Gas constant, 1.8, 1.28

If mass is measured in kilograms or grams, constant in Eq. (1.4) differs from gas to gas. But when the concept of the mole as a mass unit is used, k, can be replaced by the universal gas constant R, which, by Avogadro s law, is the same for all gases. The numerical value of R depends only on the units chosen for energy, temperature, and mass. Then Eq. (1.4) is written 

Values of R in other units for energy, temperature, and mass are given in Appendix 2. 

Although the mole is defined as a mass in grams, the concept of the mole is easily extended to other mass units. Thus, the kilogram mole (kg mol) is the usual molecular or atomic weight in kilograms, and the pound mole (lb mol) is that in avoirdupois pounds. When the mass unit is not specified, the gram mole (g mol) is intended. Molecular weight M is a pure number. 

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Boltzmann constanty k A fundamental constant. It is the gas constant per molecule, equal to R divided by Avogadro s number L. 

P = pressure M = molecular weight R = ideal gas constant T = temperature Pi = liquid density... 

R = ideal gas constant dCp = reduced correction for C, a function of and and of the acentric factor... 

In 1873, van der Waals [2] first used these ideas to account for the deviation of real gases from the ideal gas law P V= RT in which P, Tand T are the pressure, molar volume and temperature of the gas and R is the gas constant. Fie argried that the incompressible molecules occupied a volume b leaving only the volume V- b free for the molecules to move in. Fie further argried that the attractive forces between the molecules reduced the pressure they exerted on the container by a/V thus the pressure appropriate for the gas law isP + a/V rather than P. These ideas led him to the van der Waals equation of state ... 

If tlie arbitrary constant C is set equal to nRy where n is the number of moles in the system and R is the gas constant per mole, then the themiodynamic temperature T = 9j where 9j is the temperature measured by the ideal-gas themiometer depending on the equation of state... 

The principle of tire unattainability of absolute zero in no way limits one s ingenuity in trying to obtain lower and lower thennodynamic temperatures. The third law, in its statistical interpretation, essentially asserts that the ground quantum level of a system is ultimately non-degenerate, that some energy difference As must exist between states, so that at equilibrium at 0 K the system is certainly in that non-degenerate ground state with zero entropy. However, the As may be very small and temperatures of the order of As/Zr (where k is the Boltzmaim constant, the gas constant per molecule) may be obtainable. 

R is the gas constant per mole, while K is the temperature unit Kelvin). The dashed lines represent metastable extensions of the stable phases beyond the transition temperatures. 

This equation describes the additional amount of gas adsorbed into the pores due to capillary action. In this case, V is the molar volume of the gas, y its surface tension, R the gas constant, T absolute temperature and r the Kelvin radius. The distribution in the sizes of micropores may be detenninated using the Horvath-Kawazoe method [19]. If the sample has both micropores and mesopores, then the J-plot calculation may be used [20]. The J-plot is obtained by plotting the volume adsorbed against the statistical thickness of adsorbate. This thickness is derived from the surface area of a non-porous sample, and the volume of the liquified gas. 

Figure B2.4.2. Eyring plot of log(rate/7) versus (1/7), where Jis absolute temperature, for the cis-trans isomerism of the aldehyde group in fiirfiiral. Rates were obtained from tln-ee different experiments measurements (squares), bandshapes (triangles) and selective inversions (circles). The line is a linear regression to the data. The slope of the line is A H IR, and the intercept at 1/J = 0 is A S IR, where R is the gas constant. A and A are the enthalpy and entropy of activation, according to equation (B2.4.1)...

Here G is the free energy and AG the change in free energy during the reaction. R the gas constant and T the absolute temperature. 

Having detemiined A b and knowing that the gas constant R = 8.314JK from macroscopic measurements on gases, determine Avogadro s number L from the relationship... 

Calculate the % difference between L found by this method and the modem value of 6.022 X 10. Does this support the idea that the Boltzmann constant is the gas constant per particle ... 

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