Lecture Notes from CHM 1341
16 July 1996

Thermochemistry

Energy and Enthalpy

While thermodynamics arose from studies of real engines turning heat into work, it is now explained in terms of statistical expectations of the averaged states of Avogadro's Number of systems. But even with this microscopic justification (about which you'll learn more in a thermodynamics course), it is still quite useful to understand the macroscopic (real world scale) consequences first.

For example, the First Law of Thermodynamics tells us that energy is neither created nor destroyed but simply transformed from one form to another. Thus, for example, real engines turn some fraction of the heat from some rich source (combustion, perhaps) into work, another form of energy, and wasted heat dispersed into the environment.

Thermodynamics is rather precise about what constitutes the system, its environment (the surroundings...that is, the rest of the universe!), and the intercourse between them. If neither energy nor material flow between them, the system is isolated. If matter cannot be exchanged but energy can, the system is closed in the same sense that a sealed can of soda pop will react to increasing its temperature and still remain closed until the pressure of the contents becomes too high. Then the can becomes an open system rather abruptly, spraying everyone nearby with root beer or whatever.

The reason you want to study it is not only to secure yourself from a root beer dowsing but also to be able to (a) predict the energy flows during a chemical reaction by knowing the energy content of all the compounds and (b) predict not only the direction (forward or backward) of spontaneous reaction but also its stopping point (equilibrium). It will be CHEM II before we make the connection to equilibrium concentrations of species, but the rest we can start here.

ENERGY

"Dynamics" implies change. So "thermodynamics" implies change in heat (and other forms of energy). These changes are macroscopic, measurable, significant, and symbolized by the Greek capital letter delta. Delta isn't available on the Web (don't ask), so we're going to symbolize is with its English counterpart "d" even though mathematicians usually use little "d" to imply a tiny differential; for the purposes of this Web exposition, it'll mean a "difference." Thus "dE" means a difference in energy...final energy less initial energy...that sort of thing.

In particular, we'll usually focus on the changes in the energy (or other properties) of the SYSTEM and less often on its SURROUNDINGS, even though the surroundings are often the source of the energy input or the sink for energy output.

The "internal energy" means the energy of the system...the reaction that we're studying, perhaps. The collection of reactants and products may during the course of a reaction evolve heat which the surroundings absorb; they may also expand, as in the evolution of a gas, for example, and in so doing, push back the ambient atmosphere.

That pushing against atmospheric force (pressure) implies that the system is doing work. We would expect its energy level to fall if it's doing work as readily as it falls if it's passing off heat.

But the definition of internal energy change is usually made by considering the heat supplied to the system by its surroundings and the work done on the system by the surroundings. Both of those should cause the system's energy to rise as:

      dEsystem  =  qin + won

Physicists are enamoured of internal energy because they like to deal in systems in fixed volume which can neither expand or contract. Thus they can neither do nor receive work. Internal energy simplifies then to:

     dEsystem   =  qV     where the V subscript means fixed volume

ENTHALPY

Chemists, on the other hand, are a tad more practical. They know that they're most often doing chemistry in open vessels where "pressure/volume" work can be done. So they've defined a quantity which has energy units, all right, but incorporates all relevant work into itself so there's no separate "work" entry in its tables. It's called enthalpy, and it's defined as:

     dHsystem   =  qP     where the P subscript means fixed pressure

Not surprisingly, the two are related by the pressure volume work...which we'd better define. You remember from physics that work is done when a force is opposed through a distance, w = f dx. But we're imaging work done moving a piston (of area A) against a pressure P. Since P = f/A, then f = PA, and the work becomes w = PA dx = P d(Ax) = P dV and thus acquires the name pressure-volume work.

The relation between internal energy and enthalpy is thus:

     dHsystem = dEsystem + PdV

or
     H = E + PV

Indeed, we'll be dropping the system subscript pretty routinely in future, and it will just be understood that if it's gone, the variables still refer to the system.

What's amusing is that even chemists turn to the physicist's closed containers to measure enthalpy (by measuring internal energy and adding PdV). Such devices are called bomb calorimeters. And, no, they aren't supposed to do what their name implies. Instead they are isolated systems consisting of small reaction samples and a heat "bath" to absorb (or supply) heat as needed. The amount absorbed (or supplied) is calculated by reading a thermometer and knowing the heat capacity of the bath.

The heat capacity of an entity is the amount of heat, in kJ say, to raise its temperature one degree Kelvin (or Centigrade which amounts to the same thing). For water, for example, the value is exactly 4.184 J per gram per degree, in fact, that's the definition of the calorie; 1 cal = 4.184 J. So knowing the mass of water in the bath, we know how much heat it takes to generate the observed temperature change. The negative of that tells us the internal energy change, dE, in the sample undergoing reaction.

The complete energy (or enthalpy) content of a system is something of an irrelevancy; all we really want to know is how energies change during reactions. Were we nuclear physicists, we'd want to know how much some atom was worth before it split into two or more others, but as chemists, our atoms never disappear like that.

So E=mc² may give us the complete energy content, but that's meaningless.

As chemists, we want to measure energy relative to some convenient standard we can get our hands on, like the elements, say. If we knew what it took to form any compound from its elements, then differences in those enthalpic values between products and reactants would tell us how much enthalpy would be released (exothermic) or absorbed (endothermic) during the reaction. That difference is called the Standard Reaction Enthalpy, and it only has meaning for the way the reaction is written; that is, if we double all the stoichiometric coefficients, we imply twice as many moles of reactions, and the Standard Reaction Enthalpy would double correspondingly.

That means that enthalpy (and energy and moles and volume...but not temperature, for instance) are extensive variables, they scale with the amount. What's even more advantageous is that they are also State Variables which means that no matter how many processes the system undergoes, if it is brought back to the same conditions, the State Variables haven't changed.

There are entities which are not State Variables; q and w are examples, but q + w is dE, and it cares not how it arrived at any given state: it will still give the same value.

HESS'S LAW

An excellent example of the consequences a state variable is Hess's Law which justifies the use of Enthalpies of Formation from the Elements in Standard Reaction Enthalpy calculations:

     Elements:          2N2   +    2 H2    +    6 O2    (always 0 kJ)
                     ___________________________________
                                         |    |
-350.8 kJ: 4 NO2(g) + O2(g) + 2 H2O(g)   |    |
_________________________________________|    |
    Reactants                                 |
                                              |
dH°= (-696.4)-(-350.8)= -345.6 kJ             |   4 HNO3(l) -696.4 kJ
                                              |_____________________
                                                 Products

These values come from tables of dHf°, Standard Enthalpies of Formation.

The enthalpy levels of the reactants in this oxidation of nitrogen dioxide in a moist atmosphere to make nitric acid were taken from Gillespie's Table 9.1, p. 312. An only slightly more extensive table is given in the appendix C7; if you need more compounds, try the Handbook of Chemistry and Physics or the JANAF (Joint Army, Navy, Air Force) thermodynamic tables.

The difference in energy level between the products and the reactants is the Standard Reaction Enthalpy, -345.6 kJ for the reaction as written. The little superscript "o" on dH° means that "standard conditions" were assumed: 1 atmosphere pressure and 25 degrees Centigrade (Celsius). This is because enthalpy increases with temperature just as does energy; so a convenient standard temperature has been chosen.

Note the difference between STP and "standard conditions," namely, STP's temperature is water's freezing point (as close as matters) while standard conditions' temperature is near room temperature.

This reaction is a bit pathological in that 7 moles of gas have disappeared to be replaced by 4 moles of liquid. Thus the pressure volume work might be imagined to be impressive. If all the gases were ideal, -PdV = -dn RT, where dn=-7; so -PdV = 7(0.0821 J/mol K)(298 K) = 171 J = 0.171 kJ...hmmm...only 0.05% of the total standard dH.

Hess's Law would work regardless of the reference set...we could've used atoms. Then instead of mentally gutting all reactants back to their elements and reconstituting them as products, we could imagine decomposing them to their very atoms.

This sort of thinking leads to calculation of standard reaction enthalpies from bond enthalpies, but this is definitely NOT a safe approach. The reason is that tables of bond energies tabulate only average bond energies over the many bonding situations in which bond pairs might find themselves. The trivial counterexample is that

CH4 -----> H + ( CH3 -----> H + ( CH2 -----> H + ( CH  -----> H + C )))

Each successive H removal from methane is harder than the last, yet a tabulated C-H bond enthalpy (call "bond energies" erroneously in Table 9.2) is only an average over them all. Calculation of reaction enthalpies this way wouldn't even be more rigorous if one used the actual dissociation energies from each molecule, because the order of pulling off the atoms would influence the bond enthalpies obtained!

Still, if one needs an estimate for dH for gaseous reactions (bond enthalpies don't know about solid or liquid enthalpies), dH becomes the sum of reactant bond enthalpies less the sum of product ones. That's the reverse of the case for enthalpies of formation from the elements since in the latter, the molecules of interest are on the right side of a formation equation while the former has the molecules of interest on the left side of a bond dissociation equation. And reversing the direction of a reaction reverses the sign of its enthalpy.

Chris Parr
University of Texas at Dallas
Programs in Chemistry, Room BE3.506
P.O. Box 830688  M/S BE2.6 (for snailmail)
Richardson, TX  75083-0688

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