# Using Hess' Law with Heats of Formation

The example below is being used to explain WHY the formula at the end works. If all you care about is the formula, you can skip to the bottom, but don't blame me if you get lost later because you didn't really understand...

Determine the ΔHrxn of 3 BaCl2 + Al2O3 → 3 BaO + 2 AlCl3 from the following reactions:

 Ba + Cl2 → BaCl2 ΔHf BaCl2 2 Al + 3/2 O2 → Al2O3 ΔHf Al2O3 Ba + 1/2 O2 → BaO ΔHf BaO Al + 3/2 Cl2 → AlCl3 ΔHf AlCl3

Note: In this problem we are using ΔH rather than actual numbers because it will allow us to see what we have done more easily.

It is relatively easy to figure out what to do with each reaction because the product of each formation reaction can be directly linked to the original reaction.

• The first reaction will need to be flipped and multiplied by 3 (since there are 3 BaCl2 on the left side in the main reaction).
• The second reaction will need to be flipped (since the Al2O3 in the original reaction is on the left).
• The third reaction needs to be multiplied by 3 (for the 3 BaO in the main reaction).
• The fourth reaction needs to be doubled (for the 2 AlCl3 in the main reaction).

So the heat of the main reaction will look like this:

ΔHrxn = (-1)(3) ΔHf BaCl2 + (-1)ΔHf Al2O3 +(3)ΔHf BaO + (2)ΔHf AlCl3

Make sure that you agree with this before you go further...

Let's organize this a little. Let's put the positive values first and the negative values last. That will give us:

ΔHrxn = (3)ΔHf BaO + (2)ΔHf AlCl3 + (-1)(3) ΔHf BaCl2 + (-1)ΔHf Al2O3

Now, let's factor out the -1 from the last two terms. That will leave:

ΔHrxn = (3)ΔHf BaO + (2)ΔHf AlCl3 + (-1)[(3) ΔHf BaCl2 + ΔHf Al2O3]

Reorganizing just a little gives...

ΔHrxn = [(3)ΔHf BaO + (2)ΔHf AlCl3] - [(3) ΔHf BaCl2 + ΔHf Al2O3]

Make sure that you see how we got here before you read further...

All that remains is to look at what has happened. All of the heats of formation of the reactants from the original main reaction are in the second bracket and are being subtracted (because those reactions had to be flipped). Additionally, ALL of the heats of formation (even the Al2O3) are being multiplied by the coefficients from the original main reaction.

In simpler terms, what we did was multiply each heat of formation by the coefficients and then subtracted the reactants from the products. The good news is that this ALWAYS works, and therefore you NEVER have to actually do the Hess' Law work for a problem with heats of formation.

There is a simple (to use, but not to look at) formula for this idea:

## ΔHrxn = ΣΔHf products – ΣΔHf reactants

In English, this would be read “the heat of the reaction is equal to sum of (Σ) the heats of formation of the products minus the sum of the heats of formation of the reactants.

One last (good) thing about this formula, someone (actually, lots of someones) has put together a table of heats of formations for LOTS of compounds. That means for almost any reaction, you can pull out the table (which your instructor will provide you, or which you can find on-line) and determine the heat of the reaction by doing a simple math problem, rather than by doing a whole Hess' Law thing.

Let's try...