Energy Balance
Reactive Systems

Upon studying this section, you should be familiar with the following:

ΔĤ°rxn

2 ways to find ΔĤ of a reaction at STP:

As noted above, there are two ways to calculate the specific enthalpy change of a reaction at STP, ΔĤ°rxn (the "°" that follows the ΔH is a constant reminder that this is the ΔH at STP, 273.15 Kelvin and 1 atm).

  • By using other reactions given their ΔĤ°rxn's, utilizing Hess's law
  • or by using Heats of Formation, ΔĤ° f, of each species of the reaction

Using the Heats of Formation is the general route, and we will only use Hess's law if we are given ΔĤ°rxn's of other reactions.

To introduce these two methods, let's use the following reaction:

CO(g) + H2O(v) ® CO2(v) + H2(g)

Hess's law:

Here, we would be given other heats of reaction that we can manipulate algebraically to up with the heat of reaction in this example. You have seen this before, in General Chemistry, so let's just show you the mechanics in an example:

So, we would have to be given other heat's of reaction, for example, we could be given the following:

CO(g)+1/2 O2(g) ® CO2(g) : ΔĤ° rxnA = -283 kJ/mol

H2(g) + 1/2 O2(g) ® H2O(v) : ΔĤ° rxnB = -242 kJ/mol

Looking at the original equation, we want CO and H2 on the left, and CO2 and H2 on the right. So we must flip reaction B, to give,

CO(g)+1/2 O2(g) ® CO2(g) : ΔĤ° rxnA = -283 kJ/mol

H2O(v) ® H2(g) + 1/2 O2(g) : -ΔĤ ° rxnB = +242 kJ/mol

Now, we would usually be concerned with getting the stoichiometry right, but here, if we simply add these equations, we get our reaction, thus, our ΔĤ°rxn, thus, adding these equations, we get:

CO(g)+1/2 O2(g) ® CO2(g) : ΔĤ° rxn = [ΔĤ° rxnA] + [-ΔĤ° rxnB]

Thus, by making use of Hess's law, we are able to determine the ΔĤ° rxn to be -41 kJ/mol.

Heats of Formation:

For our reaction, we could easily determine ΔĤ° rxn using the heats of formation of each species (tables!). To do this, we simply do two things. First, look up the heats of formation for each species in a table (table B1 in the course text), and then apply the following formula:

ΔĤ’rxn = S prod(viΔĤ° f,i) -S reactants(viΔĤ° f,i)

where vi is the coefficient of the ith species. Applying this algorithm to our example, we get the following,

  • From Table B1,
    • ΔĤ° f, CO = -110.52 kJ/mol
    • ΔĤ° f, H20 = -241.83 kJ/mol
    • ΔĤ° f, CO2 = -393.5 kJ/mol
    • ΔĤ° f, H2 = 0 kJ/mol
and so we readily obtain,

ΔĤ°rxn = 1(ΔĤ° f,CO2) + 1(ΔĤ° f,H2) - 1(ΔĤ° f,CO) - 1(ΔĤs° f,H2O) = -41.15 kJ/mol


Thus, we have now used heats of formation to obtain ΔĤ° rxn. But what about ΔH°rxn? Well, this is even easier.

ΔH°rxn

Two steps to find ΔH°rxn:

First, we find ΔĤ° rxn, from above. Hey, we just did that. Yep, using either Hess's law or Heats of Formation.

Second, with ΔĤrxn now known, we apply the following new relation.

ΔH°rxn = x *ΔĤ°rxn


where x is as was defined in chapter 4, the extent of reaction,

x = ni, rxn/vi


where i can be any component in the reaction, and n is the number of moles that reacted and v is its stoichiometric coefficient.

For the previous example, if we had 5 moles of CO react (and thus, 5 moles of each of the other species involved in the reaction), we could calculate the ΔH°rxn, first obtaining x,

x = 5 moles / +1
so, we get,
ΔH°rxn = 5 moles * -41 kJ/mole = -205 kJ

ΔHrxn

Here we will have streams coming into and out of the reactor at different temperatures with some components possibly undergoing phase changes, in addition to the reaction. We need to consider all of this when determining the heat exchange, or the ΔHrxn (again, because Q = ΔH, for ΔEp, ΔKE, and Ws all = 0). Before we set up a problem,

Recall:

  • ΔH for ΔT, ΔĤ = ò dT from T1 to T2, or Table's B8 & B9 for some common gases, or steam tables.
  • ΔH for ΔP, ΔĤ = Vhat*ΔP for liquids and solids, ΔĤ = 0 for ideal gases
  • ΔH for a change in state, = ΔĤv (l® g), = -ΔĤv (g ® l), = ΔĤm (s ® l), = -ΔĤm (l® s)
  • and now, for a reaction, ΔĤrxn = x*ΔĤrxn, where
    • ΔĤ°rxn = Sprod|vi|ΔĤ°f,i -Srxnt|vi|ΔĤ°f,i
    • x = ni, rxn/|vi|

steps for solving energy reaction balances:

  • draw flow chart
  • perform material balances
  • draw calculation scheme
    • reactions at 25 oC and 1 atm
  • write total ΔH eqn
    • with each individual ΔH accounted for
  • determine individual ΔH's
  • sub in ΔHi's into ΔH, and compute ΔH

Now, for me, these reaction calculations are quite involving, so I would like to work and example from the book for you myself. Click here for an example.

Examples

Example 1:

5 moles of heptane is reacted to give toluene and hydrogen gas. Heptane at 500°C is fed to a reactor, which operates isothermally at this temperature. Determine the heat transferred to or from the reactor in kJ.

Goto | Check Answer | See Solution

Example 2:

Given the following two reactions of ammonia with air:

4 NH3 + 5 O2 ® 4 NO + 6 H2O
2 NH3 + 1.5 O2 ® N2 + 3 H2O

and the following flow diagram,



Determine the rate of heat transfer to or from the reactor in kW.

Goto | Check Answer | See Solution


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