Page 121 - Elements of Chemical Reaction Engineering 3rd Edition

Sec. 3.3 Stoichiometric Table 93

Equation of state PV = ZNTRT (3-30)

in which V and NT are defined as before and
T = temperature, K
P = total pressure, atm (kPa; 1 atm = 101.3 Wa)
2 = compressibility factor
R = gas constant = 0.08206 dm3 * atrdg mol K
This equation is valid at any point in the system at any time t. At time
t = 0 (i.e., when the reaction is initiated), Equation (3-30) becomes

Dividing Equation (3-30) by Equation (3-3 1) and rearranging yields

(3-32)

We now want to express the volume V as a function of the conversion X.
Recalling the equation for the total number of moles in Table 3-2,

we divide through by NTo :

NT
-- NAO l+sy,ox (3-34)
- 1+-8X=
NTO NTO
where y,, is the mole fraction of A initially present. If all the species in the
generalized reaction are in the gas phase, then
I 1
(3-23)

Equation (3-34) i,s further simplified by letting

E=- change in total number of moles for complete conversion
total number of moles fed to the reactor

Definitions of In symbols,
6andE

(3-35)
I E = YAO6 I (3-36)

Equation (3-32) naow becomes