Pressure-dependence of enthalpy

Pressure dependence of enthalpy is shown in Fig. 3 together with its components U and PV. The enthalpy increases linearly with pressure at high pressure region and decreases rapidly with pressure at low pressure. The former behavior is due to the contribution of PV, and the latter is to the internal energy. Variation of isobaric heat... 

Generally the pressure-dependence of enthalpy can be disregarded unless major changes of pressure are dealt with. Previously, based on Joule s law (3.19) and (3.23), we have shown that for an ideal gas, enthalpy is independent of the pressure. For solids and liquids, the pressure only has very little influence on the enthalpy content According to (3.11), for an adiabatic change of pressure dp in a condensed phase, dH is... 

Molecular Nature of Steam. The molecular stmcture of steam is not as weU known as that of ice or water. During the water—steam phase change, rotation of molecules and vibration of atoms within the water molecules do not change considerably, but translation movement increases, accounting for the volume increase when water is evaporated at subcritical pressures. There are indications that even in the steam phase some H2O molecules are associated in small clusters of two or more molecules (4). Values for the dimerization enthalpy and entropy of water have been deterrnined from measurements of the pressure dependence of the thermal conductivity of water vapor at 358—386 K (85—112°C) and 13.3—133.3 kPa (100—1000 torr). These measurements yield the estimated upper limits of equiUbrium constants, for cluster formation in steam, where n is the number of molecules in a cluster. 

The effect of pressure on chemical equilibria and rates of reactions can be described by the well-known equations resulting from the pressure dependence of the Gibbs enthalpy of reaction and activation, respectively, shown in Scheme 1. The volume of reaction (AV) corresponds to the difference between the partial molar volumes of reactants and products. Within the scope of transition state theory the volume of activation can be, accordingly, considered to be a measure of the partial molar volume of the transition state (TS) with respect to the partial molar volumes of the reactants. Volumes of reaction can be determined in three ways (a) from the pressure dependence of the equilibrium constant (from the plot of In K vs p) (b) from the measurement of partial molar volumes of all reactants and products derived from the densities, d, of the solution of each individual component measured at various concentrations, c, and extrapolation of the apparent molar volume 4>... 

This understanding can be used to infer the pressure dependence of k because enthalpy depends on pressure. It can be shown that... 

In recent years we have undertaken a systematic investigation of the volumes and heat capacities of transfer of alkali halides and tetraalkylammonium bromides from water to mixed aqueous solvents (1-6). These properties are important because, when combined with enthalpies and free energies, they can be used to calculate the temperature and pressure dependences of various equilibrium properties of electrolytes in mixed solvents. Since the properties of electrolytes in mixed aqueous solvents are closely related to the corresponding properties of the nonelectrolyte in an electrolyte solution, infor-... 

The thermodynamic stability of unsubstituted silacyclopropane to fragmentation has been studied by ab initio quantum mechanical methods and the enthalpy of decomposition to H2Si + CH2=CH2 was predicted to be 44.878 and 43.279 kcalmol-1. There is indirect experimental support for these theoretical estimates. When these values were employed in RRKM calculations on silirane decomposition, the pressure dependence of the bimolecular rate constant for addition of H2Si to ethylene could be accurately modeled80. 

It is, therefore, not surprising that there exists a definite relationship between Aand the enthalpy of vaporization, Av H, the former constituting a fraction between 0.2 and 0.3 of the latter, as is readily obtained from the data in Tables 3.1 and 3.9. The pressure dependence of the viscosity is also closely related to the free volume of the solvent. The fluidity (O = l/r ) is proportional to the ratio between the free and the occupied volume, the former, as mentioned above, being the difference between the actual molar volume and the intrinsic molar volume (Tables 3.1 and 3. 4) (Hildebrand 1978). In fact, the logarithm of the viscosity of liquids was found (Marcus 1998) to be described well for some 300 liquids by the empirical relationship ... 

Equation (3) above—or more generally by Equation (13) of Reference 7—including any required "utilization function costs" as described in Requirement 3 below) is a minimum with respect to all decision variables of that component—including stream parameters such as H, T, or P upon which the essergy may depend (say via Equation 2, through the familiar dependence of enthalpy and entropy upon temperature T and pressure P—if M, T, or P are not state variables, in which case their value would result from decisions in another component). 

The pressure dependence of the solubihty product constant should arise from the enthalpy dependence on the pressure ... 

The influence of temperature can be studied, and the activation parameters (e g. the activation enthalpies and entropies) can be calculated. If necessary, the high-pressure stopped-flow technique can be used to study the pressure dependence of reactions, and the corresponding volumes of activation may be calculated. 

To understand the pressure dependence of free energy, we need to know how pressure affects the thermodynamic functions that constitute free energy—that is, enthalpy and entropy (recall that G = H - TS). For an ideal... 

In order to obtain —AH at conditions other than 1 atm and 25 C from equation (43) and tables of standard heats of formation, it is necessary to compute the enthalpy change of the reactant mixture and of the product mixture in going from 1 atm and 25°C to the given p and T additional tables are available to facilitate these computations for a number of materials [13], [15] [17], [26]-[28]. Usually the pressure dependence of —AH is negligible, and from equation (38) it follows that for ideal-gas reactions,... 

Knowledge of the enthalpies of the various mixtures as functions of T and p is required in carrying out the computation. Usually equation (37) is an excellent approximation for H, and the pressure dependence of is often negligible (these results are exactly true for ideal gases) even in the few cases where these approximations are not accurate, insufficient information is available to merit using more complicated equations. In equation (37), the temperature dependence of H. is then given by... 

Ghosh T, Garca AE, Garde S. Enthalpy and entropy contributions to the pressure dependence of hydrophobic interactions. J. Chem. Phys. 2002 116 2480-2486. 

To calculate the adiabatic mixing temperature dp the pressure dependence of the specific enthalpy is neglected. Then setting... 

Denoted by AH, the heat of reaction, which the system exchanges with the surroundings at the temperature T, what is the heat of reaction, if the reaction takes place at temperature Ti In other words, we are looking for the dependence of enthalpy on temperature at constant pressure... 

In this section, four exercise problems are given based on the gas-phase refrigeration system discussed in this chapter. The degree of difficulty increases from problem 1 to 4. Readers can tackle the first three problems with any one of the following three assumptions (i) a constant Cp value - a very simplified approach (ii) Cp is a function of temperature only (i.e., neglect the pressure dependence of Cp) - a reasonable approximation and (iii) use the enthalpy and Cp correlations given below - very close to the real case. The solutions to problems 1 and 2 are available in the file GasPhaseRefrigeration.xls in the folder Chapter 8 on the CD. 

Table 9.3 shows step one of the double fractionation of LLDPE carried out with propane at 130°C. The increasing pressure profile began at 250 bar (3,600 psia) and increased to 675 bar (9,800 psia) in increments of —25 bar. The parent LLDPE with a polydispersity of 5.0 has been separated into fractions with a molecular weight range from about 10,000 to 200,000 and polydispersi-ties of 1.2 to 1.6. There is only a weak dependence of enthalpy of fusion ( usion) peak melting temperature on molecular weight. The results are consistent with the notion that molecular weight is the dominant factor in liquid-gas equilibrium. The values, which reflect the crystallinity of... 

Analysis of exchange-broadened NMR spectra (that is, the simulation of temperature-dependent spectra as a function of the exchange rate) has become the method of choice for the determination of the free activation enthalpy for intramolecular conformational equilibria and for intermolecular exchange processes. Studying, in addition, the pressure dependence of the... 

The free energy, enthalpy, entropy, and volume of the hydrated electron are measurable in principle from the temperature and pressure dependencies of the forward and reverse rates of the unimolecular reaction of this species with water to form hydrogen atom and hydroxide ion. Data presently available determine values only for free energies of activation in both directions and for enthalpy and entropy of activation in one direction. Values for the other properties can be predicted if it is assumed that the enthalpy, entropy, and volume of the hydrated electron can be calculated by extrapolating measurements on halide ions to the radius (2.98 A.) necessary to fit the free energy data. The predictions for enthalpy and entropy are thought to be reasonably accurate, but the value for volume change is less reliable. 

From this it is clear that H° is a function only of temperature. The degree superscript on any thermodynamic quantity indicates the value of that quantity at the standard pressure. (Because the dependence of enthalpy on pressure is very slight—compare with Section 7.15—we will often use standard enthalpies at pressures other than one atm the error will not be serious unless the pressure is very large, for example, 1000 atm.)... 

To understand the pressure dependence of free energy, we need to know how pressure affects the thermodynamic functions that comprise free energy, that is, enthalpy and entropy (recaii that G = H - TS). For an ideal gas, enthalpy is not pressure-dependent. However, entropy does depend on pressure because of its dependence on volume. Consider 1 moie of an ideai gas at a given temperature. At a volume of 10.0 L, the gas has many more positions avaiiable for its molecules than if its volume is 1.0 L. The positional entropy is greater in the iarger volume. In summary, at a given temperature for 1 mole of ideal gas... 

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