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Thermodynamic Properties DEAN #37261 (McGHP) RIGHT INTERACTIVE top of page SECTION 6 THERMODYNAMIC PROPERTIES 6.1 ENTHALPIES AND GIBBS ENERGIES OF FORMATION, ENTROPIES, AND HEAT CAPACITIES 6.1 6.1.1 Some Thermodynamic Relations 6.2 Table 6.1 Enthalpies and Gibbs Energies of Formation, Entropies, and Heat Capacities of Organic Compounds 6.5 Table 6.2 Heats of Fusion, Vaporization, and Sublimation and Specific Heat at Various Temperatures of Organic Compounds 6.51 Table 6.3 Enthalpies and Gibbs Energies of Formation, Entropies, and Heat Capacities of the Elements and Inorganic Compounds 6.81 Table 6.4 Heats of Fusion, Vaporization, and Sublimation and Specific Heat at Various Temperatures of the Elements and Inorganic Compounds 6.124 6.2 CRITICAL PHENOMENA 6.142 Table 6.5 Critical Properties 6.143 6.1 ENTHALPIES AND GIBBS ENERGIES OF FORMATION, ENTROPIES, AND HEAT CAPACITIES The tables in this section contain values of the enthalpy and Gibbs energy of formation, entropy, and heat capacity at 298.15 K (25ЊC). No values are given in these tables for metal alloys or other solid solutions, for fused salts, or for substances of undefined chemical composition. The physical state of each substance is indicated in the column headed “State” as crystalline solid (c), liquid (lq), or gaseous (g). Solutions in water are listed as aqueous (aq). 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. ⌬ Њ ⌬ Њ The values of f H and f G that are given in the tables represent the change in the appropriate thermodynamic quantity when one mole of the substance in its standard state is formed, isothermally at the indicated temperature, from the elements, each in its appropriate standard reference state. The standard reference state at 25ЊCfor each element has been chosen to be the standard state that is thermodynamically stable at 25ЊCand 1 atm pressure. The standard reference states are indicated in ⌬ Њ ⌬ Њ the tables by the fact that the values of f H and f G are exactly zero. The values of SЊ represent the virtual or “thermal” entropy of the substance in the standard state at 298.15 K (25ЊC), omitting contributions from nuclear spins. Isotope mixing effects are also ex- cluded except in the case of the 1H9 2H system. Solutions in water are designated as aqueous, and the concentration of the solution is expressed in terms of the number of moles of solvent associated with 1 mol of the solute. If no concentration is indicated, the solution is assumed to be dilute. The standard state for a solute in aqueous solution short is taken as the hypothetical ideal solution of unit molality (indicated as std. state or ss). In this state standard 6.1 base of DF DEAN #37261 (McGHP) LEFT INTERACTIVE top of rh 6.2 SECTION 6 base of rh cap height the partial molal enthalpy and the heat capacity of the solute are the same as in the infinitely dilute base of text real solution. For some tables the uncertainty of entries is indicated within parentheses immediately following the value; viz., an entry 34.5(4) implies 34.5Ϯ0.4 and an entry 34.5(12) implies 34.5Ϯ1.2. References: D. D. Wagman, et al., The NBS Tables of Chemical Thermodynamic Properties,in J. Phys. Chem. Ref. Data, 11: 2, l982; M. W. Chase, et al., JANAF Thermochemical Tables, 3rd ed., American Chemical Society and the American Institute of Physics, 1986 (supplements to JANAF appear in J. Phys. Chem. Ref. Data); Thermodynamic Research Center, TRC Thermodynamic Tables, Texas A&M University, College Station, Texas; I. Barin and O. Knacke, Thermochemical Properties of Inorganic Substances, Springer-Verlag, Berlin, 1973; J. B. Pedley, R. D. Naylor, and S. P. Kirby, Thermochemical Data of Organic Compounds, 2nd ed., Chapman and Hall, London, 1986; V. Majer and V. Svoboda, Enthalpies of Vaporization of Organic Compounds, International Union of Pure and Applied Chemistry, Chemical Data Series No. 32, Blackwell, Oxford, 1985. 6.1.1 Some Thermodynamic Relations 6.1.1.1 Enthalpy of Formation. Once standard enthalpies are assigned to the elements, it is possible to determine standard enthalpies for compounds. For the reaction: ϩ : ⌬ Њ ϭϪ C(graphite) O22 (g) CO (g) H 393.51 kJ (6.1) Since the elements are in their standard states, the enthalpy change for the reaction is equal to the standard enthalpy of CO2 less the standard enthalpies of Cand O 2, which are zero in each instance. Thus, ⌬ Њ ϭϪ Ϫ Ϫ ϭϪ f H 393.51 0 0 393.51 kJ (6.2) Tables of enthalpies, such as Tables 6.1 and 6.3, can be used to determine the enthalpy for any reaction at 1 atm and 298.15 K involving the elements and any of the compounds appearing in the tables. The solution of 1 mole of HCl gas in a large amount of water (infinitely dilute real solution) is represented by: ϩ : ϩϪϩ HCl(g) inf H2 O H (aq) Cl (aq) (6.3) ⌬ Њ ϭϪ ⌬ Њ The heat evolved in the reaction is H 74.84 kJ. With the value of f H from Table 6.3, one has for the reaction: ⌬ Њ ϭ ⌬ Њ ϩϪϩ ⌬ Њ Ϫ ⌬ Њ ffH H [H (aq)] fH [Cl (aq)] fH [HCl(g)] (6.4) for the standard enthalpy of formation of the pair of ions Hϩ and ClϪ in aqueous solution (standard ϭ ⌬ Њ ϩ state, m 1). To obtain the f H values for individual ions, the enthalpy of formation of H (aq) is arbitrarily assigned the value zero at 298.15 K. Thus, from Eq. (6.4): ⌬ Њ Ϫ ϭϪ ϩ Ϫ ϭϪ f H [Cl (aq)] 74.84 ( 92.31) 167.15 kJ With similar data from Tables 6.1 and 6.3, the enthalpies of formation of other ions can be deter- ⌬ Њ ϭ Ϫ mined. Thus, from the f H [KCl(aq, std. state, m 1 or aq, ss)] of 419.53 kJ and the foregoing ⌬ Њ Ϫ value for f H [Cl (aq, ss)]: ⌬ HЊ[KϩϪ (aq, ss)] ϭ ⌬ HЊ[KCl(aq, ss)] Ϫ ⌬ HЊ[Cl (aq, ss)] ff f short ϭϪ419.53 Ϫ(Ϫ167.15) ϭϪ252.38 kJ (6.5) standard long DEAN #37261 (McGHP) RIGHT INTERACTIVE top of rh THERMODYNAMICPROPERTIES 6.3 base of rh cap height 6.1.1.2 Enthalpy of Vaporization (or Sublimation) When the pressure of the vapor in equilib- base of text rium with a liquid reaches 1 atm, the liquid boils and is completely converted to vapor on absorption ⌬ of the enthalpy of vaporization Hv at the normal boiling point Tb. A rough empirical relationship between the normal boiling point and the enthalpy of vaporization (Trouton’s rule) is: ⌬Hv ϭ 88 J · molϪ1 · KϪ1 (6.6) Tb It is best applied to nonpolar liquids which form unassociated vapors. To a first approximation, the enthalpy of sublimation ⌬Hs at constant temperature is: ⌬Hs ϭ ⌬Hm ϩ ⌬Hv (6.7) where ⌬Hm is the enthalpy of melting. The Clapeyron equation expresses the dynamic equilibrium existing between the vapor and the condensed phase of a pure substance: dP ⌬Hv ϭ (6.8) dT T⌬V where ⌬V is the volume increment between the vapor phase and the condensed phase. If the con- densed phase is solid, the enthalpy increment is that of sublimation. Substitution of V ϭ RT/P into the foregoing equation and rearranging gives the Clausius-Cla- peyron equation, dP ⌬Hv ϭ (6.9) PdT RT2 or d(ln P) ⌬Hv ϭϪR (6.10) 1/T which may be used for calculating the enthalpy of vaporization of any compound provided its boiling point at any pressure is known. If an Antoine equation is available (such as Eq. (5.1), page 5.30), differentiation and insertion into the foregoing equation gives: 4.5757TB2 ⌬Hv ϭ (6.11) (T ϩ C Ϫ 273.15)2 Inclusion of a compressibility factor into the foregoing equation, as suggested by the Haggen- macher equation improves the estimate of ⌬Hv: RT2 dP T 3 P 1/2 ⌬Hv ϭ ͩͪͩ1 Ϫ c ͪ (6.12) 3 PdT TPc where Tc and Pc are critical constants (Table 6.5). Although critical constants may be unknown, the compressibility factor is very nearly constant for all compounds belonging to the same family, and an estimate can be deduced from a related compound whose critical constants are available. 6.1.1.3 Heat Capacity (or Specific Heat) The temperature dependence of the heat capacity is complex. If the temperature range is restricted, the heat capacity of any phase may be represented adequately by an expression such as: short ϭ ϩ ϩ 2 Cp a bT cT (6.13) standard long DEAN #37261 (McGHP) LEFT INTERACTIVE top of rh 6.4 THERMODYNAMICPROPERTIES base of rh cap height in which a, b, and c are empirical constants. These constants may be evaluated by taking three pieces base of text of data: (T1, Cp,1), (T2, Cp,2), and (T3, Cp,1), and substituting in the following expressions: CCC p,1 ϩϩϭp,2 p,3 Ϫ Ϫ Ϫ Ϫ Ϫ Ϫ c (6.14) (T121321233231T )(T T )(T T )(T T )(T T )(T T ) C Ϫ C p,1 p,2 Ϫ ϩ ϭ Ϫ [(T12T )c] b (6.15) T12T Ϫ Ϫ 2 ϭ (Cp,1bT 1) cT 1 a (6.16) Smoothed data presented at rounded temperatures, such as are available in Tables 6.2 and 6.4, plus Њ the Cp values at 298 K listed in Table 6.1 and 6.3, are especially suitable for substitution in the foregoing parabolic equations.
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