Standard molar reaction quantities

If a chemical process takes place at constant temperature while each reactant and product remains in its standard state of unit activity, the molar reaction quantity Af.Y is called the standard molar reaction quantity and is denoted by ArZ°. For instance, AyapH° is a standard molar enthalpy of vaporization (already discussed in Sec. 8.3.3), and ArG° is the standard molar Gibbs energy of a reaction. 

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... 

Whereas a molar reaction quantity is usually a function of T, p, and a standard molar reaction quantity is a function only of T. This is evident because standard-state conditions imply that each reactant and product is in a separate phase of constant defined composition and constant pressure p°. 

Since the value of a standard molar reaction quantity is independent of the standard molar integral and differential quantities are identical (page 317) ... 

For this reaction, using the convention that A H°, S, and AfG° are zero for the aqueous H+ ion and the fact that AfH° and AfG° are zero for the elements, we can write the following expressions for standard molar reaction quantities ... 

An efficient way of tabulating the results of experimental measurements is in the form of standard molar enthalpies and Gibbs energies of formation. These values ean be used to generate the values of standard molar reaction quantities for reactions not investigated directly. The relations between standard molar reaction and formation quantities (Sec. 11.3.2) are... 

For examples of the evaluation of standard molar reaction quantities and standard molar formation quantities from measurements made by various experimental techniques, see Probs. 12.18-12.20,14.3, and 14.4. 

One method is to calculate AfG° from values of the standard molar Gibbs energy of formation AfG° of each reactant and product. These values are the standard molar reaction Gibbs energies for the formation reactions of the substances. To relate AfG° to measurable quantities, we make the substitution im = Hi — TSi (Eq. 9.2.46) in ArG = iVifXi to give ArG = - T or... 

Some of the most useful experimentally-derived data for thermodynamic calculations are values of standard molar reaction enthalpies, standard molar reaction Gibbs energies, and standard molar reaction entropies. The values of these quantities for a given reaction are related, as we know (Eq. 11.8.21), by... 

Because G, H, and S are state functions, the thermodynamic equilibrium constant and the molar reaction quantities evaluated from Egg, g and dE°g g / dT are the same quantities as those for the reaction when it takes place in a reaction vessel instead of in a galvanic cell. However, the heats at constant T and p are not the same (page 318). During a reversible cell reaction, dS must equal dq/T, and dq/d is therefore equal to TArS° during a cell reaction taking place reversibly under standard state conditions at constant T and p. 

Or, more quickly, standard molar reaction fiee enthalpy. This denomination is misleading because it is a measurable quantity, whereas a free enthalpy cannot be measur... 

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. 

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 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. 

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

Here, AG° is the standard molar Gibbs energy change and K is the equilibrium constant for a reaction R is the gas constant (8.314 472 JIC moh ). The subscripts T and 6 denote the temperature to which a quantity pertains, the subscript p denotes constant pres-... 

The problem this creates is that we do not want to have to tabulate an enthalpy change for every process or chemical reaction which might become of interest to us - there are too many. We would like to be able to associate an enthalpy with every substance - solids, liquids, gases, and solutes - for some standard conditions, so that having tabulated these, we could then easily calculate an enthalpy change between any such substances under those standard conditions. After that, we could deal with the changes introduced by impurities and other nonstandard conditions. The method developed to allow this is to determine, for every pure compound, the difference between the enthalpy of the compound and the sum of the enthalpies of the elements, each in its most stable state, which make up the compound. This quantity is called the standard molar enthalpy of formation from the elements. For aqueous ions, the quantity determined is a little more complicated (Chapter 15), but the principle is the same. It is this enthalpy quantity which is invariably tabulated in compilations of data. 

Plan We can use standard enthalpies of formation to calculate AH for the reaction. We can then use Le ChateUer s principle to determine what effect temperature will have on the equilibrium constant. Recall that the standard enthalpy change for a reaction is given by the sum of the standard molar enthalpies of formation of the products, each multipUed by its coefficient in the balanced chemical equation, less the same quantities for the reactants. At 25 C, AHj for NH3( ) is —46.19 kj/mol. The AHJ values for H2(g) and N2(g) are zero by definition, because the enthalpies of formation of the elements in their normal states at 25 C are defined as zero (S tion 5.7). Because 2 mol of NH3 is formed, the total enthalpy change is... 

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). 

We cannot calculate AjG from the standard molar Gibbs energies themselves because these quantities are not known. One practical approach is to calculate the standard reaction enthalpy from standard enthalpies of formation (Section 1.11), the standard reaction entropy from Third-Law entropies (Section 2.5), and then to combine the two quantities by using... 

We study the action of catalysts (a substance that accelerates a reaction without itself appearing in the overall chemical equation), especially enzymes, in Chapter 8 and at this stage do not need to know in detail how they work other than that they provide an alternative, faster route from reactants to products. Although the new route from reactants to products is faster, the initial reactants and the final products are the same. The quantity is defined as the difference of the standard molar... 

One mole of matter is assumed, and unless explicitly noted on the first data card the reference state is the ideal gas at one atmosphere pressure. The enthalpy reference is chosen such that includes the enthalpy of formation as in Eq. (9) of the text. This means that values of H°/RT calculated from the polynomials can be used directly to compute enthalpies of reaction. (See text for discussion of absolute enthalpy). The usual thermochemical manipulations can be done on these polynomials to compute other thermochemical quantities such as standard molar free energies. 

Two variables of primary importance, which are interdependent, are reaction temperature and ch1orine propy1ene ratio. Propylene is typically used ia excess to act as a diluent and heat sink, thus minimising by-products (eqs.2 and 3). Since higher temperatures favor the desired reaction, standard practice generally involves preheat of the reactor feeds to at least 200°C prior to combination. The heat of reaction is then responsible for further increases in the reaction temperature toward 510°C. The chlorine propylene ratio is adjusted so that, for given preheat temperatures, the desired ultimate reaction temperature is maintained. For example, at a chlorine propylene molar ratio of 0.315, feed temperatures of 200°C (propylene) and 50°C (chlorine) produce an ultimate reaction temperature of approximately 500°C (10). Increases in preheat temperature toward the ultimate reactor temperature, eg, in attempts to decrease yield of equation 1, must be compensated for in reduced chlorine propylene ratio, which reduces the fraction of propylene converted and, thus aHyl chloride quantity produced. A suitable economic optimum combination of preheat temperature and chlorine propylene ratio can be readily deterrnined for individual cases. 

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