Page 105 - Essentials of physical chemistry

The First Law of Thermodynamics 67

CALORIMETRY AND THERMOCHEMISTRY

Now that we have analyzed some hypothetical applications of the first law of thermodynamics we
should ask how these principles apply to chemistry and chemical reactions. The key concept is that
elements react to form compounds, presumably to form lower energy situations, but that is not
always the case as we will see in the next chapter. Even so, most reactions do result in a lower
energy. Since energy is involved, we may think that DU is the key to thermochemistry, but we have
already mentioned that often pressure and=or volume changes occur during a reaction. Even though
these may be small effects, we know that we should work with DH. Thus, a question for an
experimental science like chemistry is ‘‘How can we measure DH?’’ Calorimetry involves mostly
simple mathematics but is really the main part of thermochemistry. Careful measurements of
DH comb are the backbone of thermochemistry.
Chemistry is the science of reactions between elements to form compounds. Physicists can
ponder over the creation of the universe and the big bang theory but chemists start with the
assumption of the existence of elements. Actually heavy elements are formed from lighter elements
such as H and He in the interior of stars and then are distributed throughout space when such stars
explode. Every atom (with the possible exception of hydrogen) in your body was once inside a star.
The convention assumed in thermochemistry is that ‘‘the elements are here and chemistry is the
rearrangements of these elements to form compounds so the energy changes are relative to existing
elements.’’ In the larger picture of science, we know that nuclear chemistry does occur but for the
purpose of chemistry on planet Earth we assume that the energy of formation of elements in their
most abundant form is zero! (For some elements we use the most abundant form such as graphite
for carbon.) We further specify a ‘‘standard state’’ for the element at 1 bar pressure and
0
0
DH (1 bar, 298:15 K) 0; older texts used the slightly different value as DH (1 atm,

f f
298:15 K) 0. Older texts standardize on 1 atm pressure but the newer units specify 1 bar,

which is very close to 1 atm (1 atm ¼ 1.01325 bar). The standard state is a very important
convenience so that we can tabulate the energy changes of reactions of elements to form compounds.
Another convenience on planet Earth is that our atmosphere has a lot of oxygen that is second
only to fluorine in electronegativity; it is very reactive as firemen know all too well. Thus, almost
any material will react with oxygen and give off a measurable amount of heat. This type of
measurement is called combustion calorimetry and requires a special piece of equipment based on
a high-pressure reaction container. One minor consideration in the use of a closed container is that
the energy change is measured as DU ¼ C V DT but we want DH. In Figure 4.4 [9], we see the cross
section of the total calorimeter device.
The smaller container in the center of the diagram is a heavy stainless steel reaction chamber
(Figure 4.5) [9] with thick walls and a screw-type lid with a rubber gasket so that it can be
pressurized to about 30 atm of pure O 2 along with a small sample of about 0.5 g (carefully weighed).
There is also a simple direct current electrical connection to provide ignition of the sample in the
oxygen and many materials will ignite in pure O 2 . A carefully measured amount of water (usually
2000 mL) surrounds the combustion vessel and is continuously stirred with a small propeller. In
addition, the ‘‘water bucket’’ containing the reaction vessel is within a double-walled fiberglass
container providing about 1 in. of insulating air space to further isolate the combustion reaction in a
thermal sense. The main data are obtained from a very precise thermometer in the water as to the DT
for the increase in temperature from the heat of the reaction in the sealed pressure container.
Usually, this special thermometer covers the range of about 208C–358C in small increments of
0.028. Note the heat given off by the reaction chamber is absorbed by the 2000 mL of water, so there
is a sign change in the heat flow. Next we address the small correction to convert a DU value to a
DH value using the definition DH ¼ DU þ D(PV) and D(PV) (Dn gas )RT ave , noting that we want
to use the apparatus for a small amount of n moles.
nDH comb ¼ C V DT þ (Dn gas RT ave )n: