Klotz

More complicated reactions and heat capacity functions of the foiiii Cp = a + bT + cT + are treated in thermodynamics textbooks (e.g., Klotz and Rosenberg, 2000). Unfortunately, experimental values of heat capacities are not usually available over a wide temperature range and they present some computational problems as well [see Eq. (5-46)]. 

The remaining question is how we got from G3MP2 (OK) = —117.672791 to G3MP2 Enthalpy = —117.667683. This is not a textbook of classical thermodynamics (see Klotz and Rosenberg, 2000) or statistical themiodynamics (see McQuarrie, 1997 or Maczek, 1998), so we shall use a few equations from these fields opportunistically, without explanation. The definition of heat capacity of an ideal gas... 

The rectangular isotherm has received special attention. For this, many of the constant patterns are developed fuUy at the bed inlet, as shown for external mass transfer [Klotz, Chem. Rev.s., 39, 241 (1946)], pore diffusion [Vermeulen, Adv. Chem. Eng., 2, 147 (1958) Hall et al., Jnd. Eng. Chem. Fundam., 5, 212 (1966)], the linear driving force approximation [Cooper, Jnd. Eng. Chem. Fundam., 4, 308 (1965)], reaction kinetics [Hiester and Vermeulen, Chem. Eng. Progre.s.s, 48, 505 (1952) Bohart and Adams, J. Amei Chem. Soc., 42, 523 (1920)], and axial dispersion [Coppola and LeVan, Chem. Eng. ScL, 38, 991 (1983)]. 

S, Vatavuk, W. M., W. L. Klotz, and R. L. Stallings. Carbon Adsorbers. In OAQPS Centro Cost... 

Adapted from Klotz, I. M., 1986. Introduction to Bionwleeular Energetics. New York Academic Pre.s.s. 

Klotz, I. M., 1996. Equilibrium constants and free energies in unfolding of proteins in urea solutions. Proceedings of the National Academy of Sciences 93 14411-14415. 

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Klotz, I. M. (1997). Ligand-receptor energetics A guide for the perplexed. John Wiley and Sons, New York. 

Klotz etal.U9, l2° asserted that polymers from polyethylenimine reacted with chloromethylimidazole and dodecyliodide were excellent models for hydrolase. 70 [PEI-D(10%)-Im(l 5%)] catalyzed the hydrolyses of PNPA 270 times faster than imidazole itself. The authors also found that lauroylated polyethylenimine containing hydroxamate and imidazole groups, 71 [PEI-HA(8%)-L(8%)-Im(6.6%)], had a high efficiency in hydrolyses, i. e. 310 times that of imidazole. 

Klotz and associates120 found that PEI-D-Im-type models catalyzed hydrolyses of 4-nitrocatechol sulfate by a two step mechanism resembling that of a natural enzyme. The polymer was reported to accelerate the rate by a factor of 1012 arm-pared to imidazole itself, and of 102 compared to a type-11A arylsulfatase enzyme. 

Primary amino- and SH-groups are also nucleophiles and active for hydrolyses. Klotz et al.12S 127) investigated the activities of lauroyl-substituted polyethylenimine,... 

The volume of a solution is sometimes expressed as a function of composition and the partial molar volume is then obtained by differentiation. For example, Klotz and Rosenburg2 have expressed the volume of aqueous sodium chloride solutions at 298.15 K and ambient pressure as a function of the molality m of the solution by the equation ... 

I. M. Klotz and R. M. Rosenburg, Chemical Thermodynamics Basic Theory and Methods, W. A. Benjamin Inc. Menlo Park, California. 1972, p. 276. 

Thus, p can be estimated from the observed pressure and the ideal pressure calculated from the molar volume and the ideal gas equation. Klotz and Rosenburg3 report that the error in using equation (6.23) to calculate p is less than 1% for O2 up to a pressure of 10 MPa. For CO2 (g) the error is 1% at 2.5 MPa and 4% at 5 MPa. 

The fugacity coefficient can be calculated from other equations of state such as the van der Waals, Redlick-Kwong, Peng-Robinson, and Soave,d but the calculation is complicated, since these equations are cubic in volume, and therefore they cannot be solved explicitly for Vm, as is needed to apply equation (6.12). Klotz and Rosenburg4 have shown a way to get around this problem by eliminating p from equation (6.12) and integrating over volume, but the process is not easy. For the van der Waals equation, they end up with the relationship... 

Kelvin-Planck statement of Second Law 57 Klotz. I. M. 217. 254. 256 krypton, heat capacity 577-8... 

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