Page 172 - Modelling in Transport Phenomena A Conceptual Approach

152 CHAPTER 6. STEADY-STATE MACROSCOPIC BALANCES

Analysis

System: Contents of the reactor
Since the reactor volume is constant, the inlet and outlet volumetric flow rates are
the same and equal to &. Therefore, the inventory rate equation for conservation
of species B, Eq. (6.1-7), becomes

-
Q(cB)~~ QcB,,, - (~~cA,,,cB,,,)V~~~ = 0 (1)
where CA,,, and CB,,, represent the molar concentration of species A and B in the
reactor, respectively. Dropping the subscript “Sys and defining the residence time,
T, as T = V/& reduces Eq. (1) to

Using Eq. (5.3-17), the extent of the reaction can be calculated as

Therefore, the concentrations of species A and B in the reactor are

CA = (CA)in + QA e = 1 - 0.3 = 0.7mol/L
CB = (Cg)in + QB = 1 - (2)(0.3) = 0.4mol/L

Substitution of the numerical values into Eq. (3) gives
1 - 0.4
= (2) (0.025)(0.7) (0.4) = 42.9 min

6.2 CONSERVATION OF MASS

Summation of Eq. (6.1-2) over all species gives the total mass balance in the form

Note that the term
(6.2-2)