Page 35 - Basic physical chemistry for the atmospheric sciences

Chemical thermodynamics 2 1

where dQ is the heat added to the system, dU the increase in internal
energy of the system, and pdV the work done by the system when
its volume increases by dV. For the air parcel dQ = 1 0 7 J and
(
pdV = 1 . 0 1 3 x 1 0 5)(22) = 0.22 x 1 0 7 J. Therefore,
1
-
=
dU = d Q - pdV = 0 7 0 . 2 2 x 1 0 7 7 .8 x 1 0 6 J
If the molecules in the air exer< no forces on each other, the internal
energy of the air must consist entirely of the kinetic energy of the
molecule , that s , on the temperature of the air. 1 From the definition
i
s
of cp. the energy required to raise a mass m of a system by !l. 'I' C
at constant pressure is mc P !l.T. Hence, dU = mc P !l. T or !l.T= dU!mc .
p
1
Substituting dU = 7 . 8 x 1 0 6 J , m = S x 1 0 3 kg and cP = 0 0 4 J deg-1 kg-1 t
i n to this expression yields the temperature rise of the air parcel,
namel , !l. T= 0.97°C.
y
2.2 Enthalpies of reaction and formation
If the temperature is kept constant, changes in the concentrations of
chemical species or changes in the volume or pressure of a system do
not change the equilibrium constants Kc or K . However, changes in
P
temperature do change the equilibrium constants. These changes can
be represented by
fi
( - !l. � x)
K = Aexp (2. 1 3 )
R * T
where SH?-x is called the molar standard enthalpy (or heat) o f reac­
tion, R* is the universal gas constant, and T is the temperature (in K) .
A and tl.mx are constants (over a reasonable temperature range) for
any given chemical reaction. The line above the H indicates that the
molar amounts of the reactants and products given by the numerical
coefficients in the balanced chemical equation are involved. The su­
perscript zero to H indicates that the reactants and products must be
in their standard states, which are generally defined to be the chemical
2
forms most stable at l atm and 25°C. For the forward reaction of the
general chemical reaction l .5), tl.mx is given by
(
tl.mx = [g !l. ll? (G) + h tl."l( H ) + . . . ­
J
[a tl.ffl(A) + b tl.ffl(B) + . . . ] (2. 1 4 )
where tl."l(X) is the difference in enthalpy between one mole of
l:Ompound X in its standard state and its elements in their standard