In this screencast we are going to show how to use the heat of reaction method to solve
for the energy balance. In other words what is the Q that comes out of the reactor. We
have this reaction and it goes in at 300 degrees C and it comes out at 500 degrees C. Since
we are using the heat of reaction method the steps we need to do are first do the material
balance however, since it is a heat of reaction method it means we are going to have to use
the extent of reaction method. Then we are going to put together an enthalpy table that
has to include the references and because we are using the heat of reaction method our
references have to be 25 degrees C, 1 atmosphere and the molecular species. We use molecular
species to find our heat of reaction. Once we have done that we are going to input the
enthalpies that are based on the temperature change. In other words the change from our
reference temperature of 25 degrees to 300 degrees C for our reactants and 500 degrees
C for our products. Then we, using the heat of formation that can be found in any book,
calculate the heat of reaction and finally we calculate Q which is this extent of reaction
times the heat of reaction plus the sum of our enthalpies in our table so this is out
minus in. Let's start with doing our material balances. Let's say that we are given 1 mole
of CO with 50% excess of H2O which means that we have 1.5 moles of H2O. Our conversion is
80% so 0.80 equals moles of CO in minus moles of CO out divided by the moles in and that
allows us to find the moles of carbon monoxide out. It also allows us to fin the extent of
reaction because the moles of carbon monoxide out equal the moles in minus the extent of
reaction. The reason it is negative is because it is a reactant and we are using is up. Therefore
our extent of reaction is 0.8 and we use that to find the moles of our products. Finally,
we have to find the number of moles of H2O which is going to be the moles in and again
it's a reactant so we subtract the extent of reaction and finally we are left with 0.7.
Now that we have our material balances taken care of we put together our enthalpy table.
Now we can fill in our enthalpy table. Notice our references at the top. 25 degrees C, 1
atmosphere, and molecular species. From our material balance we know that we have 1 moles
of CO, 1.5 mole of H2O coming in and None of this coming out. Then coming out of the
reactor 0.2, 0.7, 0.8, and 0.8. the first thing we are going to look at are the enthalpy
in of carbon monoxide and H2O vapor. Because our reference is 25 degrees C we can actually
look in the enthalpy table for ideal gases for these enthalpy at 300 degrees. This is
8.17 kJ/mol, this is 9.57 kJ/mol and again for the H out only this time we look at it
under 500 degrees. That is 14.38, 17.01, 21.34, and finally 13.82. We have put together our
table. The next thing that we have to do is find out heat of reaction. To find the heat
of reaction it is the sum of the heats of formation of the products multiplied by each
of their stoichiometric coefficient minus the sum of the heat of formation of the reactants
again multiplied by their stoichiometric coefficient. In our particular problem each of the stoichiometric
coefficients are 1. The heat of formation of carbon monoxide is -110.53. The heat of
formation of H2O, and these are all vapor, is -241.83. The heat of formation of CO2 is
-393.5 and again these are all kJ/mole and you can look them up in any table of physical
properties. The heat of formation of substances in their elemental form such as H2 equals
0. Now let's calculate this heat of reaction which is -393.5 kJ/mol minus -241.83 plus
-110.53. Those are ours coming in and our heat of reaction is -41.14 kJ/mole. Now the
only thing that we have to do is add everything together. Our Q is going to be, let's go back
to this table to show you exactly how we are going to use it. We are going to use 0.2 times
14.38 plus 0.7 times 17.01 plus 0.8 times 21.34 plus 0.8 times 13.82. That is our enthalpies
times their moles out and we are going to subtract from it 1 times 8.17 and 1.5 times
9.57. Let's do that but we are not done yet because we have to add to that our extent
of reaction times our heat of reaction. So when we calculate this out we find that our
Q is -12.6 kJ.