Page 161 - Modelling in Transport Phenomena A Conceptual Approach

5.3. RATE OF GENERATION IN MASS TRANSPORT 141

On the other hand, molar extent is unique for a given reaction. Comparison of
Eqs. (5.3-10) and (5.3-11) indicates that

(5.3- 12)

The total number of moles, nT, of a reacting mixture at any instant can be
calculated by the summation of Eq. (5.3-10) over all species, i.e.,

nT = nTo + &E (5.3- 13)
where nTo is the initial total number of moles and CY = Ci ai.

Example 5.2 A system containing 1 mol AI, 2 mol A2 and 7 mol A3 undergoes
the following reaction
Al(9) + A2(9) + 3/2A3(9) + A4(9) + 3A5(9)
Determine the limiting reactant and fractional conversion with respect to each re-
actant if the reaction goes to completion.
Solution
Since ni 2 0, it is possible to conclude from Eq. (5.3-10) that the limiting reactant
has the least positive value of nio/(- ai). The values given in the following table
indicate that the limiting reactant is AI.

Species nio /(- ai)
A1 1
A2 2
A3 4.67

Note that the least positive value of nio/(- ai) is also the greatest possible vdue
of E. Since the reaction goes to completion, species A1 will be completely depleted
and E = 1. Using Eq. (5.3-12), fractional conversion values are given as follows:

Species X
A1 1
A2 0.50
A3 0.21

Example 5.3 A system containing 3 mol A1 and 4 mol A2 undergoes the fol-
lowing reaction
2Ai(g) +3A2(9) -+A3(9)+2A4(9)
Calculate the mole fractions of each species if E = 1.1. What is the fractional
conversion based on the limiting reactant 7