Pure substances, standard enthalpy formation

The third law of thermodynamics establishes a starting point for entropies. At 0 K, any pure perfect crystal is completely constrained and has S = 0 J / K. At any higher temperature, the substance has a positive entropy that depends on the conditions. The molar entropies of many pure substances have been measured at standard thermodynamic conditions, P ° = 1 bar. The same thermodynamic tables that list standard enthalpies of formation usually also list standard molar entropies, designated S °, fbr T — 298 K. Table 14-2 lists representative values of S to give you an idea of the magnitudes of absolute entropies. Appendix D contains a more extensive list. 

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 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) ... 

Having thus settled on Pedley s tables for the pure organic compounds, we have then decided to use NBS Tables to derive the solution enthalpies in figure 2.1. The values can be easily evaluated from the differences between the standard enthalpies of formation of the compounds in solution and the standard enthalpies of formation of pure substances, viz. 

The standard enthalpy of formation, AHf°, of a substance is the standard reaction enthalpy for the formation of a substance from its elements in their most stable form. (Phosphorus is an exception white phosphorus is used because it is much easier to obtain pure than the other, more stable allotropes.) Standard enthalpies of formation are expressed in kilojoules per mole of the substance (kj-mol-1). We obtain AHf for ethanol, for instance, from the thermochemical equation for its formation from graphite (the most stable form of carbon) and gaseous hydrogen and oxygen ... 

The reference states for pure solids and liquids are chosen to be those forms stable at 1 atm, just as in the definition of standard states for enthalpy of formation (see Chapter 12) and Gibbs free energy of formation (see Chapter 13). Pure substances in their reference states are assigned activity of value 1. 

The thermodynamic quantities listed are for one mole of substance in its standard state, that is at 1 atm pressure. The enthalpies and free energies of formation of substances are the changes in those thermodynamic properties when a substance in its standard state is formed from its elements in their standard states. The standard state of an element is its normal physical state at 1 atm, and for the data given in these tables, 298.15 K. The entropies listed are absolute in the sense that they are based on the assumption that the entropy of a pure substance is zero at the absolute zero of temperature. 

Such identical conditions in the formation of different compounds are called standard conditions. This is pressure 10 Pa = 1 bar. Before, the standard pressure was 1 atm = 1982 101.325 kPa. The same pure substance under such conditions may be in a different a regate state (gas, liquid, solid). In particular, compound H O may be in liquid and vapor states. That is why mean free enthalpy is evaluated as substance formation to its most stable state imder standard conditions, which is called standard state. For the compoimd H O such standard state is liquid, for methane -gaseous, for NaCl - solid. 

Exceptions are ions, which cannot exist outside of the water solution in pure form. That is why free enthalpy of their formation is compared under conditions of some standard solution. As such was selected a single-molal water solution of one ion with properties of ideal, i.e., infinitely diluted, under standard conditions. In other words, the standard state of dissolved ions is considered rmder conditions of their interaction only with solvent, which is considered a pure substance. 

In thermodynamic data tables (standard enthalpies or Gibbs energies of formation and standard molar entropies) which relate to compounds other than ions in a solution, the common convention that is applied involves setting the values of standard enthalpy and standard Gibbs energy of formation (or chemical potential) equal to OJmor for all simple pure elements in their stable physical state at the temperature in question. The data therefore refer to the formation of substances from simple elements. 

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. 

Recall that we defined standard enthalpies of formation, AHf, as the enthalpy change when a substance is formed from its elements under defined standard conditions. oGo (Section 5.7) We can define standard free energies of formation, AGf, in a similar way AGf for a substance is the free-energy change for its formation from its elements under standard conditions. As is summarized in Table 19.2, standard state means 1 atm pressure for gases, the pure solid for solids, and the pure liquid for liquids. For substances in solution, the standard state is normally a concentration of 1 M. (In very accurate work it may be necessary to make certain corrections, but we need not worry about these.)... 

There are extensive compilations of AH/ and AG for many compounds. The subscript / designates these as, respectively, the enthalpies and free energies of formation of the compound from its constituent elements. The superscript is used to designate data that refer to the substance in its standard state, i.e., the pure substance at 25°C and 1 atm. These compilations can be used to calculate the enthalpy or free energy of a given reaction if the data are available for each reactant and product ... 

The main application of such a calorimeter, the burning of substances inside a sealed, pressure-tight reaction vessel, was developed by Berthelot (1827-1907) into a standard procedure. Berthelot was the first to fill the reaction vessel with pure oxygen to excess pressure in order to obtain a quick, thorough combustion into definite reaction products. Calorimeters of this type were soon given the name bomb calorimeter because of the bomb-like appearance of the reaction vessel. Berthelot s numerous thermochemical measurements owe their success to this experimental procedure. Even today, this instrument remains a valuable aid for the determination of the standard enthalpies of formation of chemical compounds, of the combustion heats of foodstuffs, and of the gross heating values of fuels (Rossini, 1956 Skinner, 1962). 

The enthalpy change of formation, AH, of a substance is the heat change (at constant pressure) on production of one mole of the pure substance from its elements in their standard states under standard thermodynamic conditions (298 K and 1 atm pressure). 

Some data consist of single numbers only. Examples are critical constants and temperature and pressure for three phase equilibria of pure substances (triple points). Some kinds of data are single numbers by definition, such as normal boiling temperatures and standard enthalpies of formation at 298.15 K. Other data are functions of one or more independent variables. In general, the number of independent variables for a system is determined by the Gibbs phase rule. The database structure must allow for the maintenance of information on the phase or phases present, any constraints and other essential metadata, as discussed below. The distinction between a property and the... 

Thermodynamic and transport properties of pure substances includes the various thermodynamic functions (//, S, G, Cp, etc.), density, vapor pressure, viscosity, thermal conductivity, and many others. These properties are functions of temperature and pressure, but an important subset consists of values defined under standard conditions, such as Af//°, the standard state enthalpy of formation of a compound from its elements. 

A consequence of the first law of thermodynamics, the conservation of energy, is that we can combine standard enthalpies of reactions to produce the standard enthalpy of another reaction. If a reaction can be accomplished in a set of steps, each a reaction with a known standard enthalpy, the sum of the standard enthalpies of the steps is the standard enthalpy of the overall reaction. This statement is often called Hess s law (Germain Henri Hess, Russia, 1802-1850). Standard enthalpies of formation are available in published tables, and a few selected values are listed in Table 6.1. Enthalpies of formation are reaction enthalpies for which the reactants are pure elemental substances. Thus, if we can develop a set of reaction steps where the reactants in each step are elemental substances, the overall reaction enthalpy will be a combination of enthalpies of formation. Here is an example ... 

At the present time, values for the thermodynamic properties of cells cannot be found in compendia in the literature. Cells are not pure substances. They have some of the properties of precipitates in that they are insoluble (i.e., they are visible)[37], and do not have standard thermodynamic properties in the usual sense. Nevertheless, a unit mass of anything, impure or otherwise, does have a finite enthalpy, entropy, and fi ee-energy of formation, and this also applies to cells. The unit mass is taken as the ICCmol, represented here by formula (B). Sueh a formula accounts for more than 99% of the total mass, and formulae of this kind are probably the best that can be obtained for something as complex and as variable as different kinds of cells. 

Several comments need to be made concerning the state of aggregation of the substances. For gases, the standard state is the ideal gas at a pressure of 1 bar this definition is consistent with the standard state developed in Chapter 7. When a substance may exist in two allotropic solid states, one state must be chosen as the standard state for example, graphite is usually chosen as the standard form of carbon, rather than diamond. If the chemical reaction takes place in a solution, there is no added complication when the standard state of the components of the solution can be taken as the pure components, because the change of enthalpy on the formation of a compound in its standard state is identical whether we are concerned with the pure... 

It follows, in general, that the standard chemical potential p) of a chemical compound i corresponds to the free enthalpy of formation for one mole of the compound substance i at the standard state, the value of which is tabulated in chemical handbooks as shown for a few compounds in Table 5.1. For ions in electrolytic solutions the chemical potential in their pure state can not be defined, but we may use the standard state of an ion in which the ionic activity is equal to unity (a, = 1) to define the unitary chemical potential of the ion as will be discussed in chapter 9. 

As mentioned in Sections 1.1 and 2.9, the third law of thermodynamics makes it possible to obtain the standard Gibbs energy of formation of species in aqueous solution from measurements of the heat capacity of the crystalline reactant down to about 10 K, its solubility in water and heat of solution, the heat of combustion, and the enthalpy of solution. According to the third law, the standard molar entropy of a pure crystalline substance at zero Kelvin is equal to zero. Therefore, the standard molar entropy of the crystalline substance at temperature T is given by... 

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. 

The reference point for all enthalpy expressions is called the standard molar enthalpy of formation (AHf) which is defined as the heat change that results when 1 mole of a compound in its standard state is formed from its elements in their standard states. The standard state of a liquid or solid substance is its most thermodynamically stable pure form at 1 bar pressure. The standard state for gases is similar, except that standard state gases are assumed to obey the ideal gas law exactly. The standard state for solutes dissolved in solution will be discussed in Chapter 10. In the notation AHf, the superscript represents standard-state conditions (1 bar), and the subscript f stands for formation. Although the standard state does not specify a temperature, we will assume, unless otherwise stated, AH° values are measured at 25°C. 

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