### Enthalpy

This concept involves a fair amount of very precise, very carefully phrased terminology. It seems that every word used in a definition must then also be defined and then those words have to be defined

If that's not enough, the concepts themselves are abstract and many are definable only in terms of mathematical equations. If you're not really careful, you can get bogged down real fast.

What I'm going to do is work through a series of equations to wind up at a very important quantity called enthalpy. A very, very important consideration is that everything below happens at a constant pressure. The calorimeter used to measure the changes described has an opening to the atmosphere and is not, I repeat NOT sealed.

So, here we go:

We define U = the total internal energy of a system.

Some books use E in place of U.

At some point in time, the total internal energy equals U1 and at some different point in time, it equals U2. So that then means, the change (over this time interval) in the total internal energy of the system, ΔU, is:

ΔU = U2 - U1

a) energy - the ability to do work or produce heat.
b) work - a force acting over distance
c) heat - a transfer of energy due to temperature differences.
d) temperature - a property directly proportional to the random motions of particles in a substance

Please note we are using the absolute temperature scale only. Also, what in the world is "the system?"

Let's consider ΔU for a moment. It is some amount of energy that happens to be the difference between two other energy amounts. According to the definition above, energy has only two components: heat and work. This allows us to write:

ΔU = q + w

q is the standard symbol for heat and w for work. Here is the next equation on the way to enthalpy:

U2 - U1 = q + w

Hopefully that's pretty simple.

The next step is a consequence of the system being at constant pressure. Because of this, the chemical system can carry out what is called "PV work." (Remember, the symbol for work is "w.") Consequently we write:

U2 - U1 = (q)p - PΔV

or

U2 - U1 = (q)p - P(V2 - V1)

(q)p stands for the heat flow at constant pressure.

Rearranging gives:

U2 - U1 + PV2 - PV1 = (q)p

and then:

(U2 + PV2) - (U1 + PV1) = (q)p

Now we get to define enthalpy. It is H = U + PV.

Substituting into the above equation, we have:

H2 - H1 = (q)p

or

ΔH = (q)p

The change in enthalpy of the system is the heat transferred from surroundings to system in a constant pressure process. It has the energy unit of Joules. Note that at constant volume (q)v = ΔU, not ΔH.