Untitled - Aerobib - Universidad Politécnica de Madrid

182 CHAPTER 6. LAMINAR FLAMES
From (6.182) and (6.179) the following expressions may be deduced for mole
fractions X 5 of NH 2 and X 6 of N 2 H 3 :
X 5 = 2k 1 + k 4 cX 7
, (6.185)
k 2 c
X 6 = 2k 1 + k 4 cX 7
k 3
X 1 . (6.186)
If the values for X 7 and X 5 given by (6.184) and (6.185) are substituted into
the hydrazine reaction velocity given by (6.173), the following is obtained
− w 1
M 1
= cX 1 (3k 1 + kX 1/2
1 ), (6.187)
where
( ) 4k
2 1/2
k = 4 k 1
= 4 × 10 11 e −37 000/RT . (6.188)
k 5d
It is easily seen that the first term in the parenthesis of Eq. (6.187) may be neglected
respect to the second. Hence it finally results
− w 1
M 1
= kcX 3/2
1 . (6.189)
Let us assume that the proportion between concentrations of products NH 3 , N 2 and
H 2 is the one corresponding to the complete reaction, and the concentrations of radicals
are very small, then the following relations will be obtained between the mole
fractions and the mass fractions of the main species
Furthermore, the mean mole mass of the mixture will be
X 1 + 2X 2 = 1, (6.190)
Y 1
= X 1
M 1 M , (6.191)
Y 2
= X 2
M 2 M . (6.192)
M = M 1 X 1 + X 2
(M 2 + 1 2 M 3 + 1 2 M 4
From the system of equations (6.190) to (6.193) it results
)
. (6.193)
1 − 32
X 1 = 17 Y 2
1 + 32 . (6.194)
17 Y 2
The reaction velocity of ammonia results to be
⎛
w 2
= − w 1 − 32 ⎞3/2
1 ⎜
= kc ⎝
17 Y 2
⎟
M 2 M 1
1 + 32 ⎠ . (6.195)
17 Y 2