In this example we have a gas phase irreversible reaction, A plus 2B goes to C, and it takes place in an isothermal
packed reactor. We are given the composition of the feed, the pressure, and the temperature.
The inlet volumetric flow rate is 10 liters per minute, and it says the outlet volumetric flow rate
is also 10 liters per minute, and the conversion is 70% for reactant A, and the question is what is the
outlet pressure?
So essentially in this problem what we are looking at is, there is a decrease
in the number of moles in the gas phase, which should result then in a decrease in the volumetric
flow rate, and then there is a decrease in the pressure through the packed bed, which
results in an increase in the volumetric flow rate, and these two effects initially cancel each other so
that the volumetric flow rate does not change. So the problem really is looking at using
the ideal gas law for a flowing system, where this is the volumetric flow rate and this
is a total molar flow rate. So as the pressure decreases, the volumetric flow rate increases
according to this equation. As the molar flow rate decreases, the volumetric flow
rate decreases. So first let's draw a diagram to represent this system. So I'm going to apply the
ideal gas law at the initial conditions, inlet of the reactor, and at the exit of the reactor, and what
I am going to do is divide these two equations. The volumetric flow rates are the same, so
these cancel, RT constant, because temperature is constant. So this equation says the final
pressure is equal to the initial pressure times the final total molar flow rate over
the initial total molar flow rate. So we need to determine the values of these flow rates,
and what we are going to do is pick a basis of 1 mole, the flow rate is certainly different
then this in moles per time. We are going to look at the inlet. We get inlet for 1 mole,
there is 0.25 moles of A, and 0.75 moles of B, no moles of C, so the total is 1 mole,
that's our basis. The outlet, what it says is the... lets write it first in terms of conversion,
1-x, and for every mole of A, 2 moles of B react. So we have 0.25x moles of A that react,
twice that speed, then C is 0.25x. Now, since x is 0.7, I can calculate each of these values.
This is 0.075, 0.40, and then C is 0.175. I add these together, 0.65. So now I can go back
to the problem. Inlet pressure is 2 bar, outlet molar flow rate is 0.65, inlet is 1. Of course it
is proportional to those values, we do not need to calculate the actual value, and so
1.3 bar is then the pressure at the reactor outlet to keep the volumetric flow rate constant.