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

9.2 Heat explosions 209
I
Conclusions:
• The quantity that determines whether the system is stable or not is the wall
temperature 0 ,because 0 determines the initial point of the heat removal line.
• Smaller surface-to-volume ratio is dangerous, because smaller surface at a given
volume leads to a smaller slope of the heat removal line y instability!
• Security measure: internal cooling system (cold water pipes, heat exchanger).
• Emergency measure: when cooling system fails, the reaction mixture should be
strongly diluted by addition of solvent immediately!
I Quantitative estimation of the stability limits:* At point (4) in Fig. 9.4, we have:
=
(9.27)
y ( − 0 )= ∆ ª 0 − (9.28)
=
(9.29)
y = ∆ ª 0 −
2 (9.30)
Eq
Eq y 2
=( − 0 ) (9.31)
y 2 −
+
y =
2 ± s µ
2
0 =0 (9.32)
2
−
0 (9.33)
Solution is: ⎧
⎪⎨
= 1 ³
+ p ´ ⎫
( 2 2
− 4 0 )
⎪⎬
⎪ ⎩ = 1 ³
− p ´
( 2 2
− 4 0 )
⎪⎭
This can be simplified:
(9.34)
(1) For practically important reactions, we have:
À 0 y 0 ¿
(9.35)
(2) We also can exclude unreasonably hight temperatures y only the −-sign before
∗ s
= µ 2
2 − −
2 0 (9.36)
=
2 − r
1 − 4 0
(9.37)
2
√ counts: y
=
2
à r
1 −
!
1 − 4 0
(9.38)