# Calculating Energy and Enthalpy

We have already discussed the fact that we must use reference states in order to get numerical values for the energy and enthalpy (since we can not know the actual numbers!). This didn't bother us since we are only interested in differences in these quantities (so that the reference state that we choose cancels out!).

We will assume that we have "ideal mixtures" in all cases! (That means that the total energy or enthalpy of a mixture will be equal to the sum of all of the component's energy/enthalpy.)

NOTE

This is not strictly true! In fact, it is only a good approximation for gas mixtures or mixtures of similar liquids. We will not get a chance to talk about energy/enthalpy of mixing, but it is a simple way to alleviate our assumption.

### Fictitious Paths

Since we know that the Energy depends on:

• Temperature
• State of Aggregation (phase)
• Chemical Composition

and we know that H = U + PV, then H depends on all of these as well as P.

So, there are four things (\$\Delta T\$, \$\Delta P\$, phase change, rxn) that may cause a change in energy or enthalpy.

NOTE

You are already familiar with the "heat" (change in enthalpy) involved in changing the state of aggregation (Latent Heat of vaporization, for example)

We will talk ahout changes in chemical composition in a few lectures.

We need to deal with changes in T and P

So in order to calculate enthalpies or energies, we need to determine the changes that occur as we move fromour (required!) reference state to our actual state.

Let's consider a simple example:

Is there a reason we should choose one of these paths over the other?

NOTE

When we calculate energies or enthalpies we need to choose a path (perhaps ficticious, but whichever is easiest!) that represents the changes that the substance undergoes.

Our ideal fictitious path can be decomposed into the smallest number of steps that are each of 1 of the following several types: a change in T (at constant P and constant phase), a change in P (at constant T and constant phase), and phase changes (again, we will consider reactions later).

OUTCOME:

Generate "fictitious paths" from your reference state to your desired state

TEST YOURSELF

Develop a path for calculating the enthalpy of steam at 200C and 1.5atm relative to a reference state of ice at -10C and 1 atm. How about internal energy?