Page 377 - Elements of Chemical Reaction Engineering Ebook

348 Nonelementary Reaction Kinetics Chap. 7

Given the following reaction sequence:
For the active intermediates: CH3 , C2 H, , H the net rates of reaction are
-
rc,H,m - r2c2n5- f r3c2n5. + r4c2u5. + r5c2 H~. = 0
-
_- '2C2H6- r3C2H4- r4C2H6+ r5C2H5. = 0 (E7-2.2)
rH. = '3'3 H4 + )"4C2H6 = (E7-2.3)
'CH3. = -2rlC2H6 + r2C2H6 = (E7-2.4)
Substituting the rate laws into Equation (E7-2.4) gives

Zk1 iCZ H6i - k2 LCH3 I[c2 H6i = 0 (E7-2.5)
2k
[CH3*] = I (E7-2.6)
k2
Adding Equations (E7-2.2) and (E7-2.3) yields

-'2C2H6 ' r5C2H5- =
k2 [CH3* ] [C, H6] - k5 [C2 H5* I2 = 0 (E7-2.7)
Solving for [ C2 H, ] gives us

(E7-2.8)

I Substituting for C2H,* in Equation (E7-2.1) yields

Substituting the rate laws in Equation (E7-2.3), we find that
k,[C2H5* l-k4 [H* I[C2H61 = 0
Using Equation (E7-2.8) to substitute for C2H, gives

112
[He ] = 5 p) [C2H6J-1/2 (E7-2.11)
k4 k,
The rate of disappearance of ethane now becomes

(E7-2.12)