Page 73 - The engineering of chemical reactions

Chemical Equilibrium 57

Example 2-9 A reaction with a heat of reaction of -25 kcaUmole takes place in aque-
ous solution with a reactant concentration of 2 moles/liter and To =50°C. What is the
temperature if this reaction goes to completion in an adiabatic reactor? What is the final
temperature?

The specific heat of water is 1 Cal/cm3 K or 1000 cat/liter K. Therefore, the final
adiabatic temperature is
25000
-2
T =50+ 1ooo = 50+50 = 100°C

Anyone designing a reactor (and indeed anyone working near one) should be very
aware of the heat absorbed or liberated in the chemical reactor and should be especially aware
of the adiabatic temperature predicted. This heat must be released whenever a chemical
reaction occurs, and this temperature will be attained if this heat is not removed.
The chemical reactor is the most hazardous unit in any chemical plant because
most accidents occur by uncontrolled reaction, either within the reactor or after reactants
have escaped the reactor and perhaps reacted with oxygen in air. Obviously no reactor or
piping can withstand the temperatures and pressures of total combustion unless designed
specifically for these conditions. We will consider the energy balance and temperature
variations in continuous reactors in more detail in Chapters 5 and 6, while flames and
explosions will be considered in Chapter 10.
Thus we see why it is essential to consider the energy balance very carefully in
designing chemical reactors. The isothermal reactor assumption, while a good starting
point for estimating reactor performance (the next two chapters), is seldom adequate for
real reactors, and neglect of heat release and possible temperature increases can have very
dangerous consequences.

CHEMICAL EQUILIBRIUM

No reactor can produce yields of products beyond those predicted by chemical equilibrium,
and the second calculation anyone should perform on a process (after calculating the
adiabatic temperature for safety considerations) is the equilibrium composition.
We discussed thermodynamic equilibrium previously in relating kinetics to reversible
reactions. One should always estimate these quantities and keep them in mind before
performing more detailed design of reactors and separation units. We also note that one
must consider all chemical reactions that may occur for a given feed, not just the one
desired.
To obtain the equilibrium conversion for a single reaction, we need to solve the
equation

fi ay = exp(-AGi/RT) = Keq
j=l
for the relevant activities aj. For gases we usually define AG” with a standard state (aj = 1)
as the ideal gas at 1 atm; so the above expression becomes