Page 296 - Elements of Chemical Reaction Engineering 3rd Edition

268 Collection and Analysis of Rate Data Chap. 5

SUMMARY

I. Differential method for constant-volume systems

dCA - kC1 (S5-1)
dt

a. Plot ACA/At as a function of t.
b. Determine dcA/dt from this plot.
c. Taking the In of both sides of (S5-1) gives
[ d2]
In -- =lnk+alnCA (S5-2)

Plot h(-d,C,/dt) versus lnCA. The slope will be the reaction order
a. We could also use finite-difference formulas or software packages
to evaluate -dC,ldt as a function of time and concentration.
2. Integral method
a. Guess the reactioR order and integrate the mole balance equation.
b. Calculate the resulting function of concentration for the data and
plot it as a function of time. If the resulting plot is linear, you have
probably guessed the correct reaction order.
c. If the plot is not linear, guess another order and repeat the procedure.
3. Method of initial rates: In this method of analysis of rate data, the
slope of a plot of ln(-rAo) versus lnCAO will be the reaction order.
4. Modeling the differential reactor: The rate of reaction is calculated
from the equation

(S5-3)

In calculating the reaction order, a,

the concentration of A is evaluated either at the entrance conditions or
at a mean value between CAo and CAe.
5. Least-squares analysis
a. Linear least-squares: Linearize the rate law and solve the resulting
algebraic equations [i.e., Equations (5-26) through (5-28)] for the
reaction rate law parameters.

Y = a. + a,X, + a,X2 (55-4)
b. Nonlinear least-squares: Search for the parameters of the rate law
that will minimize the sum of the squares of the difference between
the measured rate of reaction and the rate of reaction calculated