Page 130 - Elements of Chemical Reaction Engineering 3rd Edition

1 02 Rate Laws and Stoichiometry Chap. 3

(c) Assuming the reaction is elementary, express the rate of reaction solely as a
function of conversion for a flow system and for a batch system.

Solution

A e
2B
At equilibrium the concentrations of the reacting species are related by the relation-
ship dictated by thermodynamics [see Equation (3-10) and Appendix C]

(E3-8.1)

(a) Batch system-constant volume, V = V, . See Table E3-8.1.

TABLE E3-8.1. STOICHIOMETRIC TABLE
Species Symbol Initial Change Remaining
N*O, A NAO -NAoX NA = NAo (1 - X)
NO* B 0 +2NA0X NB = 2NA0X
Nro = NAO NT = NTO + NAdr

1
For batch systems Ci = Ni V ,
(E3-8.2)

(E3-8.3)

YAOPO -
c,, = - atm)
-
RT, (0.082 atm . dm3/grnol' K)(340 K)
= 0.07174 mol/dm3
At equilibrium X = X, and we substitute Equations (E3-8.2) and (E3-8.3) into
Equation (E3-8.1),

(E3-8.4)

We will use POLYMATH to solve for the equilibrium conversion and let xeb repre-
sent the equilibrium conversion in a constant-volume batch reactor. Equation
(E3-8.4) written in POLYMATH format becomes