Page 88 - Introduction to chemical reaction engineering and kinetics

70 Chapter 4: Development of the Rate Law for a Simple System

(2) The calculation of time quantities: half-life (t& in a BR and a CSTR (constant
density), problem 2-1; calculation of residence time t for variable density in a
PFR (Example 2-3 and problem 2-5).
(3) The integrated form for constant density (Example 3-4), applicable to both a BR
and a PFR, showing the exponential decay of cA with respect to t (equation 3.4-
10), or, alternatively, the linearity of In CA with respect to t (equation 3.4-11).
(4) The determination of kA in an isothermal integral PFR (Example 3-7).
(5) The identity of Arrhenius parameters EA and EAp, and A and A,, based on CA
and PA, respectively, for constant density (Section 4.2.3).

The rate of hydration of ethylene oxide (A) to ethylene glycol (C,H,O + H,O -+ C,H,O,)
in dilute aqueous solution can be determined dilatometrically, that is, by following the
small change in volume of the reacting system by observing the height of liquid (h) in a
capillary tube attached to the reaction vessel (a BR, Figure 3.1). Some results at 2O”C, in
which the catalyst (HClO,) concentration was 0.00757 mol L-l, are as follows (Brbnsted
et al., 1929):

t/mm h/cm tlmin h/cm

0 18.48 (h,) 270 15.47
30 18.05 300 15.22
60 17.62 330 15.00
90 17.25 360 14.80
120 16.89 390 14.62
240 15.70 1830 12.29 (h,)

Determine the order of this reaction with respect to ethylene oxide at 20°C and the value
of the rate constant. The reaction goes virtually to completion, and the initial concentration
of ethylene oxide (c,&) was 0.12 mol L-t.

SOLUTION

We make the following assumptions:
(1) The density of the system is constant.
(2) The concentration of water remains constant.
(3) The reaction is first-order with respect to A.
(4) The change in concentration of A (cAO - CA) is proportional to the change in height
(ho - h).
To justify (l), Brijnsted et al., in a separate experiment, determined that the total change
in height for a l-mm capillary was 10 cm for 50 cm3 of solution with CA,, = 0.2 mol L-l;
this corresponds to a change in volume of only 0.16%.
The combination of (2) and (3) is referred to as a pseudo-first-order situation. H,O is
present in great excess, but if it were not, its concentration change would likely affect the
rate. We then use the integral method of Section 3.4.1.1.2 in conjunction with equation
3.4-11 to test assumption (3).