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Encyclopedia of Physical Science and Technology EN014A-654 July 28, 2001 16:35

30 Reactors in Process Engineering

Thereactioncoordinateprovidesarelationshipbetween II, ... , r reactions. In this case,
the initial number of moles N i0 , the reaction coordinate ε,
i = 1, 2,..., n
and the number of moles N i at any point or stage in the
dN i, j = ν i, j dε j
j = I, II, ... ,r
reaction. Since the units of the stoichiometric numbers ν i
are dimensionless, the reaction coordinate has the same
and
units as N i (for example, mol, kg mol, or kg mol/sec).

a. Example. For the gas phase reaction, i = 1, 2,..., n
dN i = ν i, j dε j
2A + B = R + S j j = I, II, ... ,r.
7 mol of A are reacted with 4 mol of B in a batch reactor. Integration gives N i = N i0 + j ν i, j ε j
Agas-mixtureanalysisafterreactionshowedthefinalmix- b. Example.
ture contained 20 mol% R. Calculate the mole fractions 1
C 2 H 4 + O 2 = C 2 H 4 O
of the other components. 2
C 2 H 4 + 3O 2 = 2CO 2 + 2H 2 O.
Knowns:
Initially, 1 mol of C 2 H 4 and 3 mol of air (≈21% O 2 ) react.
1. N A0 = 7. Derive an expression relating the mole fractions of each
2. N B0 = 4. of the components. For the reactions
3. Y R = 0.20. 1
A + B = C
4. N R0 = 0, N S0 = 0. 2
ε I (extent of reaction, first reaction)
Let: N T = final number of moles, N 0 = initial total num- and
ber of moles, and ν = ν i .
A + 3B = 2D + 2E
N A = N A0 + ν A ε = 7 − 2ε
ε II (extent of reaction, second reaction)
N B = N B0 + ν B ε = 4 − 1ε
Knowns:
N R = N R0 + ν R ε = 0 + ε
N S = N S0 + ν S ε = 0 + ε
1. N A0 = 1 mol.
N T = N 0 + νε = 11 − ε 2. N B0 = (.21)(3) = 0.63 mol.
3. N C0 = N D0 = N E0 = 0.
since
4. N 2 is an inert, that is, N I0 = N I = (0.79)(3) =
7 − 2ε 4 − ε
N A N B 2.37 mol.
Y A ≡ = Y B ≡ =
N T 11 − ε N T 11 − ε
ε ε
N R N S In general,
Y R = = Y S = = ,
N T 11 − ε N T 11 − ε
N i = N i0 + ν i, j ε j (J = I, II)
but j
N R ε N A = N A0 + ν A,I ε I + ν A,II ε II = 1 − ε I − ε II
Y R = = 0.2 = , 1
N T 11 − ε
N B = N B0 + ν B,I ε I + ν B,II ε II = 0.63 − ε I − 3ε II
2
so ε = 1.83. Therefore, Y S = 0.20 (as expected from stoi-
N C = N C0 + ν C,I ε I + ν C,II ε II = 0 + ε I
chiometry) and
N D = N D0 + ν D,I ε I + ν D,II ε II = 0 + 2ε II
Y S = 0.20
Y R = 0.20 N E = N E0 + ν E,I ε I + ν E,II ε II = 0 + 2ε II
Y A = 0.36 N I = N I0 + ν I,I ε I + ν I,II ε II = 2.37 + 0ε I + 0ε II
Y B = 0.24
1
N T = N T0 + ν i, j ε j = 4 − ε I .
Y i = 1.00. i j 2
A similar analysis can be made for many reactions Therefore,
occurring simultaneously. If we have r independent re-
1 − ε I − ε II
actions with n species, their stoichiometric coefficients Y A = .
1
can be termed ν i, j , with i = 1, 2,..., n species and j = I, 4 − ε I
2