Page 50 - Introduction to chemical reaction engineering and kinetics

32 Chapter 2: Kinetics and Ideal Reactor Models

From equations 2.3-4 to -7, rA may be interpreted in various ways as2

t-r.41 = (FAo - FA)IV = -AFAIV = -AF,IqT (2.3-8)
(2.3-9)
= FAO~AIV
= - vAt/v (2.3-10)

(2.3-11)
= (cAo% - cAq)lv

where subscript o in each case refers to inlet (feed) conditions. These forms are all
applicable whether the density of the fluid is constant or varies, but apply only to steady-
state operation.
If density is constant, which is usually assumed for a liquid-phase reaction (but is
usually not the case for a gas-phase reaction), equation 2.3-11 takes a simpler form,
since q. = q. Then

(-rA) = tcAo - cA)i(vbd
= - AcAlt (constant density) (2.3-12)

from equation 2.3-1. If we compare equation 2.2-10 for a BR and equation 2.3-12 for a
CSTR, we note a similarity and an important difference in the interpretation of rA. Both
involve the ratio of a concentration change and time, but for a BR this is a derivative,
and for a CSTR it is a finite-difference ratio. Furthermore, in a BR, rA changes with t as
reaction proceeds (Figure 2.2), but for steady-state operation of a CSTR, rA is constant
for the Stationary-State conditions (CA, T, etc.) prevailing in the vessel.

For a liquid-phase reaction of the type A + . . . + products, an experimental CSTR of
volume 1.5 L is used to measure the rate of reaction at a given temperature. If the steady-
state feed rate is 0.015 L s-l, the feed concentration (CA,,) is 0.8 mol L-l, and A is 15%
converted on flow through the reactor, what is the value of (- rA)?

SOLUTION

The reactor is of the type illustrated in Figure 2.3(a). From the material balance for this
situation in the form of equation 2.3-9, together with equation 2.3-7, we obtain

(-rA) = FAOfAIV = cAOqOfA/V = 0.8(0.015)0.15/1.5 = 1.2 X 10-3mOlL-1~-’

2For comparison with the “definition” of the species-independent rate, I, in footnote 1 of Chapter 1 (which
corresponds to equation 2.2-2 for a BR),

r(CSTR) = rilvi = (llvi)(AFilV) = (l/viq)(AFi/n (2.3~8a)