Page 456 - Elements of Chemical Reaction Engineering Ebook

Sec. 8.2 The Energy Balance 427

The reaction is exothermic and the reactor is operated adiabatically. As a result, the
temperature will increase with conversion down the length of the reactor.

Solution

I. Design equation:
dX - -, (E8- 1.1)
-_
dV FAO
2. Rate law: -rA = kC, (E8-1.2)
3. Stoichiometry (liquid phase):

c, = c, (1 - X) (EEL I .3)

4. Combining and canceling the entering concentration, C,, , yields
dX - k(l - X) (EEI-1.4)
-_-
dV UO
Recalling the Arrhenius equation,

k = k, enp[! (i - (E8- 1.5)

we know that k is a function of temperature, T. Consequently, because T var-
ies along the length of the reactor, k will also vary, which was not the case for
isothermal plug-flow reactors. Combining Equations (E8-1.4) and (ES- 1.5)
gives us

-_
Why we need the dX - (E8,- 1.6)
energy balance dV
We see that we need another relationship relating X and T or T and V to solve
this equation. The energy balance will provide us with this relationship.

8.2 The Energy Balance

8.2.1 First Law of Thermodynamics

We begin with the application of the first law of thermodynamics first to
a closed system and then to an open system. A system is any bounded portion
of the universe, moving or stationary, which is chosen for the application of
the various thermodynamic equations. For a closed system, in which no mass