CHAPTER 11 REACTIONS AND OTHER CHEMICAL PROCESSES
11.4 ENTHALPIES OFSOLUTION ANDDILUTION 327
same before and after the process. Themolar integral enthalpy of dilutionis the ratio of
ÅH(dil) and the amount of solute in the solution. For a dilution process at constant solute
amountnBin which the molality changes fromm^0 Btom^00 B, this book will use the notation
ÅHm.dil,m^0 B!m^00 B/:
ÅHm.dil,m^0 B!m^00 B/DÅH(dil)
nB(11.4.8)
The value ofÅHm.dil,m^0 B!m^00 B/at a givenTandpdepends only on the initial and final
molalitiesm^0 Bandm^00 B.
There is a simple relation between molar integral enthalpies of solution and dilution,
as the following derivation demonstrates. Consider the following two ways of preparing a
solution of molalitym^00 Bfrom pure solvent and solute phases. Both paths are at constantT
andpin a closed system.
Path 1: The solution forms directly by dissolution of the solute in the solvent. The en-
thalpy change isnBÅHm.sol,m^00 B/, where the molality of the solution is indicated in
parentheses.
Path 2: Starting with the unmixed solvent and solute, the solute dissolves in a portion of
the solvent to form a solution of compositionm^0 B(more concentrated thanm^00 B). The
enthalpy change isnBÅHm.sol,m^0 B/. In a second step of this path, the remaining pure
solvent mixes with the solution to dilute it fromm^0 Btom^00 B. The enthalpy change of the
second step isnBÅHm.dil,m^0 B!m^00 B/.
Since both paths have the same initial states and the same final states, both have the same
overall enthalpy change:
nBÅHm.sol,m^00 B/DnBÅHm.sol,m^0 B/CnBÅHm.dil,m^0 B!m^00 B/ (11.4.9)or
ÅHm.sol,m^00 B/DÅHm.sol,m^0 B/CÅHm.dil,m^0 B!m^00 B/ (11.4.10)
Equation11.4.10is the desired relation. It shows how a measurement of the molar integral
enthalpy change for a solution process that produces solution of a certain molality can
be combined with dilution measurements in order to calculate molar integral enthalpies of
solution for more dilute solutions. Experimentally, it is sometimes more convenient to carry
out the dilution process than the solution process, especially when the pure solute is a gas
or solid.
11.4.3 Molar enthalpies of solute formation
Molar integral enthalpies of solution and dilution are conveniently expressed in terms of
molar enthalpies of formation. The molar enthalpy of formation of a solute in solution is
the enthalpy change per amount of solute for a process at constantT andpin which the
solute, in a solution of a given molality, is formed from its constituent elements in their
reference states. The molar enthalpy of formation of solute B in solution of molalitymB
will be denoted byÅfH(B,mB).
As explained in Sec.11.3.2, the formation reaction of a solute in solution does not
include the formation of the solvent from its elements. For example, the formation reaction
for NaOH in an aqueous solution that has 50 moles of water for each mole of NaOH is
Na(s)C^12 O 2 (g)C^12 H 2 (g)C 50 H 2 O(l)!NaOH in 50 H 2 O