CALCULATING VAPOR AND LIQUID COMPOSITIONS IN IDEAL MIXTURES.pptx

CALCULATING VAPOR AND LIQUID COMPOSITIONS IN IDEAL MIXTURES

1. CALCULATING VAPOR AND LIQUID COMPOSITIONS IN IDEAL MIXTURES

2. A vapor-liquid system is considered to be in equilibrium when there are no longer any detectable changes occurring in the system. Generally, a system is assumed to be in equilibrium when the mass, energy, and composition of each phase remain constant with time. An example of a system in equilibrium is a mixture of water and air in a closed vessel. After some time, there will be no change in temperature, in the amount of water in the vapor phase, or in the number of gas molecules dissolved in the water. The system is in equilibrium. Equilibrium also applies to systems that are not static. We may have equilibrium in an overhead condenser separator of a distillation column. The vapor and liquid leaving the separator are in equilibrium, and their compositions can be described by relationships for systems in equilibrium.

3. Ideal and Nonideal Gases Ideal gases are those whose behavior can be described by the ideal gas law, which is stated mathematically as: PV = nRT or PV / nRT = 1.0 The ideal gas law indicates that the product of pressure P times volume V is proportional to the number of molecules of the component, n, times the absolute temperature T. R is an ideal gas proportionality constant. The values of R in various units are given in Work Aid 1. Gases tend to behave as ideal gases at temperatures higher than their critical temperature and pressures well below their critical pressure.

4. Real-Gas Equations If the ideal gas equation is applied to situations with elevated pressures, significant errors may result. Deviations from the ideal gas law at high pressure can be attributed to the assumptions inherent in the law's derivation, namely, that all molecules are hard spheres that do not interact with one another and that occupy negligible volume. Therefore, the ideal gas law is independent of the composition of the gas. For example, the ideal gas law implies that one mole of any gas will occupy the same volume as one mole of any other gas at the same temperature and pressure. In this sense, it implies that all gases are identical on a molar basis. This assumption is not correct because different gases have radically different molecular and chemical structures. As an example, take the specific volumes of hydrogen sulfide, propane, and nitrogen at 400 psia and 180_F. From the ideal gas law and n = 1, V = RT/P = [10.73 psia-ft3/lb-mole-°R x (180 + 460)°R]/400 psia = 17.17 ft3/lb-mole

5. The experimental molar volumes for these three gases are as follows: Component Molar Volume Propane 11.44 ft3/lb-mole Hydrogen sulfide 16.28 ft3/lb-mole Nitrogen 16.82 ft3/lb-mole Thus, although the ideal gas law provides a qualitative measure of the behavior of gases, it does not predict PVT behavior accurately for most gases and cannot be used for liquids. The compressibility factor Z expresses the deviation from the ideal gas equation. It can be used to predict real gas properties. The compressibility factor is the ratio of the real gas volume to that of the ideal gas at the same temperature and pressure: PV= ZnRT or PV nRT = Z For an ideal gas, the compressibility factor is 1.0. The compressibility factor Z can be obtained from generalized graphs such as those in Maxwell, pages 148-153 or the GPSA Engineering Data Book, Chapter 16.