### Standard Enthalpy of Formation

Before explaining the concepts involved, here is an important idea:

The standard enthalpy of formation for an element in its standard state is zero.

Now I know you don't know exactly what that means, but please remember it. When you move on to calculating various values, the above piece of information becomes quite important. Go on and study the concept and then return to the above statement. You'll understand it better in a few moments.

First two definitions of chemistry words with very specific meanings:

(1) Standard - this means a very specific temperature and pressure: one atmosphere and 25 °C (or 298 K). If a solution is being discussed, then everything in solution will be at a 1.00-molar concentration.

(2) Formation - this word means a substance, written as the product of a chemical equation, is formed DIRECTLY from the elements involved. The substance in question is always written with a coefficient of one. Here are some examples:

C(s. graphite) + O2(g) ---> CO2(g)
C(s, graphite) + 12O2(g) ---> CO(g)
H2(g) + O2(g) ---> H2O2(ℓ)
H2(g) + 12O2(g) ---> H2O(ℓ)
C(s, graphite) + 2H2 (g) + 12O2(g) ---> CH3OH(ℓ)

By the way, here is the discussion on enthalpy, if you missed it.

(1) Every substance is shown in its standard state. This is the physical state (solid, liquid, or gas) that a substance would be in under standard conditions. Thus, the standard state for carbon is solid, for water is liquid and for hydrogen is gas. Why? Because at 1.00 atm. and 25 °C, these substances are in the physical state specified.

You need to know the specifics of a substance's standard state, but it is not something that gets taught. You just sorta absorb it. For example, the standard state for carbon is graphite (remember, a solid), not diamond!!! The standard state for the element bromine (Br2) is liquid and iodine (I2) is solid. You will need to pick up these facts on your own in most classes. One hint: there will be a table of standard enthalpies of formation somewhere in your text. Examine the various compounds and elements for (s), (l), and (g) markings, as well as (aq).

Also, please note that for many elements, the standard state is monoatomic. For example, Cu(s) or Hg(l). (Yes, the standard state for mercury is liquid.). However, there are some elements for which the standard state is diatomic (H2 and Cl2 are two of the seven diatomics, with two others in the previous paragraph.). There is also P4 and S8 (which are not diatomic, but you get the point).

An example: the enthalpy of formation for Br2 in its standard state is zero. The enthalpy of formation for Br (monoatomic gas) is 111.881 kJ/mol. This is because Br (monoatomic gas) is not bromine in its standard state. Only Br2 (diatomic liquid) is.

(2) There is never a compound on the reactant side, only elements. What is being written is a formation reaction. Look again at the definition of formation. Here is an example of a chemical reaction that IS NOT a formation reaction:

6CO2(g) + 6H2O(ℓ) ---> C6H12O6(s) + 6O2(g)

Here is the formation reaction for C6H12O6:

6C(s, graphite) + 6H2(g) + 3O2(g) ---> C6H12O6(s)

Once again, a formation reaction involves making a substance from its elements and ONLY the elements.

(3) Formation reactions sometimes are "fake" reactions, in that they cannot possibly happen as written. For example:

H2(g) + O2(g) ---> H2O2(ℓ)

is simply not possible. You can't make hydrogen peroxide by reacting hydrogen and oxygen directly. When you do that, you ALWAYS get water. Hydrogen peroxide is made a different way, but you can still write the formation reaction. And it is still useful, as you will see.

The symbol for the standard enthalpy of formation is:

$\text{ΔH}{\text{}}_{f}^{o}$

All chemical reactions involve a change in enthalpy (defined as the heat produced or absorbed during a reaction at constant pressure). The symbol for the change is ΔH. The subscripted "f" is taken to mean formation when used in the thermochemistry area. (There are other uses of a subscripted "f," however the differences in context will be obvious.) The symbol "°" is taken to mean "standard conditions." (Yes, I know that symbol is also used for degrees Celsius. Context is all important!!!!)

Exothermic chemical reactions will have a negative ΔH and endothermic reactions have a positive ΔH. The reason for the sign convention has to do with chemistry's viewpoint of the system and the surroundings.

What all this means is that EACH formation reaction has an enthalpy change value associated with it. (Notice I discuss enthalpy changes, since absolute enthalpy values for a given substance cannot be measured.) For example, here is the formation reaction for carbon dioxide:

C(s, graphite) + O2(g) ---> CO2(g)

The product(s) have some unknown absolute enthalpy value (call it H2) and the reactant(s) have another value (also unknown), called H1. Even though those two values cannot be measured, we can measure the difference (H2 minus H1 is called ΔH) in an experiment using a calorimeter.

These experiments have been repeatedly carried out over a number of years by a variety of professional chemists. The values have been checked and rechecked and are now tabulated in reference sources. For example, here is a link to obtain the standard enthalpy of formation for carbon dioxide.

By the way, standard enthalpies of various substances are still being determined. Here is an example from 2007. Values of this type remain in the professional literature and are incorporated into future editions of standard reference sources.

Another typical source for these values is in an appendix to a textbook. However, when you examine one, you will see that only the substance and the value are listed. For example, the Ag2S(s) value in one textbook is −32 kJ/mol. Two points:

(1) The equation is never listed, since "formation" means something very specific: making the substance directly from the elements. This would be the formation reaction for Ag2S (s):
2Ag(s) + 18S8(s) ---> Ag2S(s)

(2) Textbook values will differ, depending on which set of past experiments were used to compile the reference source used by the textbook author. The different values tend to be fairly close. As a student, make sure to use the values provided by your teacher and not try to make these differences be an issue.

The standard enthalpy of formation for an element in its standard state is ZERO!!!! Elements in their standard state are not formed, they just are. So, $\text{ΔH}{\text{}}_{f}^{o}$ for C (s, graphite) is zero, but the $\text{ΔH}{\text{}}_{f}^{o}$ for C (s, diamond) is 2 kJ/mol. That is because graphite is the standard state for carbon, not diamond.

Practice Problems

(1) Identify the standard state (solid, liquid or gas) for the following elements:

(a) bromine
(b) sodium
(c) nitrogen
(d) mercury
(e) phosphorus

(2) Phosphorus comes in three allotrophic forms: red, white and black. Which one is the standard state?

(3) This question uses the NIST Chemistry WebBook. What is the value (use the first one given) for the standard enthalpy of formation, $\text{ΔH}{\text{}}_{f}^{o}$, for the following substances:

(a) Ethyl alcohol, C2H5OH
(b) Acetic acid, CH3COOH
(c) sodium chloride, NaCl

Warning, there is a trick in 3c.

(4) Write the full chemical equation of formation for the substances in question 3.