Page 156 - Physical chemistry understanding our chemical world

INDIRECT MEASUREMENT OF ENTHALPY 123

mol −1 and H O =−1207.13 kJ mol −1 , calculate the value of H r
f (aragonite)
for the transition process:
(3.35)
CaCO 3(s, calcite) −−−→ CaCO 3(s, aragonite)

Why does dissolving a salt in water liberate heat?

Hess’s Law Applied to Ions: Constructing Born–Haber Cycles

Dissolving an ionic salt in water often liberates energy. For example, 32.8kJ mol −1
of energy are released when 1 mol of potassium nitrate dissolves in water. Energy is
released, as experienced by the test tube getting warmer.
Before we dissolved the salt in water, the ions within the crys-
tal were held together by strong electrostatic interactions, which The ‘lattice enthalpy’ is
obeyed Coulomb’s law (see p. 313). We call the energetic sum defined as the standard
of these interactions the lattice enthalpy (see p. 124). We need change in enthalpy
to overcome the lattice enthalpy if the salt is to dissolve. Stated when a solid sub-
another way, salts like magnesium sulphate are effectively insolu- stance is converted
ble in water because water, as a solvent, is unable to overcome the from solid to form
gaseous constituent
lattice enthalpy.
ions. Accordingly, val-
But what is the magnitude of the lattice enthalpy? We cannot
ues of H (lattice) are
measure it directly experimentally, so we measure it indirectly, with
always positive.
a Hess’s law energy cycle. The first scientists to determine lattice
enthalpies this way were the German scientists Born and Haber:
we construct a Born–Haber cycle, which is a form of Hess’s-
law cycle. It is common to see
Before we start, we perform a thought experiment; and, for con-
values of H (lattice)
venience, we will consider making 1 mol of sodium chloride at called ‘lattice energy’.
◦
25 C. There are two possible ways to generate 1 mol of gaseous Strictly, this latter term
Na and Cl ions: we could start with 1 mol of solid NaCl and is only correct when the
+
−
vaporize it: the energy needed is H O . Alternatively, we could temperature T is 0 K.
(lattice)
start with 1 mol of sodium chloride and convert it back to the ele-
ments (1 mol of metallic sodium and 0.5 mol of elemental chlorine gas (for which
O
the energy is − H ) and, then vaporize the elements one at a time, and ionize each
f
in the gas phase. The energies needed to effect ionization are I for the sodium and
E (ea) for the chlorine.
In practice, we do not perform these two experiments because we can calculate a
value of lattice enthalpy H (lattice) with an energy cycle. Next, we appreciate how
generating ions from metallic sodium and elemental chlorine involves several pro-
cesses. If we first consider the sodium, we must: (i) convert it from its solid state to
gaseous atoms (for which the energy is H O ); (ii) convert the gaseous atoms
(sublimation)
to gaseous cations (for which the energy is the ionization energy I). We next consider
the chlorine, which is already a gas, so we do not need to volatilize it. But: (i) we
O
must cleave each diatomic molecule to form atoms (for which the energy is H );
BE