Question

For mixed flow of particles containing a single unchanging size and uniform gas composition, the fraction unconverted for chemical reaction controlling is ____

(a) \(\int_0^τ\)(1-\(\frac{t}{τ}\))^3\(\frac{e}{t}^\frac{-t}{t}\) dt

(b) \(\int_0^τ\)(1-\(\frac{t}{τ}\))^2\(\frac{e}{t}^\frac{-t}{t}\) dt

(c) \(\int_0^τ\)(1-\(\frac{t}{τ}\))\(\frac{e}{t}^\frac{-t}{t}\) dt

(d) \(\int_0^τ\)(1-\(\frac{t}{τ}\))^0.5\(\frac{e}{t}^\frac{-t}{t}\) dt

The question was posed to me in class test.

My question is from Design of Fluid Particle Reactors in division Fluid-Particle Reactions: Kinetics of Chemical Reaction Engineering

Answer 1

The correct choice is (a) \(\int_0^τ\)(1-\(\frac{t}{τ}\))^3\(\frac{e}{t}^\frac{-t}{t}\) dt

Best explanation: For chemical reaction controlling, \(\frac{t}{τ}\) = 1-(1- XB)\(^\frac{1}{3}\). Hence, 1-\(\overline{X_{(B)}}\) = ∫0^τ(1-\(\frac{t}{τ}\))^3\(\frac{e}{t}^\frac{-t}{t}\) dt.