[Luyben] Process Mod.. - Student subdomain for University of Bath

36 MATHEMATICAL MODELS OF CHEMICAL ENGINEERING SYSTEMS
In a binary system the relative volatility c( of the more volatile compone\nt
compared with the less volatile component is
Y/X
IX = (1 - y)/(l - x)
Rearranging,
ax
y = 1 + (a - 1)x
(2.66)
3. K values. Equilibrium vaporization ratios or K values are widely used, particularly
in the petroleum industry.
Kj =t (2.67)
The K’s are functions of temperature and composition, and to a lesser extent,
pressure.
4. Activity coefficients. For nonideal liquids, Raoult’s law must be modified to
account for the nonideality in the liquid phase. The “fudge factors” used are
called activity coefficients.
NC
P = c xjp,syj
j=l
(2.68)
where yj is the activity coefficient for the jth component. The activity coeficient
is equal to 1 if the component is ideal. The y’s are functions of composition
and temperature
2.2.7 Chemical Kinetics
We will be modeling many chemical reactors, and we must be familiar with the
basic relationships and terminology used in describing the kinetics (rate of
reaction) of chemical reactions. For more details, consult one of the several excellent
texts in this field.
A. ARRHENIUS TEMPERATURE DEPENDENCE. The effect of temperature on
the specific reaction rate k is usually found to be exponential :
k = Cle.-E/RT (2.69)
where k = specific reaction rate
a = preexponential factor
E = activation energy; shows the temperature dependence of the reaction
rate, i.e., the bigger E, the faster the increase in k with increasing temperature
(Btu/lb * mol or Cal/g * mol)
T = absolute temperature
R = perfect-gas constant = 1.99 Btu/lb. mol “R or 1.99 Cal/g. mol K