Free energy of formation | Applications of thermodynamics | AP Chemistry | Khan Academy

• [Instructor] Free energy is symbolized by G. And the change in free energy is delta G. When there's a subscript of F, this is talking about the change in the free energy of formation, which refers to the change in the free energy for the formation of one mole of a substance from its elements in their standard states.

These superscript naught refers to the fact that the substances are in their standard states. By convention, the standard change in free energy of formation for an element and its standard state is equal to zero. Therefore, if we think about forming one mole of oxygen gas, we would be making it from elemental oxygen, which is also oxygen gas.

So forming one mole of oxygen gas from one mole of oxygen gas means there will be no change and therefore the standard change in free energy of formation is equal to zero. Textbooks often tabulate data for standard change in free energy of formation of substances at 25 degrees Celsius. However, it doesn't have to be that temperature. The units are in kilojoules per mole.

We've already seen that the standard change in free energy of formation for an element is equal to zero. Therefore, for elemental oxygen, O2, delta G naught is equal to zero. And for carbon in the solid state in the form of graphite, delta G naught is also equal to zero. The value for carbon monoxide is not equal to zero.

Delta G naught is equal to negative 137.2 kilojoules per mole. So if we think about forming one mole of carbon monoxide from its elements, carbon monoxide is composed of carbon and oxygen. And the elemental form of oxygen is O2 gas and the elemental form of carbon is the solid form in graphite.

So this value for the standard change in free energy of formation of carbon monoxide is talking about the change in free energy for the formation of one mole of carbon monoxide from its elements in their standard states. Standard changes in free energy of formation of substances are useful because they can be used to calculate the standard change in free energy for a chemical reaction.

The standard change in free energy of a chemical reaction is equal to the sum of the standard change in free energy of formation of the products and from that, you subtract the sum of the standard change in free energy of formation of the reactants. For our reaction, let's look at the synthesis of ammonia gas from nitrogen gas and hydrogen gas.

Our goal is to calculate the standard change in free energy for this reaction at 25 degrees Celsius. First, we need to think about our products. For this reaction, we have only one product, and that's ammonia. Notice how there's a two as a coefficient in front of ammonia in the balanced equation.

So we would need to look up the standard change in free energy of formation of ammonia at 25 degrees Celsius. And because this value is per mole of ammonia, we would need to multiply it by two because we have two moles in our balanced equation. Next, we think about our reactants.

And we have two reactants, nitrogen and hydrogen. And we need the sum of their standard changes in free energy of formation. So we would write the standard change in free energy of formation of nitrogen. And because there's a one in our balanced equation, we multiply that value by one, and to that, we add the standard change in free energy of formation of hydrogen gas.

And since we have a three in our balanced equation, we would multiply that by three. So going back to ammonia, the standard change in free energy of formation is equal to negative 16.5 kilojoules per mole, multiply that by two moles, and the moles will cancel out. For nitrogen and hydrogen, those are both elements in their standard states, and therefore their standard free energy of formations are equal to zero.

So this is just zero plus zero. So the standard change in free energy for this reaction is equal to negative 33.0 kilojoules at 25 degrees Celsius. Standard state for a gas refers to the pure gas at a pressure of one atmosphere.

So we think about all three of our gases at a partial pressure of one atmosphere at a temperature of 25 degrees Celsius. The standard change in free energy for this reaction is negative 33.0 kilojoules. Since the change in free energy is negative, that tells us the reaction is thermodynamically favorable in the forward direction.

So nitrogen and hydrogen will react together to form more ammonia. Textbooks often give the units as kilojoules for the standard change in free energy of a chemical reaction. However, sometimes you also see kilojoules per mole of reaction.

Per mole of reaction simply refers to how the balanced equation is written. And here we have the formation of two moles of ammonia. So we can write a conversion factor of two moles of ammonia per one mole of reaction. For standard free energies of formation, the units are kilojoules per mole of the substance.

So in this case, it's negative 16.5 kilojoules per mole of ammonia. So moles of ammonia would cancel out, which gives kilojoules per mole of reaction for the units.