Question

QUESTION 1 The binary gaseous diffusion coefficients of air in methyl chloride CH;Cl at 298 K and 1 atm have been determined. A simple diffusion cell was used, in which concentration changes of the diffusing gas were followed by infrared spectro- photometre. The diffusion coefficient DAB value measured is 1.434 x10 m2/s a) State two assumption of kinetic gas theory (4 Marks) b) Determine the diffusion coefficient, DAB using Chapman Enskog calculated by a kinetic theory equation using the Lennard-Jones 6-12 potential function. (17 Marks) c) Find the error difference between calculated and experimental valuc of DAB. (3 Marks) d) Solubility is the maximum amount of solute that can dissolve in a certain amount of solvent or solution at a certain temperature. How can a chemical engineer increase the mass transfer property which is solubility of a gas above a surlace of a solution through manipulation of process variables? Explain two of the relevant variables. (6 Marks)

Answer 1

a) Two assumptions of Kinetic theory of gases are (i) The gas is composed of a large number of identical molecules moving in random directions separated by distances that are large compared with their size (ii) the molecules undergo perfectly elastic collisions (no energy loss) with each other and with the walls of the container, but otherwise do not interact. b) The Chapman-Enskog equation is given by 0.5 1.858*10*T15*+ MA M AB AB Here T- absolute temperature in K MA, Mg molecular weights of the components A and B P-total pressure in atm ƠAB-a characteristic length parameter of the binary, in Angstrom ΩD collision integral which is a function of kTeAB (where k is Boltzmann's constant and ea is another characteristic binary parameter (CA1%) and εΑΒ is calculated by ε'[eAEg] 05 U potential parameters for various compounds

E/ (K-78 140 001 47 210 002 360 013 $15 34 59 201 454 C- HHHNO HHS Ai C C C C C 7067 .0 9 4 3 3 0 1 3 e/ (K-10 012 350 48 24 300 200 ssi 999 $25 48 800 sse 71 35 25434444553223 eCHH EHHNNS

Fiom the table 3·ア11 印· 182 340 2 5. 350 (340-2- 58).. k345. 0 b 298 0.863 e- 345- 0 3 944 65 2. chapman Ens koa Dn 0 3.94 65、0.763 2. 22r x 106

d) The effects of pressure on the solubility of gases in liquids can best be described through a combination of Henry's law and Le Châtelier principle. Henry's law dictates that when temperature is constant, the solubility of the gas corresponds to its partial pressure. Consider the following formula of Henry's law: p-k,C where: p is the partial pressure of the gas above the liquid, kh is Henry's law constant, and C is the concentrate of the gas in the liquid. . · This formula indicates that (at a constant temperature) when the partial pressure decreases, the concentration of gas in the liquid decreases as well, and consequently the solubility also decreases. Conversely, when the partial pressure increases in such a situation, the concentration of gas in the liquid will increase as well; the solubility also increases. Extending the implications from Henry's law, the usefulness of Le Châtelier's principle is enhanced in predicting the effects of pressure on the solubility of gases Consider a system consisting of a gas that is partially dissolved in liquid. An increase in pressure would result in greater partial pressure (because the gas is being further compressed). This increased partial pressure means that more gas particles will enter the liquid (there is therefore less gas above the liquid so the partial pressure decreases) in order to alleviate the stress created by the increase in pressure, resulting in greater solubility. The converse case in such a system is also true, as a decrease in pressure equates to more gas particles escaping the liquid to compensate