gutman and Vychera 1966). There are several problems with the DN scale. One is the fact that calorimetric equipment... 

The problem discussed here is common to all partial molar quantities. It is for this and similar reasons, which we have already indicated, that reference and standard states are defined (see Chapter 8). 

The quantity gk T) in Equation (7.67) is again a molar quantity, characteristic of the individual gas, and a function of the temperature. It can be related to the molar Gibbs energy of the fcth substance by the use of Equation (7.67). The first two terms on the right-hand side of this equation are zero when the gas is pure and ideal and the pressure is 1 bar. Then gk(T) is the chemical potential or molar Gibbs energy for the pure fcth substance in the ideal gas state at 1 bar pressure. We define this state to be the standard state of the fcth substance and use the symbol 1 bar, yk = 1] for the... 

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 quantity AH° is the change of enthalpy for the change of state represented by a balanced chemical equation under the condition that all substances are in their standard states at the temperature and pressure in question. The overbar is used here because some of the individual enthalpies, Hf, may be partial molar quantities. 

The extent of the reaction of carbon dioxide with water to form carbonic acid is fairly well known—less than 1%. However, for thermodynamic purposes we make no distinction between the two nonionized species, C02 and H2C03. We are thus concerned with the sum of the concentration of these species, a quantity that can be determined experimentally. We must therefore develop the methods used to define the standard state of the combined nonionized species and the standard molar Gibbs energies of formation. 

Here, is termed the specific chemical enthalpy, B, the specific thermal enthalpy and Bp the specific pressure enthalpy. The combination of the specificrthermal enthalpy, Bp, and the specific pressure enthalpy, Bp, may he named the specific physical enthalpy. When the material species is one of the components in a solution, Equations A-l through A-7 are valid, provided that the specific quantities are changed to the partial molar quantities. Note that superscript 0 refers to the standard state, and subscript 0 refers to the dead state cp is the specific heat, and v is the specific volume. 

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