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

3.2 Application of the steady-state assumption 44
I Rates equations: With the steady state approximations (i.e., [X] ≈ 0) for[Br]
and [H], weobtain 23
[H]
[Br]
[HBr]
= + 2 [Br] [H 2 ] − 3 [H] [Br 2 ] − 4 [H] [HBr] ≈ 0 (3.16)
y 2 [Br] [H 2 ] − 4 [H] [HBr] = + 3 [H] [Br 2 ] (3.17)
2 [Br] [H 2 ]
y [H]
=
3 [Br 2 ]+ 4 [HBr]
(3.18)
(3.19)
= +2 1 [Br 2 ] − 2 [Br] [H 2 ]+ 3 [H] [Br 2 ]+ 4 [H] [HBr]
| {z }
=−
[H]
≈0
−2 5 [Br] 2 (3.20)
= +2 1 [Br 2 ] − 2 5 [Br] 2 ≈ 0 (3.21)
µ 12 1
y [Br]
= [Br 2 ]
(3.22)
5
µ 12 1
2 [H 2 ]
y [H]
= [Br 2 ] ×
(3.23)
5 3 [Br 2 ]+ 4 [HBr]
= 2 [Br] [H 2 ]+ 3 [H] [Br 2 ] − 4 [H] [HBr] (3.24)
Using 2 [Br] [H 2 ] − 4 [H] [HBr] = + 3 [H] [Br 2 ] (Eq. 3.17) and substituting [H]
(Eq.
3.18), the last line simplifies to
[HBr]
=2 3 [H] [Br 2 ] (3.25)
µ 12 1
2 [H 2 ]
=2 3 [Br 2 ] × [Br 2 ] ×
5 3 [Br 2 ]+ 4 [HBr]
(3.26)
= 2 2 ( 1 5 ) 12 [H 2 ][Br 2 ] 12
1+( 4 3 )[HBr] [Br 2 ]
(3.27)
=
0 [H 2 ][Br 2 ] 12
1+ 00 [HBr] [Br 2 ]
(3.28)
I
Result:
with
[HBr]
= 0 [H 2 ][Br 2 ] 12
1+ 00 [HBr] [Br 2 ]
(3.29)
0 =2 2 ( 1 5 ) 12 and 00 = 4 3 (3.30)
I Conclusion: We see that HBr acts as an inhibitor of the total reaction.
23 For the photolysis induced reaction, 1 has to be replaced by 0 1 ,where is the light intensity and
0 1
the corresponding photolysis rate constants (related to the absorption coefficient).