- 5 A Semi Infinite Medium Of Material B Extends From The Plane Boundary X 0 To X 00 At Time T 0 Substance A Is Br 1 (35.34 KiB) Viewed 12 times
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5. A semi-infinite medium of material B extends from the plane boundary x = 0 to x = 00. At time t = 0 substance A is brought into contact with this medium at the plane x = 0, the surface concentration being C20. Substances A and B react to produce C according to the irreversible first-order reaction A + B = C. It is assumed that A is present in such a small concentration that the equation describing the diffusion plus chemical reaction process is OCA CA - kica A =D AB at ox²
In which ki is the first-order rate constant. This equation has been solved for the initial condition that ca = 0 at t 0, and the boundary conditions that CA = C40 at x = 0, and cA = 0 at x = 0. The solution is = X CA 1 = exp 2 x de cop van herid Mubar Verticale are your kıx? D kyr? ✓kt exp erfd + Skyt с 40 4D ABI DAB AB a) Verify that the previous equation satisfies the differential equation and the boundary conditions. b) Show that the molar flux at the interface x = 0 is Nax=0 exp(- kt) | erfſtyt) + C AVDARK ſocket c) Show further that the total moles absorbed across area A up to time t is 1 MA = AC 40 VDA = = kat + erlyJ67)+ ABT exp(- kyt) Vi 2. kat d) Show that, for large values of kıt, the expression in part c reduces asymptotically to 1 = MA= AC 40VDABkn + + 2ki