Kinetics of H2 and O2 Explosion reaction - thermal decomposition of N2O5 - H2 and Br2 chain reaction and thermal decomposition of acetaldehyde

1. KINETICS OF THERMOCHEMICAL CHAIN
REACTIONS
Dr.P.GOVINDARAJ
Associate Professor & Head , Department of Chemistry
SAIVA BHANU KSHATRIYA COLLEGE
ARUPPUKOTTAI - 626101
Virudhunagar District, Tamil Nadu, India

2. Kinetics of Explosion Reaction
2H2 + O2 2H2O
Explosion reactions are the chain reactions in which the rate of one (or) more
steps increases suddenly in a very short period of time by means of chain branching
steps leading to explosion.
Explosion reactions
Example
The best example for explosion reaction is

3. Mechanism
i) Chain initiation
H2 2H
O2 2O
ii) Chain Branching
O2 + H OH + O
H2 + O OH + H
k0
k2
k3
iii) Chain Propagation
H2 + OH H2O + H
k1
Kinetics of Explosion Reaction
k0
iii) Chain termination
H + Wall ½ H2
H + O2 + M HO2 + M
k4
k5

4. Kinetics of Explosion Reaction
• Since OH and O radicals are rapidly consumed , the principal chain carrier is H atom, so that
the rate equation for the free-radical density n* is taken to be the same as that for [H] atoms.
i.e., 𝑑𝑛
∗
𝑑𝑡
=
𝑑[𝐻]
𝑑𝑡
--------(1)
= k0[H2] + k1 [H2][OH] + k3 [H2][O] – k2 [O2][H] – k4 [H] – k5 [H][O2][M]
--------(2)
• Since [O] and [OH] are lower than [H] , we can assume that [O] and [OH] are at steady-state
𝑑[𝑂𝐻]
𝑑𝑡
= k2 [O2][H] + k3 [H2][O] - k1 [H2][OH] = 0 ---------(3)
𝑑[𝑂]
𝑑𝑡
= k0[O2] + k2 [O2][H] - k3 [H2][O] = 0 ---------(4)
i.e., rate of formation of O radicals = rate of disappearance of O radicals
rate of formation of H radicals = rate of disappearance of H radicals

5. Kinetics of Explosion Reaction
• Rearranging equation (3) and (4) gives [OH] and [O]
[OH] =
k2 [O2][H] + k3 [H2][O]
k1 [H2]
---------(5)
[O] =
k0[O2] + k2 [O2][H]
k3 [H2]
---------(6)
• Substituting for [O] (i.e., equation 6 ) in equation 5 we get
[OH] =
2k2 [O2][H] + k0 [O2]
k1 [H2]
---------(7)
• Substitute equation (6) and (7) in (1) we get
𝑑𝑛
∗
𝑑𝑡
= k0[H2] + k1[H2]
2k2 [O2][H] + k0 [O2]
k1 [H2]
+ k3 [H2]
k0[O2] + k2 [O2][H]
k3 [H2]
- k2 [O2][H] −k4 [H] – k5 [H][O2][M]

6. Kinetics of Explosion Reaction
𝑑𝑛
∗
𝑑𝑡
= k0 ([H2] + 2[O2]) + 2k2 [O2] − (k4 + k5 [O2][M]) [H] --------(8)
Put
k0 ([H2] + 2[O2]) = W0
2k2 [O2] = f
(k4 + k5 [O2][M]) = g
[H] = n*
in equation (8), we get
𝑑𝑛
∗
𝑑𝑡
= W0 + (f - g) n* ---------(9)
Where
f = chain branching
g = chain termination

7. Kinetics of Explosion Reaction
• There are two possible conditions
1. g > f :
Termination exceeds branching so that O2 pressure is low and n* increases
linearly and reaches a steady state value. i.e., there is no explosion.
2. g < f :
Branching exceeds termination so that O2 pressure is high, the free- radical
concentration increases exponentially and the reaction velocity increases rapidly.
This is termed as an explosion.

8. Kinetics of Explosion Reaction
• The explosion boundary for the H2 – O2 reaction is the function of temperature and
pressure shown in the diagram

9. Kinetics of Explosion Reaction
Region I : The reaction is wall - recombination limited and proceeds to a steady - state
Region II : f begins to exceeds g, the branched chain reaction takes over and explosion
takes place
Region III : As the pressure is further increased, the explosion is quenched and another
regime of steady-state is encountered. Here kinetics are dominated by relatively
unreacted HO2 radicals.
At a still high pressure, the amount of heat liberated in the exothermic
steps of the mechanism becomes larger and can be conducted by thermal
transport processes so that the temperature rises. As a result, increases the
rates of initiation and provides heat for endothermic chain – branching
reactions leading to more heat release, resulting in a thermal explosion
Region IV :

10. Kinetics of Explosion Reaction
• Experimentally observed (P-T) boundaries of H2 – O2 reaction in a closed vessel is
shown below

11. Kinetics of thermal decomposition of Nitrogen pentoxide
2N2O5 2N2O4 + O2
The decomposition of nitrogen pentoxide is
Mechanism
Chain initiation
Chain propagation
Chain termination
--------(2)
N2O5 NO2 + NO3
NO2 + NO3 NO2 + O2 + NO
NO + N2O5 3NO2
NO2 + NO3 N2O5
--------(1)
--------(3)
--------(4)
k1
k2
k3
k-1

12. Kinetics of thermal decomposition of Nitrogen pentoxide
• The intermediates NO3 and NO are present in smaller amounts. So that steady-state concept
is applied on NO3 and NO, we get
• NO2 and NO3 react together in two different ways, to give NO2, O2 and NO in
reaction (2) and also to give N2O5 in reaction (4)
𝑑[𝑁𝑂3]
𝑑𝑡
= 0
k1[N2O5] = k2 [NO2][NO3] + k-1 [NO2][NO3]
i.e., rate of formation of NO3 = rate of disappearance of NO3
k1[N2O5] - k2 [NO2][NO3] - k-1 [NO2][NO3] = 0
k1[N2O5] – (k2 + k-1) [NO2][NO3] = 0 --------(5)

13. Kinetics of thermal decomposition of Nitrogen pentoxide
i.e., rate of formation of NO = rate of disappearance of NO
k2 [NO2][NO3] = k3 [NO][N2O5]
k2 [NO2][NO3] – k3 [NO][N2O5] = 0 --------(6)
• The rate of decomposition of N2O5 is
−
𝑑[𝑁2 𝑂5]
𝑑𝑡
= k1[N2O5] + k3 [NO][N2O5] - k-1 [NO2][NO3] --------(7)
• On rearranging the equation (6), we get
k3 [NO][N2O5] = k2 [NO2][NO3]
k2 [NO2][NO3] = k3 [NO][N2O5]
[NO] =
k2 [NO2][NO3]
k3 [N2O5]
--------(8)
and also
𝑑[𝑁𝑂]
𝑑𝑡
= 0

14. Kinetics of thermal decomposition of Nitrogen pentoxide
• Substitute equation (8) in (7), we get
−
𝑑[𝑁2
𝑂5
]
𝑑𝑡
= k1[N2O5] + k2 [NO2][NO3] - k-1 [NO2][NO3]
−
𝑑[𝑁2
𝑂5
]
𝑑𝑡
= k1[N2O5] + (k2 - k-1 )[NO2][NO3] --------(9)
• On rearranging equation (5) we get
k1[N2O5] = (k2 - k-1 )[NO2][NO3]
(k2 + k-1 )[NO2][NO3] = k1[N2O5]
[NO2][NO3] =
k1[N2O5]
(k2 + k −1 )
--------(10)
• Substitute equation (10) in (9), we get
−
𝑑[𝑁2
𝑂5
]
𝑑𝑡
= k1[N2O5] +
(k2 − k −1 ) k1[NO2][NO3]
(k2 + k −1 )

15. Kinetics of thermal decomposition of Nitrogen pentoxide
−
𝑑[𝑁2
𝑂5
]
𝑑𝑡
= k1[N2O5] 1+
k2 − k −1
(k2 + k −1)
−
𝑑[𝑁2 𝑂5]
𝑑𝑡
= k1[N2O5]
k2 + k−1+k2 − k −1
(k2 + k −1)
−
𝑑[𝑁2
𝑂5
]
𝑑𝑡
=
k1[N2O5] 2k2
(k2 + k −1)
−
𝑑[𝑁2
𝑂5
]
𝑑𝑡
=
2k1k2[N2O5]
(k2 + k −1 )
--------(11)
• Since the rate constant k2 is very small compared to k -1 and it is neglected in the denominator
of equation (11), we get
−
𝑑[𝑁2
𝑂5
]
𝑑𝑡
=
2k1k2[N2O5]
k −1
--------(12)
• This is the rate equation for the decomposition of N2O5 and this reaction follows first
order kinetics

16. Kinetics of thermal reaction between Hydrogen and Bromine
Mechanism
H2 + Br2 2HBr
The thermal reaction between H2 and Br2 is
Chain initiation
Chain propagation
Chain inhibition
Br2 2Br --------(1)
Br + H2 HBr + H ---------(2)
H + Br2 HBr + Br ---------(3)
H + HBr Br + H2 ---------(4)
k1
k2
k3
k-2
Chain termination
2Br Br2 ---------(5)
k-1

17. Kinetics of thermal reaction between Hydrogen and Bromine
rate = -
𝑑[𝐻2
]
𝑑𝑡
= vt = k2[Br][H2] – k-2 [H][HBr]
• The rate of reaction is the rate of consumption of H2 , which is
• An additional reaction (4) accounts for the inhibition of the reaction by the product HBr
i.e., vt = k2[Br][H2] – k-2 [H][HBr] ---------(6)
• Since the intermediate Br and H are present at very low concentrations, the steady- state
concept can be applied to H and Br, we get
𝑑[𝐻]
𝑑𝑡
= 0
i.e., rate of formation of H = rate of disappearance of H
k2[Br][H2] = k3[H][Br2] + k-2 [H][HBr]
k2[Br][H2] - k3[H][Br2] - k-2 [H][HBr] = 0 --------(7)

18. Kinetics of thermal reaction between Hydrogen and Bromine
and also,
𝑑[𝐵𝑟]
𝑑𝑡
= 0
i.e., rate of formation of Br = rate of disappearance of Br
k1[Br2] + k3[H][Br2] + k-2 [H][HBr] = k2[Br][H2] + k-1[Br][Br]
k1[Br2] + k3[H][Br2] + k-2 [H][HBr] - k2[Br][H2] - k-1[Br][Br] = 0 --------(8)
k2[Br][H2] - k3[H][Br2] - k-2 [H][HBr] + k1[Br2] + k3[H][Br2] + k-2 [H][HBr]
- k2[Br][H2] - k-1[Br][Br] = 0
• On addition equation (7) and (8) , we get
k1[Br2] - k-1[Br]2 = 0
k1[Br2] = k-1[Br]2
k-1[Br]2 = k1[Br2]
[Br]2 =
k1
k −1
[Br2]

19. Kinetics of thermal reaction between Hydrogen and Bromine
[Br] =
k1
k −1
½
[Br2]½ --------(9)
• On substituting equation (9) in equation (7) , we get
k2
k1
k −1
½
[Br2]½[H2] - k3[H][Br2] - k-2 [H][HBr] = 0
k2
k1
k −1
½
[Br2]½[H2] = k3[H][Br2] + k-2 [H][HBr]
k3[H][Br2] + k-2 [H][HBr] = k2
k1
k −1
½
[Br2]½[H2]
[H]{k3[Br2] + k-2[HBr]} = k2
k1
k −1
½
[Br2]½[H2]
[H] =
k2 (k1/k −1)½[Br2]½[H2]
k3[Br2] + k −2[HBr]
--------(10)

20. Kinetics of thermal reaction between Hydrogen and Bromine
• Substitute equation (6) in equation (7), we get ,
vt = k3[H][Br2] ---------(11)
vt - k3[H][Br2] = 0
• Substitute equation (10) in equation (11), we get
vt =
k3k2 (k1/k −1)½[Br2]½[H2][Br2]
k3[Br2] + k−2[HBr]
vt =
k3k2 (k1/k −1)½[Br2]3/2 [H2]
k3[Br2] + k −2[HBr]
---------(12)
• Divide both numerator and denominator of equation (12) by k3[Br2] , we get
vt =
k2 (k1/k −1)½[Br2]1/2 [H2]
1 + (k −2 /k3 ) {[HBr]/[Br2]}
---------(13)
• Equation (12) and (13) are the rate equation for thermal reaction between H2 and Br2 and
the reaction was found to be fractional order.

21. Kinetics of thermal decomposition of Acetaldehyde
CH3CHO CH4 + CO
Mechanism
i) Chain initiation step
CH3CHO CH3 + CHO
ii) Chain Propagation steps
CH3 + CH3CHO CH4 + CH3CO
CH3CO CH3 + CO
k1
k2
k3
iii) Chain termination step
CH3 + CH3 C2H6
k4
The radical CHO undergoes further reactions, but for simplicity they are ignored here
The Thermal decomposition of Acetaldehyde is

22. i.e., rate of formation of methyl radical = rate of disappearance of methyl radical
𝑑[𝐶𝐻4
]
𝑑𝑡
= k2[CH3][CH3CHO] ------(1)
• Applying steady state approximation on methyl radicals
The rate of formation of Methane is
k1[CH3CHO] + k3[CH3CO] = k2[CH3][CH3CHO] + k4[CH3][CH3]
k1[CH3CHO] + k3[CH3CO] - k2[CH3][CH3CHO] - k4[CH3][CH3] = 0 ------(2)
Kinetics of thermal decomposition of Acetaldehyde

23. • Applying steady state approximation on CH3CO radicals
i.e., rate of formation of CH3CO = rate of disappearance of CH3CO
k2[CH3][CH3CHO] = k3[CH3CO]
k2[CH3][CH3CHO] - k3[CH3CO]= 0 ------(3)
• Adding equation (2) and (3) we get the concentration of methyl radicals
k1[CH3CHO] + k3[CH3CO] - k2[CH3][CH3CHO] - k4[CH3][CH3] + k2[CH3][CH3CHO] -
k3[CH3CO] = 0
k1[CH3CHO] - k4[CH3]2 = 0
k1[CH3CHO] = k4[CH3]2
Kinetics of thermal decomposition of Acetaldehyde

24. k1[CH3CHO] = k4[CH3]2
[CH3]2 =
k1
k4
[CH3CHO]
k4[CH3]2 = k1[CH3CHO]
[CH3] =
k1
k4
1/2
[CH3CHO]1/2
-------(4)
• Substitute (4) in (1) we get
𝑑[𝐶𝐻4]
𝑑𝑡
= k2
k1
k4
1/2
[CH3CHO]1/2 [CH3CHO]
𝑑[𝐶𝐻4]
𝑑𝑡
= k2
k1
k4
1/2
[CH3CHO]3/2
• This is the rate equation for thermal decomposition of CH3CHO and the
overall order of this reaction is 3/2
Kinetics of thermal decomposition of Acetaldehyde