Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ...

3.2 Application of the steady-state assumption 45
3.2.2 Further examples
I
I
Exercise 3.1: The thermal decomposition of acetaldehyde according to the overall
reaction
CH 3 CHO → CH 4 +CO (3.31)
is known to proceed via the following elementary steps (Rice-Herzfeld mechanism):
CH 3 CHO → CH 3 +HCO (1)
CH 3 +CH 3 CHO → CH 4 +CH 3 CO (2)
(3.32)
CH 3 CO → CH 3 +CO (3)
CH 3 +CH 3 → C 2 H 6 (4)
Derive an expression for the production rate of [CH 4 ]. (Hint: Use the steady-state
approximations for [CH 3 CO] and [CH 3 ] and neglect the HCO for the derivation of the
expression.) ¤
A more complete mechanism takes into account the thermal decomposition of the HCO
radicals according to HCO → H + CO (5) followed by the reaction H + CH 3 CHO →
H 2 +CH 3 CO (6).
Solution 3.1: With the steady state approximations for [CH 3 CO] and [CH 3 ],weobtain
[CH 3 CO]
= 2 [CH 3 ][CH 3 CHO] − 3 [CH 3 CO] ≈ 0 (3.33)
y [CH 3 CO]
= 2 [CH 3 ][CH 3 CHO]
3
(3.34)
and
y
[CH 3 ]
= 1 [CH 3 CHO] − 2 [CH 3 ][CH 3 CHO] (3.35)
+ 3 [CH 3 CO] − 2 4 [CH 3 ] 2 (3.36)
= 1 [CH 3 CHO] − 2 [CH 3 ][CH 3 CHO] (3.37)
+ 3 2 [CH 3 ][CH 3 CHO]
− 2 4 [CH 3 ] 2
3
(3.38)
= 1 [CH 3 CHO] − 2 4 [CH 3 ] 2 ≈ 0 (3.39)
µ 12 1 [CH 3 CHO]
y [CH 3 ]
=
(3.40)
2 4
[CH 4 ]
[CH 4 ]
= 2 [CH 3 ][CH 3 CHO]
= 2
µ
1
2 4
[CH 3 CHO] 32 (3.41)
¥
I Exercise 3.2: The thermal decomposition of ethane gives mainly H 2 +C 2 H 4 . In
addition, small amounts of CH 4 are formed. The decay of the C 2 H 6 concentration can
be described by the reaction steps
C 2 H 6 → CH 3 +CH 3 (1)
CH 3 +C 2 H 6 → CH 4 +C 2 H 5 (2)
C 2 H 5 → C 2 H 4 +H (3)
(3.42)
H+C 2 H 6 → C 2 H 5 +H 2 (4)
H+C 2 H 5 → C 2 H 6 (5)