Phase changes
Although phase changes are not chemical reactions, a quantity of heat is still required, for
example, to transform ice at 0 C to water at 0 C. This quantity of heat is called the
enthalpy of fusion:
Similarly, a quantity of heat is needed to transform water at 100 C to steam at 100 C.
This quantity of heat is known as the enthalpy of vaporization:
As an example of the use of heats of fusion and vaporization, consider the following
example:
A sample of copper having a mass of 40.0 g is heated to a temperature of 500 and then
plunged into an ice-water mixture containing 90.0 g of water and 10.0 g of ice at 0 .
The mixture is contained in a closed styrofoam cup, which absorbs a negligible amount
of heat, but maintains the system at constant pressure. Calculate the final temperature of
the system.
Solution: The amount of heat lost by the copper sample goes into melting 10.0 g of ice
and then heating 100.0 g of water to a final temperature measured in
final temperature of the copper sample. Thus, we have an equation:
The number of moles of ice is
Thus,
Substituting the appropriate numbers in yields
.
is also the
Standard-state enthalpies
Absolute enthalpies of substances, like absolute energies, cannot be measured - only
changes in enthalpy can be measured. Thus, it is necessary to have a reference state, just
as it is necessary to establish a reference point for computing potential energies.
The reference state for reaction enthalpies is called the standard state. This is defined as
follows:
1.
For liquids and solids, the standard state is the thermodynamically stable state at a
pressure of 1 atm and a specified temperature. The stable state could be liquid or
solid.
2.
For gases, the standard state is the gaseous state at a pressure of 1 atm and a
specified temperature, based on the assumption of ideal gas behavior.
3.
For dissolved species, the standard state is a 1 M solution at a pressure of 1 atm
and specified temperature, based on the assumption of ideal solution behavior.
Given this definition of the standard state, a scale needs to be defined by arbitrarily
setting the enthalpies of selected reference substances to 0. The choice of reference is the
following: the enthalpies of chemical elements in their standard states at 298.15 K are
defined to be 0. For elements that can exist in several forms, we choose that form which
is most stable at 1 atm and 298.15 K. For example, oxygen can exist as O (g) or O (g).
The former is more stable, so it is defined to have a 0 enthalpy. Carbon can exist as
graphite, diamond, or fullerene. Graphite is the most stable of these at 1 atm and 298.15
K, so it is assigned an enthalpy of 0. For any reaction, the standard state enthalpy is
denoted
.
In order to have useful enthalpy data to tabulate, one more concept is introduced. The
standard enthalpy of formation of a compound is the enthalpy change for a reaction that
produces 1.00 mol of the compound from its elements at 1 atm pressure and 25 . For
example, the standard enthalpy of formation of water is the standard enthalpy of the
reaction:
For species that dissolve into ions in solution, ions of both positive and negative charge
will be produced. Clearly, we cannot measure the enthalpy of formation of ions of only
one type of charge, rather, only the sum of the enthalpies of formation of ions of both
positive and negative charges can be measured. Thus, one more arbitrary assignment
must be made, namely, that the standard enthalpy of formation of
(aq) is 0.
An example of the use of tabulated standard state enthalpies, consider the following:
What is the standard state enthalpy of the reaction
We need to consider this as a two-step process, wherein CO is broken down into its
elements, then these elements recombine to form CO(g). The two steps of the reaction are
It is easy to verify that the sum of these two reactions reproduces the desired reaction
above. In Appendix D of the book, the following standard enthalpies of formation are
given:
Thus, for the reaction we are considering, the standard enthalpy of formation is the sum
of the standard enthalpies of formation for the two individual steps:
As one final consideration of standard state enthalpies, we define the bond enthalpy as
the enthalpy required to break 1 mol of a particular chemical bond in the gas phase. Since
energy is required to break a chemical bond, bond enthalpies are always positive. An
example of a bond enthalpy is the breaking of a C-H bond in methane:
Although the products in this reaction are not stable, i.e., they react quickly with other
molecules, it is possible to produce such reactions in the lab, and study properties of the
products over the period of their brief existence. This, then, is how bond enthalpies are
tabluated. Often, bond enthalpies are tabulated as averages of a particular bond breaking,
e.g. a C-H bond, over many compounds. Given the relative constancy of bond enthalpies
of a particular kind of bond over different molecules, such an averaging is a good
measure of the bond enthalpy one might expect in an arbitrary specific situation.