Enthalpy tabulations

Problem Estimate A//f°[C2H5OH(g)] from the bond enthalpies tabulated above. 

Explain the significance of the specific internal energies and enthalpies tabulated in the steam tables (B.5, B.6, and B.7), remembering that we can never know the true values of either variable in a given state. Given any process in which a specified mass (or mass flow rate) of water changes from one state to another, use the steam tables to calculate Af/ (or Af/) and/or (or H). 

For all practical purposes, the bond energy is the same as bond enthalpy. Tabulated values of average bond energies are actually average bond enthalpies. We use the term bond energy rather than bond enthalpy because it is common practice to do so. 

Strictly speaking, the enthalpies tabulated in A.2-9 are for saturated Uquid, meaning that the pressure on the liquid equals the vapor pressure. Here the pressure on the feed is probably 1 atm (or 14.7 psia) rather than 0.3622 psia (the vapor pressure). Pressure has a very weak effect on the enthalpy of Uquid water and the effect of pressure usually neglected. For example, the effect of a change on pressure equal to latm on the enthapy of Uquid water can be estimated as... 

Using the bond enthalpies tabulated in Table 8.4, estimate AH for each of the following gas-phase reactions ... 

The properties of the solids most commonly encountered are tabulated. An important problem arises for petroleum fractions because data for the freezing point and enthalpy of fusion are very scarce. The MEK (methyl ethyl ketone) process utilizes the solvent s property that increases the partial fugacity of the paraffins in the liquid phase and thus favors their crystallization. The calculations for crystallization are sensitive and it is usually necessary to revert to experimental measurement. 

Tables 2,3, and 4 outline many of the physical and thermodynamic properties ofpara- and normal hydrogen in the sohd, hquid, and gaseous states, respectively. Extensive tabulations of all the thermodynamic and transport properties hsted in these tables from the triple point to 3000 K and at 0.01—100 MPa (1—14,500 psi) are available (5,39). Additional properties, including accommodation coefficients, thermal diffusivity, virial coefficients, index of refraction, Joule-Thorns on coefficients, Prandti numbers, vapor pressures, infrared absorption, and heat transfer and thermal transpiration parameters are also available (5,40). Thermodynamic properties for hydrogen at 300—20,000 K and 10 Pa to 10.4 MPa (lO " -103 atm) (41) and transport properties at 1,000—30,000 K and 0.1—3.0 MPa (1—30 atm) (42) have been compiled. Enthalpy—entropy tabulations for hydrogen over the range 3—100,000 K and 0.001—101.3 MPa (0.01—1000 atm) have been made (43). Many physical properties for the other isotopes of hydrogen (deuterium and tritium) have also been compiled (44).

A tabulation of the partial pressures of sulfuric acid, water, and sulfur trioxide for sulfuric acid solutions can be found in Reference 80 from data reported in Reference 81. Figure 13 is a plot of total vapor pressure for 0—100% H2SO4 vs temperature. References 81 and 82 present thermodynamic modeling studies for vapor-phase chemical equilibrium and liquid-phase enthalpy concentration behavior for the sulfuric acid—water system. Vapor pressure, enthalpy, and dew poiat data are iacluded. An excellent study of vapor—liquid equilibrium data are available (79). 

Thermodynamic data on H2, the mixed hydrogen—deuterium molecule [13983-20-5] HD, and D2, including values for entropy, enthalpy, free energy, and specific heat have been tabulated (16). Extensive PVT data are also presented in Reference 16 as are data on the equihbrium—temperature... 

Values rounded off from Chappell and Cockshutt, Nat. Res. Counc. Can. Rep. NRC LR 759 (NRC No. 14300), 1974. This source tabulates values of seven thermodynamic functions at 1-K increments from 200 to 2200 K in SI units and at other increments for two other unit systems. An earlier report (NRC LR 381, 1963) gives a more detailed description of an earlier fitting from 200 to 1400 K. In the above table h = specific enthalpy, kj/kg, and = logio for m isentrope. In terms of... 

Values extracted and sometimes rounded off from tte tables of McCarty, Hord, and Roder, NBS Monogr. 168, 1981. This source contains an exhaustive tabulation of property values for botb tbe normal and tbe para forms of hydrogen, v = specific volume, mVkg h = specific enthalpy kj/kg s = specific entropy, kJ/(kg-K). 

Values reproduced or converted from a tabulation by Tsykalo and Tabacbnikov in V A. Rabinovich (ed.), Theimophysical Propeities of Gases and Liquids, Stan-dartov, Moscow, 1968 NBS-NSF transl. TT 69-55091, 1970. Tbe reader may be reminded that very pure hydrogen peroxide is very difficult to obtain owing to its decomposition or instability, c = critical point. Tbe FMC Corp., Philadelphia, PA tech. bull. 67, 1969 (100 pp.) contains an enthalpy-pressure diagram to 3000 psia, 1100 K. 

Equimolal proportions of the reactants are used. Thermodynamic data at 298 K are tabulated. The specific heats are averages. Find (1) the enthalpy change of reaction at 298 and 573 K (2) equilibrium constant at 298 and 573 K (3) fractional conversion at 573 K. 

Values of enthalpy constants for approximate equations are not tabulated here but are also computed for each stage based on the initial temperature distribution. 

Because these various quantities are characteristics of the reactants and products but are independent of the reaction path, they cannot provide insight into mechanisms. Information about AG, AH, and AS does, however, indicate the feasibility of any specific reaction. The enthalpy change of a given reaction can be estimated from tabulated thermochemical data or from bond-energy data such as those in Table 1.3 (p. 14) The exan le below illustrates the use of bond-energy data for estimating the enthalpy of a reaction. 

Whether AH for a projected reaction is based on bond-energy data, tabulated thermochemical data, or MO computations, there remain some fundamental problems which prevent reaching a final conclusion about a reaction s feasibility. In the first place, most reactions of interest occur in solution, and the enthalpy, entropy, and fiee energy associated with any reaction depend strongly on the solvent medium. There is only a limited amount of tabulated thermochemical data that are directly suitable for treatment of reactions in organic solvents. Thermodynamic data usually pertain to the pure compound. MO calculations usually refer to the isolated (gas phase) molecule. Estimates of solvation effects must be made in order to apply either experimental or computational data to reactions occurring in solution. 

Enthalpy may be expressed as a total above absolute zero, or any other base which is convenient. Tabulated enthalpies found in reference works are often shown above a base temperature of - 40°C, since this is also - 40° on the old Fahrenheit scale. In any calculation, this base condition should always be checked to avoid the errors which will arise if two different bases are used. 

For the electrochemical cell reaction, the reaction free energy AG is the utilizable electrical energy. The reaction enthalpy AH is the theoretical available energy, which is increased or reduced by an amount TAS. The product of the temperature and the entropy describes the amount of heat consumed or released reversibly during the reaction. With tabulated values for the enthalpy and the entropy it is possible to obtain AG. ... 

Table 2.2 Enthalpies and temperatures of fusion and vaporization. Normal melting and boiling points and enthalpies of fusion and vaporization are tabulated by type of...

Thus, values for C°p m T, S°m T, (H°m T - H°m 0) and (G°mT H°m0) can be obtained as a function of temperature and tabulated. Figure 4.16 summarizes values for these four quantities as a function of temperature for glucose, obtained from the low-temperature heat capacity data described earlier. Note that the enthalpy and Gibbs free energy functions are graphed as (// , T - H°m 0)/T and (G T — H q)/T. This allows all four functions to be plotted on the same scale. Figure 4.16 demonstrates the almost linear nature of the (G°m T H°m 0)/T function. This linearity allows one to easily interpolate between tabulated values of this function to obtain the value at the temperature of choice. 

Enthalpy and free energy functions can also be tabulated using T = 298.15 K as a reference temperature by making use of the relationships... 

Table 4.3 summarizes values taken from the JANAF tables for the Gibbs free energy functions and standard enthalpies of formation for a few common substances. The JANAF tables provide a more complete tabulation. 

Relative partial molar enthalpies can be used to calculate AH for various processes involving the mixing of solute, solvent, and solution. For example, Table 7.2 gives values for L and L2 for aqueous sulfuric acid solutions7 as a function of molality at 298.15 K. Also tabulated is A, the ratio of moles H2O to moles H2S(V We note from the table that L — L2 — 0 in the infinitely dilute solution. Thus, a Raoult s law standard state has been chosen for H20 and a Henry s law standard state is used for H2SO4. The value L2 = 95,281 Tmol-1 is the extrapolated relative partial molar enthalpy of pure H2SO4. It is the value for 77f- 77°. 

Also tabulated is 4>L, the apparent partial molar enthalpy. We will define this quantity and describe its application later. 

Values of mixing processes. For example, for the integral enthalpy of solution process given in Example 7.1, we used L and L2 values to show that for the process... 

Extensive tabulations of standard enthalpies of formation and related thermodynamic data can be found in the literature.5 Table 9.1 summarizes selected values from these sources. 

Table A4.6 gives the internal rotation contributions to the heat capacity, enthalpy and Gibbs free energy as a function of the rotational barrier V. It is convenient to tabulate the contributions in terms of VjRTagainst 1/rf, where f is the partition function for free rotation [see equation (10.141)]. For details of the calculation, see Section 10.7c.

In contrast to the situation observed in the trivalent lanthanide and actinide sulfates, the enthalpies and entropies of complexation for the 1 1 complexes are not constant across this series of tetravalent actinide sulfates. In order to compare these results, the thermodynamic parameters for the reaction between the tetravalent actinide ions and HSOIJ were corrected for the ionization of HSOi as was done above in the discussion of the trivalent complexes. The corrected results are tabulated in Table V. The enthalpies are found to vary from +9.8 to+41.7 kj/m and the entropies from +101 to +213 J/m°K. Both the enthalpy and entropy increase from ll1 "1" to Pu1 with the ThSOfj parameters being similar to those of NpS0 +. Complex stability is derived from a very favorable entropy contribution implying (not surprisingly) that these complexes are inner sphere in nature. 

Reaction enthalpies can be estimated by using mean bond enthalpies to determine the total energy required to break the reactant bonds and form the product bonds. In practice, only the bonds that change are treated. Because bond enthalpies refer to gaseous substances, to use the tabulated values, all substances must be gases or converted into the gas phase. 

This is an integral balance written for the whole system. The various terms deserve discussion. The enthalpies are relative to some reference temperature, Tref. Standard tabulations of thermodynamic data (see Chapter 7) make it convenient to choose rre/ = 298K, but choices of 7 re/ = 0K or Tref = Q°C are also common. The enthalpy terms will normally be replaced by temperature using... 

Reaction enthalpies may also vary with temperature. Most tabulations of thermodynamic functions are for T = 298 K, so we assume that is the temperature unless otherwise specified. 

Example applies tabulated enthalpies to a reaction occurring at elevated temperature and pressure. 

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