Page 378 - Elements of Chemical Reaction Engineering Ebook

Sec. 7.2 Searching for a Mechanism 349

For a constant-volume batch reactor, the combined mole balances and rate laws for
disappearance of ethane (Pl) and the formation of ethylene (P5) are

1 /2
dC,, = -[ (3k1Cp,) + k3k] Ci?] (E7-2.13)
dt

(E7-2.lL4)

The P in P1 (is., Cpl) and P5 (Le., Cp5) is to remind us that we have used rhe
PSSH in arriving at these balances.
At 1000 K the specific reaction rates are k, = 1.5 X s-l, = 2.3 X 1106
dm3/niol-s, k3 = 5.71 X 104 s-l, k4 = 9.53 X lo8 dm3/mol.s, and k5 = 3.98 X IO9
dm3/~101.
S.
For an entering ethane concentration of 0.1 mol/dm3 and a temperature of
1000 IC, Equations (E7-2.13) and (E7-2.14) were solved and the concentrations of
ethane, Cpl, and ethylene, Cp3, are shown as a function of time in Figures E7-2.1
and E;!-2.2.
In developing the above concentration-time relationship, we used PSSH.
However, we can now utilize the techniques described in Chapter 6 to solve the full
set of equations for ethane cracking and then compare these results with the much
simpler PSSH solutions.

Part ob) Testing the PSSH for Ethane Cracking
The thermal cracking of ethane is believed to occur by the reaction sequence given
in Part (a). The specific reaction rates are given as a function of temperature:
s
, - 10e(s7,000/~)(i/nzso- i/qS-i k2 = 8-45 X 106e(13,000/R)(1/1z50-1/~dm3/mol.
'1 -
. - 3.2 x 106e(40,MM/R)(l/l250- l/T)s-1 k4 = 2-53 X 109e(97001R)(l/1250-1/T)dm3/mol.
'3 -
!j
r5 = 3.90 x 109 dm3/m01. s E=O
Part (b): Plot the concentrations of ethane and ethylene as a function of time and
compare with the PSSH concentration-time measurements. The initial concentration
of ethane is 0.1 n101/dm3 and the temperature is lo00 K.

Solutioirt Part (b)
kt 1 =' &J&, = CH3*,3 = CH4,4 = C2H5*, 5 = C2&, 6 = H*, 7 = H2, and
2
8 = C4H10. The combined mole balances and rate laws become