Page 58 - The engineering of chemical reactions

42 Reaction Rates, the Batch Reactor, and the Real World

We could also write the above reaction as

2A -+ 2B, r=kC;
which looks like the standard form we suggested with mA = -VA. However, these are
exactly the same reactions except by the latter definition the rate coefficient k in this
expression is i of that above because VA = -2. This emphasizes that all stoichiometric
coefficients can be multiplied or divided by an arbitrary constant, but the rate expression
must be consistent with the stoichiometry chosen. The reaction and the corresponding rate
must be consistent, and we recommend that one always write them out together as

. ..+ . . . . yz...
so that the reaction and the rate are defined together.

Example 2-3 The reaction A + B obeys second-order kinetics with k = 0.01 liter
mole-l sect. The initial concentration is CAM = 2 moles/liter. What time is required for
90% conversion in a batch reactor? For 99%? For 99.9%?

Application of the equation yields

= 450 set = 7.5 min

for 90% conversion,
t=&(&-k)= lOO(50 - 0.5) = 4950 set = 1.38 h

for 99% conversion, and
t=i&&-1)= lOO(500 - 0.5) = 49,950 set = 13.9 h

for 99.9% conversion. Once we have an equation for the solution, we can frequently
solve the problem even without a hand calculator.

The nth-order irreversible reaction

For the nth-order irreversible reaction
A + products, r=kCz
we obtain
dC.4
- = -kc;
dt