So in this screencast we are going to take a look at molecular species balances, which
are one method that can be used to determine unknown flow rates in a reactive process.
So for this example let's take a look at the reaction of NO2, a pollutant, over a catalytic converter to
produce nitrogen gas and oxygen gas. So first step in this process is we want to balance
the equation, and now we want to do a degree of freedom analysis on this problem.
So the degree of freedom analysis for any molecular species balance is going to be
the number of unknown variables plus the number of chemical reactions minus the number of
independent molecular species minus the number of other equations we have. So let's define
our process a little bit more concretely. So coming into our catalytic converter, let's
say we have 100 moles per hour of NO2 and coming out let's say we have 10 moles per hour
of NO2, but we are also going to have a flow of oxygen coming out. We are also going to
have a flow of N2 coming out. So if we do a degree of freedom analysis on this system,
we are going to see that we have 2 unknown variables: the flow of O2 and the flow of
N2. We are going to have 1 independent reaction, and we have 3 independent species, and if
we sum these up we can see that we have 0 degrees of freedom. So we know that this problem
is solvable. So the next step of this process is that we want to take a look at the general
material balance equation. The general material balance equation is just that input plus generation plus accumulation equals output
plus consumption. So we can perform a general material balance on each of the components
of our system. So the first component that we will take a look at is the NO2. So for
the NO2 we have an input term because coming into the system we have NO2. We are not generating
NO2 so we don't have a generation term. Nor are we accumulating NO2, so we do not have
an accumulation term. So we can see that input is the only thing left in the left handed
side. Coming out we have both output and consumption of NO2. So now we can fill in for what we
know. We have 100 moles per hour coming in, and we can see that we have 10 moles per hour
coming out, and then whatever is left must be our consumption. So in this case consumption would
be 90 moles per hour of NO2. So the next species that we will perform a balance on will be the
oxygen gas. So in the case of oxygen, O2 is only the product in this reaction. So its
output is going to equal its generation. So for every 90 moles of NO2 consumed per hour
we can say that we make 1 mole of O2 produced for every 1 mole of NO2 consumed. So we can
see that we would produce 90 moles per hour of O2, and this is also going to equal our
n dot O2. So the final species to balance is the N2. In this case the only place we
have N2 is in our generation term. So we can see again that output equals generation. So
in this case we again have our 90 moles of NO2 consumed per hour, but in this case for
1 mole of N2 produced, we have 2 moles of NO2 consumed. So this leaves us with a production
of 45 moles of N2 produced per hour, and this would then leave us with our other unknown flow
rate of n dot N2 equals 45 moles per hour. So again molecular species balances are one
method of determining these unknown flow rates in a reactive system, but many times other
methods like atomic species balances are much easier to perform.