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CHE 324: FINAL EXAMINATION
1. Show that jA + jB = 0 for a binary system consisting of species A and B; where j denotes the diffusive mass flux. (12 points)
2. In leaching substance A from solid particles by a solvent B, the rate controlling step is the diffusion of A from the particle surface through a stagnant liquid film (B) of thickness δ out into the main stream (as shown in the below figure). The molar solubility of A in B is xA0 and the concentration in the main stream is xAδ. Assume that DAB is constant, and that A is only slightly soluble in B. Neglect the curvature of the particle.
Write down the postulate for this case and obtain (i) the steady state concentration profile for species A (in terms of xA) (ii) sketch the concentration profile and (iii) obtain the molar flux at z = 0 using the Equation of Continuity for Species A (Appendix B.11). (26 points)
3. A solid sphere (radius R) of substance A is suspended in a liquid B in which it is slightly soluble, and with which it undergoes a first-order chemical reaction with rate constant k1‴. Write down the postulate for this case and perform a shell mass balance to obtain the differential equation for concentration of A. Assume R is a constant and steady state conditions. The molar solubility of A in B is CA0.
Note: Do not solve for the concentration profile. (14 points)
4. Estimate the diffusivity of acetic acid in a dilute solution of acetone at 313 K using the Wilke Chang equation. The viscosity at this temperature is 0.264 cp. The molecular weight of acetic acid is 60.05 g/mol and density is 1.05 g/cm3. The molecular weight of acetone is 58.08 g/mol. The dimensionless “association parameter” for acetone is 1. (10 points)
5. Consider the flow of an incompressible Newtonian fluid between parallel plates of length L and width W. The top plate (at x = b) moves in the positive z direction with speed v and the bottom plate (at x = 0) remains at rest. There is no pressure gradient, so the fluid moves as a result of the motion of the top plate. The velocity profile for this system is given as:
In addition, in this set-up, the bottom plate is maintained at a temperature of T0 and the heat flux (qx) at x = b is 0. As the plate moves, the friction between adjacent layers of the fluid produces heat and hence the viscous dissipation cannot be neglected.
(i) Draw a schematic of the set-up with an appropriate coordinate system and write down the postulates.
(ii) Using the equation of energy (Appendix B.9), obtain an expression for the steady state temperature profile and show that it is given by:
(28 points)
6. ANewtonian liquid (density = 955 kg/m3) is flowing in a circular tube of length 50 cm and radius 0.75 mm. The pressure drop in the tube (in terms of modified pressure) is 490 kPa and the mass flow rate through the tube is 3 × 10-3 kg/s. Find the viscosity of the liquid.
Note: The appropriate equation for this problem can be used directly. (10 points)