# Reactive Energy Balances

Our previous methods for solving energy balances equations is no longer strictly valid for reactive systems. In particular, the issue with our technique lies in our previous statement regarding choosing reference states. For non-reactive systems, we can arbitrarily choose a reference state for each species, this is simply not the case for reactive systems. Let's take a look...

Using our old method, we could simply choose CH4 and O2's reference points to be at 100C and 1 atm, while we choose CO2 and H2O's reference points to be at 250C and 1 atm. This would lead us to conclude that $\Delta$H was zero, which we know from experience is clearly not true! (Can you prove this to yourself?)

In order to solve this dilemma, we can choose one of two (equivalent) methods for solving reactive systems (much like we chose one of two methods to do reactive mass balances):

• Heat of Formation Method
• Heat of Reaction Method

# Heat of Formation Method

In the heat of formation method we change our previous procedure in two very significant (but rather simple) ways:

• Reference states are chose as elemental species at a reference temperature and pressure (298K and 1atm). This is somewhat similar to doing an atomic material balance for reactive systems.
• First step in calculating $\hat H$ is to form the molecular species from their elemental species (the reference states).

Following that first step (once our molecular species is formed), we then simply follow our fictitious path, stepwise, summing $\hat H$ for each step as we go (changes in T, P, and phase).

An example $\hat H$, might therefore include (with first formation and them a T change and then a P change):

$\hat H_{CH_4} = \Delta H_{f_{CH_4}}^o + \int_{298K}^{373K} c_{p_{CH_4}} dT + \hat V\Delta P$

# Heat of Reaction Method

In the heat of reaction method we now follow a trend more analogous to the extent of reaction method of reactive material balances. Again, our previous (nonreactive) energy balance procedure changes in three very significant (but rather simple) ways:

• We must first look up the heat of reaction for each reaction taking place and note under what conditions the reaction takes place for the tabulated data (298K and 1atm). (NOTE that this does not mean that all reactions listed can actually happen at STP, simply that if they did happen at STP that this would be their heat of reaction).
• Use the T, P, and state of aggregation from the heat of reaction formula as the reference state for each species.
• Calculate $\hat H$'s following our fictitious path, stepwise, summing $\hat H$ for each step as we go (changes in T, P, and phase), but now we add the extent of reaction times the heat of reaction to the total $\Delta$ H expression (or add multiple extents of reaction of heats of reaction if multiple reactions take place).

An example $\hat H$, and $\Delta H$ calculation might therefore look like (for the example above):

$\hat H_{CH_4} = \int_{298K}^{373K} c_{p_{CH_4}} dT + \hat V\Delta P$

$\Delta H = \hat H_{CO_2}\dot n_{CO_2} + \hat H_{H_2O}\dot n_{H_2O} - (\hat H_{CH_4}\dot n_{CH_4} + \hat H_{O_2}\dot n_{O_2}) + \dot \xi \Delta \hat H_{rxn}^o$

OUTCOME:

Explain how chemical reactions are handled in the General Energy Balance