Enthalpy

So, what is enthalpy? Change in enthalpy is defined as:

which is the sum of change in internal energy minus the work.

We use change in enthalpy usually and not just enthalpy because it is extremely difficult to find the pure enthalpy of a system. It's easier to quantify the energy transfer through the change in enthalpy.

For simplistic terms, enthalpy can also be defined as the total heat content of a system, as that is ultimately defined by the internal energy and the work on the system. So, enthalpy is used interchangeably with heat in many scenarios for this reason.

By the way, if you see the degree symbol ° next to a thermodynamic quantity, it means that that quantity is at standard state(not to be confused with STP). These conditions mean that the pressure is 101325 Pascals, or 1 bar, temperatures at 25 C or 298 K, and 1 M concentrations.

Note that when the change in enthalpy of a process is negative, that process releases energy, meaning it is exothermic. When the change in enthalpy of a process is positive, that process requires energy, meaning it is endothermic.

The internal energy of a thermodynamic system is quite simple. It's simply the total energy of the system. That energy is usually just the kinetic energy of the molecules in that system, which is why internal energy is related to temperature by the equation:

The change in internal energy of a system is defined by the first law of thermodynamics, given by:

Whether or not you believe it, this is one of the most important laws in the universe. How come? Well, let's look at the equation. The equation tells us that the internal energy of a system can only change if work is done on it or if it is heated up.

However, it tells us a more important thing. It tells us that energy can never be destroyed or created, only converted. As you can see, the internal energy of the system only changes when you add energy. This is very different from conventional ideas towards energy. Take friction for example. If you were to roll a ball down a street, friction would eventually stop it. People see this as a system losing energy but in reality, all that's happening is the ball's kinetic energy is being converted to heat due to friction. Therefore, the energy only converted forms, but wasn't created nor destroyed.

The standard enthalpy of combustion is the change in enthalpy when 1 mole of a substance burns/combusts.

Note that standard enthalpy of combustion is for one mole of substance combusted, so other species in the reaction can have fractional stoichiometric coefficients. Obviously, this isn't chemically possible but for the purpose of the enthalpy, it is conventionally used.

The standard enthalpy of formation is the change in enthalpy for when one mole of a substance is formed from elements in their stable states.

This is important because in chemical processes, it may be hard to know how much heat is involved in a reaction, but these quantities help with understanding the efficiencies of many potentially dangerous and impractical chemical reactions.

Note that standard enthalpy of combustion is for one mole of substance formed, so other species in the reaction can have fractional stoichiometric coefficients. Obviously, this isn't chemically possible but for the purpose of the enthalpy, it is conventionally used.

Hess's Law allows us to find the change in enthalpy across entire reactions. There's two forms of it: one of which is very simple and can be shown right now. The first equation that Hess's Law deals with is:

What this equation says is that the standard change in enthalpy of a reaction is the sum of the stoichiometric coefficients of each product times their standard enthalpy minus the sum of the stoichiometric coefficients of each reactant times their standard enthalpy.

For example, let's take the reaction below:

2H₂ + O₂ → 2H₂O

The standard change in enthalpy would be the twice the enthalpy of water minus twice the enthalpy of hydrogen plus the enthalpy of oxygen. In other words:

Now, the other way of looking at Hess's Law is through these rules:

1) If you add or subtract two chemical reactions, you must add or subtract their standard changes in enthalpy, respectively.

2)If you multiply a reaction by a coefficient, you must multiply the reaction's standard change in enthalpy by the same coefficient

These two rules basically state that if you algebraically manipulate a chemical reaction, you must do the same for the reaction's change in enthalpy. This goes the same for entropy and Gibbs free energy

Bond enthalpies are actually quite simple. The bond enthalpy of a given bond is the amount of energy released when the bond is formed/the amount of energy required to break the bond(both are the same, but the energy released is negative while the energy required is positive).

This may be unintuitive because you'd think putting two atoms together requires energy. However, energy is released when atoms form bonds to make molecules because when molecular bonds form, the electrons in atomic orbitals have to go to lower energy molecular orbitals to stabilize. By going to a lower energy, they're losing energy and so that lost energy is released in the form of heat or light.

Similarly, think of breaking a bond like this. Imagine a molecule was a tree, with branches representing bonds between atoms. To break these branches, you need some energy and have to put in effort using a saw to cut it down. This is why breaking bonds is endothermic: you have to manually put in energy to break it.

To find the change in enthalpy given the bond enthalpies, you have to first find how many of each bond type is one molecule of each species. You then sum up the enthalpies for one molecule based on this. For example, if a molecule has hypothetically 2 H-H bonds and 4 C-O bonds, you take twice the bond enthalpy of the H-H bond and add it to quadruple the bond enthalpy of the C-O bonds. You then multiply this by the stoichiometric coefficient of the molecule in the balanced chemical equation. You do this for every species.

Then, lastly, you take the sum of the previous step for the reactants(the bonds being broken) and the products(bonds being formed), and subtract products from reactants.

This is different from just standard enthalpies, which go products minus reactants. You can only do reactants minus products for bond enthalpies

Essentially,