Reaction Eng

DEPARTMENT OF CHEMICAL ENGINEERING
Reaction Engineering
CGC035 / CGC052

Problem Sheet 3 - Fluid-fluid reactions

1. The reaction rate for the heterogeneous reaction A(g) + B(l)→ products is second order according to the expression -rA=kCACB and it is relatively slow compared to mass transfer so it takes place in the bulk of the liquid. Combine the following rate expressions for diffusion through the gas and liquid films, -rA=kAga(pA-pAi) and
-rA=kAlaCAi-CA, with Henry’s law pAi=HACAi and the reaction rate equation given above, to eliminate the pressure and concentration at the interface (pAi and CAi) and to prove that the final rate expression for the overall rate of the process is
-rA=pA1kAga+HAkAla+HAkCB

Solution
-rA=kAga(pA-pAi) (1) -rA=kAlaCAi-CA, (2) pAi=HACAi (3)
-rA=kCACB (4)

From (1) -rA=kAgapA-pAi=kAgapA-kAgapAi
-rA=kAgapA-kAgapAi=kAgapA-kAgaHACAi (5)
From (2) if we solve for CAi
-rA=kAlaCAi-kAlaCA and
CAi=-rA+kAlaCAkAla (6)
We substitute (6) in (5)
-rA=kAgapA-kAgaHACAi=kAgapA-kAgaHA-rA+kAlaCAkAla
-rA=kAgapA+rAkAgaHAkAla-kAgaHACA (7)

-rA-rAkAgaHAkAla=kAga(pA-HACA)
From (4)
-rA=kCACB→CA=-rAkCB (8)
We substitute (8) in (7)
-rA=kAgapA+rAkAgaHAkAla-kAgaHA-rAkCB
-rA=kAgapA+rAkAgaHAkAla+rAkAgaHAkCB

-rA-rAkAgaHAkAla-rAkAgaHAkCB=kAgapA
-rA1+kAgaHAkAla+kAgaHAkCB=kAgapA
-rAkAga1kAga+HAkAla+HAkCB=kAgapA
-rA1kAga+HAkAla+HAkCB=pA
-rA=pA1kAga+HAkAla+HAkCB

2. Combine the following relationships for mass transfer through the gas and liquid films with Henry’s law
NA=kAgpA-pAi, NA=KAgpA-pA*
NA=kAlCAi-CA, NA=KAlCA*-CA pAi=HACAi, pA=HACA*, pA*=HACA to show that the overall coefficient for mass transfer is given by the expression
1KAl=1HAkAg+1kAl

Solution

NA=KAlCA*-CA (1)

NA=KAlCA*-CA
NA=KAlCA*-CA

3. Consider the reaction A(g) + B(l) → products, described by the reaction rate equation -rA=kpACB. Sketch the pressure and concentration profiles for