Enthalpy pressure dependence

Chlorine, a member of the halogen family, is a greenish yellow gas having a pungent odor at ambient temperatures and pressures and a density 2.5 times that of air. In Hquid form it is clear amber SoHd chlorine forms pale yellow crystals. The principal properties of chlorine are presented in Table 15 additional details are available (77—79). The temperature dependence of the density of gaseous (Fig. 31) and Hquid (Fig. 32) chlorine, and vapor pressure (Fig. 33) are illustrated. Enthalpy pressure data can be found in ref. 78. The vapor pressure P can be calculated in the temperature (T) range of 172—417 K from the Martin-Shin-Kapoor equation (80) ... 

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. 

Solution A rigorous treatment of a reversible reaction with variable physical properties is fairly complicated. The present example involves just two ODEs one for composition and one for enthalpy. Pressure is a dependent variable. If the rate constants are accurate, the solution will give the actual reaction trajectory (temperature, pressure, and composition as a function of time). If ko and Tact are wrong, the long-time solution will still approach equilibrium. The solution is then an application of the method of false transients. 

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>... 

The reaction enthalpy, AHr, is the quantity of heat that is either absorbed by the system (endothermic reaction) or released by the system (exothermic reaction), at constant pressure, as determined by the reaction equation. The reaction enthalpy AHr depends both on the chemical nature of the individual reactants and their physical states. 

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-... 

In addition to the equation of state, it will be necessary to describe other thermodynamic properties of the fluid. These include specific heat, enthalpy, entropy, and free energy. For ideal gases the thermodynamic properties usually depend on temperature and mixture composition, with very little pressure dependence. Most descriptions of fluid behavior also depend on transport properties, including viscosity, thermal conductivity, and diffusion coefficients. These properties generally depend on temperature, pressure, and mixture composition. 

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 ... 

MPa, and 81.5% only at 4.8 MPa [16], In absorption process, the reaction of magnesium with hydrogen is a nucleation and growth mechanism where the nucle-ation rate is pressure dependent. They estimated the enthalpy and corresponding entropy of MgH2 formation as -70.0 kJ/mol and -126 J/mol K, respectively. 

In this equation 2.31 the second term on the right hand side is the thermal part and the third term is the pressure-dependent part. Normally, the pressure-dependent part is very small compared with the thermal part as shown in Eq. 2.18 for ideal gases, in which (dHldp)T = 0, and Eq. 7.27 for liquids and solids. For most purposes then the enthalpy may be regarded as independent of pressure and is given by Eq. 2.32... 

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. 

Chemical reactions are often highly pressure-dependent. As a matter of fact, high pressure is an elegant way to perturb reversibly chemical equilibria and reactions. Another advantage of using the pressure parameter is that reactions are slowed or accelerated depending on the type of chemical interaction involved. For instance, pressure weakens electrostatic interactions, but stimulates some hydrophobic interactions, such as stacking between aromatic residues. Similarly to the activation enthalpy, obtained from... 

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. 

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... 

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