Pure substances, standard enthalpy

The values of the thermodynamic properties of the pure substances given in these tables are, for the substances in their standard states, defined as follows For a pure solid or liquid, the standard state is the substance in the condensed phase under a pressure of 1 atm (101 325 Pa). For a gas, the standard state is the hypothetical ideal gas at unit fugacity, in which state the enthalpy is that of the real gas at the same temperature and at zero pressure. 

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. 

For pure solids and liquids, the standard enthalpy is the enthalpy of the substance at the specified temperamre and at 1 bar. 

While changes in internal energy and enthalpy (AC/ and Ai/) may be determined, it is not possible to measure either U or//absolutely. Consequently, an arbitrary datum is defined at which the enthalpy is zero. For this purpose, the enthalpy of all elements in their standard states is taken as zero at the stated reference temperature. The standard state of a pure substance at temperature T is defined as follows ... 

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 ... 

If we want to calculate the entropy of a liquid, a gas, or a solid phase other than the most stable phase at T =0, we have to add in the entropy of all phase transitions between T = 0 and the temperature of interest (Fig. 7.11). Those entropies of transition are calculated from Eq. 5 or 6. For instance, if we wanted the entropy of water at 25°C, we would measure the heat capacity of ice from T = 0 (or as close to it as we can get), up to T = 273.15 K, determine the entropy of fusion at that temperature from the enthalpy of fusion, then measure the heat capacity of liquid water from T = 273.15 K up to T = 298.15 K. Table 7.3 gives selected values of the standard molar entropy, 5m°, the molar entropy of the pure substance at 1 bar. Note that all the values in the table refer to 298 K. They are all positive, which is consistent with all substances being more disordered at 298 K than at T = 0. 

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 chemical potential of a pure substance i indicates the thermodynamic energy level of the substance relative to the energy level of the chemical elements that make up the substance i. In chemical thermodynamics the chemical potentials of elements are conventionally all set zero in the stable state of them at the standard temperature 298 K and pressure 101.3 kPa. The chemical potential of a substance (a chemical compound) / at the standard state, as a result, is equal to the free enthalpy (Gibbs energy) required to form one mole of the substance i from its constituent elements in their stable standard state. 

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. 

Reactants and products in their standard states (pure substance at I bar) at 298.15 K Bond enthalpies for diatomic molecules are given in Table 6.7 in the text. 

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. 

Enthalpy change does depend on conditions of temperature, pressure and concentration of the initial and final states, and it is important to specify these. Standard states are defined as pure substances at standard pressure (1 bar), and... 

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. 

Tables of average standard bond enthalpies make the assumption that the standard enthalpy of a bond is independent of the molecule in which it exists. This is only roushly true. Since standard bond enthalpies vary from one compound to another, the use of avaage standara bond enthalpies gives only approximate values for standard enthalpies of reaction calculated from them. Experimental methods are used to obtain standard enthalpies of reaction whenever possible. Calculations bwd on average standard bond enthalpies are used only for reaaiona which cannot ce studied experimentally —for example, the reactions of a substance which has not been isolated in a pure state.

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. 

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. 

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 ... 

For the ideal gaseous standard state, is evidently the molar enthalpy of an ideal gas. For standard states based on Henry s law, where y 1 as X ot m 0,lTi is the partial molar enthalpy of the solute in the hypothetical pure substance having yg = 1 or the hypothetical ideal one molal solution respectively. Substances in these strange states have partial molar enthalpies (and volumes) equal to that at infinite dilution, hence providing a method of measurement. This can be seen by considering Equations (8.38) and (8.39), which show that 71° becomes equal to // when y is 1.0. Therefore for Henryan standard states where y, -> 1 as X or m 0, must be the partial molar enthalpy of i at infinite dilution, and for Raoultian standard states where y, 1 as Xj -> 1, //° must be the partial molar enthalpy (the molar enthalpy) of pure i (confirming what we stated by simple inspection, above). 

The chapter reviews the existing experimental data for standard enthalpies and entropies of solution of pure substances in various solvents and gives derived entropies of transfer of molecules, ions, and groups from one solvent to another and from the gas phase to water. The data are summarized in 22 tables and cover both Inorganic and organic substances, electrolytes and non electrolytes. There are 146 references to the literature. 

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