Universal gas constant The combined

Thus, if the saturated vapor pressure is known at the azeotropic composition, the activity coefficient can be calculated. If the composition of the azeotrope is known, then the compositions and activity of the coefficients at the azeotrope can be substituted into the Wilson equation to determine the interaction parameters. For the 2-propanol-water system, the azeotropic composition of 2-propanol can be assumed to be at a mole fraction of 0.69 and temperature of 353.4 K at 1 atm. By combining Equation 4.93 with the Wilson equation for a binary system, set up two simultaneous equations and solve Au and A21. Vapor pressure data can be taken from Table 4.11 and the universal gas constant can be taken to be 8.3145 kJ-kmol 1-K 1. Then, using the values of molar volume in Table 4.12, calculate the interaction parameters for the Wilson equation and compare with the values in Table 4.12. 

The ideal gas equation combines the variables of temperature, pressure and volume that we have been dealing with in the previous sections, but also allows us to calculate the mass in either grammes or moles and also an approximate molar mass for the particular gas. The previous gas laws involved an unknown constant that we eliminated from the calculation by taking temperatures, etc, at two different levels. In the ideal gas equation, we are introduced to the universal gas constant, R, which enables us to do the measurements under one set of conditions only. The difficulty arising from this is that the units of the gas constant are dependent on the units in which the other variables are measured, so it is important to think about the units you are working in. A selection of values for R using different units is listed in Table 4.5.3. 

Find the value for the universal gas constant R for the following combinations of units ... 

Equipment design procedures for separation operations require phase enthalpies and densities in addition to phase equilibrium ratios. Classical thermodynamics provides a means for obtaining all these quantities in a consistent manner from P-v-T relationships, which are usually referred to as equations of state. Although a large number of P-v-T equations have been proposed, relatively few are suitable for practical design calculations. Table 4.2 lists some of these. All the equations in Table 4.2 involve the universal gas constant R and, in all cases except two, other constants that are unique to a particular species. All equations of state can be applied to mixtures by means of mixing rules for combining pure species constants. 

As the osmotic pressure is a colligative property it is directly proportional to the molar concentration of the solute if the temperature remains constant thus tt is proportional to the concentration nIV, where n is the number of moles of solute, and V the solvent volume. The osmotic pressure is also proportional to the absolute temperature. Combining these two proportionalities gives JtV = nCT, which has the same form as the gas equation, PV = nRT, and experimental values of C are similar to those for R, the universal gas constant. This gives considerable support to the kinetic theory of colligative properties. 

These three laws can be combined into the ideal gas law, PV = nRT, where R is called the universal gas constant. This equation makes it possible to calculate any one of the properties—volume, pressure, temperature, or moles of gas present—given the other three. A gas that obeys this equation is said to behave ideally. 

Equation of state (EOS) n. For an ideal gas, if the pressure and temperature are constant, the volume of of the gas depends on the mass, or amount of gas. Then, a single property called the gas density (ratio of mass/volume). If the mass and temperature are held constant, the product of pressure and volume are observed to be nearly constant for a real gas. The product of pressure and volume is exactly for an ideal gas. This relationship between pressure and volume is called Boyle s Law. Finally, if the mass and pressure are held constant, the volume is directly proportional to the temperature for an ideal gas. This relationship is called Charles and Gay-Lussac s law. The gas laws of Boyle and Charles and Gay-Lussac can be combined into a single equation of state PV = nRT, where P is pressure, V volume, Tabsolute temperature, n number of moles and R is the universal gas constant. Ane-rodynamicists us a different form of the equation of state that is specialized of air. Regarding polymers and monomers, equation of state is an equation giving the specific volume (v) of a polymer from the known temperature and pressure and, sometimes, from its morphological form. An early example is the modified Van der Waals form, successfully tested on amorphous and molten polymers. The equation is ... 

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