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144 CHAPTER 5. RATE OF GENERATION
The mole fractions of CzH4 and CI& are given in the problem statement. These
values are used to deternine the extent of the reactions as
E1
xc2n4 = - 0.25 j tl = 0.333
=
1 +e1
-
XCH4 = - 0.05 + ~2 = 0.033
2E2
-
1 +E1
Therefore, the mole fmctaons of CzHs, H2 and the inerts are
0.85 - ~1 - €2 - 0.85 - 0.333 - 0.033 = 0,363
-
1+E1 1 + 0.333
0.333 - 0.033
-- - = 0.225
~1 - ~2
1+E1 1 f 0.333
0.15 = 0.112
1 + 0.333
5.3.3 Rate of Reaction
The rate of a chemical reaction, r, is defined by
(5.3-22)
where V is the volume physically occupied by the reacting fluid. Since both V and
&/dt are positive, the reaction rate is intrinsically positive. Note that the reaction
rate has the units of moles reacted per unit time per unit volume of the reaction
mixture. The reaction rate expression, T, has the following characteristics:
0 It is an intensive property,
0 It is independent of the reactor type,
0 It is independent of a process.
Changes in the molar extent of the reaction can be related to the changes in
the number of moles of species i by differentiating Eq. (5.3-10). The result is
1
&= -dni (5.3-23)
ai
Substitution of Eq. (5.3-23) into Eq. (5.3-22) gives
1 1 dni
r=--- (5.3-24)
If the rate of generation of species i per unit volume, %i, is defined by
(5.3-25)