MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

nobs = 1 (KCs )
2
2
1
[KCs − ln(1+ KCs )] (1 + KCs )
It can be seen that the observed reaction order in Zone II (n obs) for the Langmuir rate
equation is a complex function of a non-dimensional number KC s. An important
49
(5.13)
implication of Eq. (5.13) is that the value of n obs ranges from 0.5 to 1 (see Table 5.1), just
like the range of n obs in Eq. (5.8), as shown in Figure 5.1. That is, in Zone II the observed
reaction order (n obs) cannot be less than 0.5 if the reaction is sufficiently described by the
Langmuir rate equation, assuming the reaction rate contributed from the external surface
area of the particle is negligible compared to that from the internal surface area. Similarly,
the observed reaction order can be estimated from Eqs. (5.11), (5.9) and (5.5):
1 KCs 1
nobs = +
1+ KC 1
[1−
s 2KCs +
2(1+ KC ) s
1 + KCs 2 ] (5.14)
or from Eqs. (5.12), (5.9) and (5.5):
1
nobs =
1+ KCs + KC s
2KC s +1
(5.15)
Table 5.1. The values of n obs at different values of KC s based on the standard
general modulus and simpler general moduli
KCs 0 0.125 0.25 1 4 16 64 ∞
nobs from (5.13) 1.00
*
0.962 0.931 0.815 0.669 0.572 0.527 0.500
nobs from (5.14) 1.00 0.955 0.931 0.850 0.678 0.557 0.515 0.500
nobs from (5.15) 1.00 0.989 0.967 0.833 0.644 0.544 0.512 0.500
* Note: Zero divided by zero situation. Value exists only in the limit.
The theory developed above provides a new way to estimate the kinetic
parameter K in the Langmuir rate equation. By measuring the observed reaction order in