We have an adiabatic CSTR that's not at steady state.
So the volume is constant, the feed rate is constant, and we're given the conditions,
and we're given the initial conditions of the reactor.
So it's at 325 Kelvin, and a concentration of A of 5 millimoles per cubic centimeter.
We're given other properties such as heat of reactions, first order reaction, and the
question is, if we start at these conditions, does the concentration of A in the reactor
increase or decrease initially as it approaches steady state?
So the steady state concentration is some other concentration than 5 millimoles, how
does it approach that steady state?
Turns out that for this problem, what we really are asking is, what is the derivative of concentration
of A with respect to time?
And so if we look at a mass balance, we have an accumulation term, and it's a constant
density system so I'm going to write it as the volume of the reactor, which is a constant,
change in concentration of A with respect to time.
This is what we want to determine, just its sign.
And so that's equal to the volumetric flow rate times the concentration coming into the
reactor, the volumetric flow rate's constant, concentration leaving the reactor, and then
the rate of reaction, so it's first order, so concentration of A in the reactor is the
same as concentration of A leaving the reactor, times the reactor volume.
So essentially, we can substitute the values into the right side of the equation to determine
whether the right side is greater than or less than 0.
So let's look at the values.
The volumetric flow rate is 250 cubic centimeters per second, and we'll factor that out, and
so the concentration coming in is 10 millimoles per cubic centimeter, and leaving is 5, so
millimoles per centimeter cubed.
The other term now is the rate constant, 10^11, exponential, and now for starting temperature
we're going to use the temperature in the reactor, which is 325 Kelvin, and the concentration
in the reactor, which is 5, and then the reactor volume, which is 50,000 cubic centimeters.
So we need to check that the units are going to be consistent, and I forgot to write the
units down, seconds to the minus 1 is the units for rate constant, so you can see we're
going to end up with millimoles, in this term the cubic centimeters cancel, millimoles per
second.
Likewise here, millimoles per second.
So if I calculate these values, 1.25 minus 1.08, 0.17 moles per second, greater than
0, therefore concentration with A with respect to time is greater than 0, and so the question
is, what happens, does C_A increase or decrease?
This says it increases initially as it approaches steady state.