Page 339 - Physical Chemistry

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Chapter 10 The convention adopted is that G° of the aqueous H ion is zero at every
f
Nonideal Solutions
temperature:

¢ G° 3H 1aq24 0 by convention (10.85)
T
f

The reaction of formation of H (aq) in its standard state at temperature T and pressure
1 bar P° from H gas in its standard state is
2
1
2 H 1ideal gas, P°2 S H 1aq, m m°, g 12 e 1ss2 (10.86)
m
2

where e (ss) indicates 1 mole of electrons in some particular standard state, which we
shall leave unspecified. Whatever the value of G° for (10.86) actually is, this value
will cancel in calculating thermodynamic-property changes for ionic reactions in
aqueous solutions. The value of G° for (10.86) will not cancel in calculations on
reactions that involve transport of ions from one phase to another, for example, the

reaction H (g) → H (aq), or on half-reactions, for example, (10.86). Hence, the con-
vention (10.85) cannot be used to calculate thermodynamic quantities for ion-transport
reactions or half-reactions. Such reactions are not readily studied experimentally but
can be discussed theoretically using statistical mechanics.
We have d G°/dT S°. Since G° for (10.86) is taken as zero at every tem-

perature, d G°/dT for (10.86) equals zero and S° for the H (aq) formation reaction
(10.86) is zero at every temperature:

¢ S°3H 1aq24 0 by convention (10.87)
f
T
We also have for the reaction (10.86), H° G° T S° 0 0 0. Hence

¢ H°3H 1aq24 0 by convention (10.88)
T
f
In tables of thermodynamic properties of ions, the standard-state entropy and heat

capacity of H (aq) at every temperature are taken as zero by convention:

S° 3H 1aq24 0 by convention (10.89)
T

C° 3H 1aq24 0 by convention (10.90)
P,T

Having adopted conventions for H (aq), we can find thermodynamic properties

of aqueous ions relative to those of H (aq), as follows. Equation (10.44) gives for the
electrolyte i with formula M X in solution: m° n m° n m° , where the molal-
n n i
ity scale is used. Subtraction of G° from each side of this equation and the use of
elem
(10.78) and corresponding equations for the ions gives
¢ G°3i1aq24 n ¢ G° n ¢ G° (10.91)

f
f
f
where G° and G° are G° of the cation and anion in solution. For example,

f

f
f

2
G°[BaCl (aq)] G°[Ba (aq)] 2 G°[Cl (aq)].
T
f
2
f
T
f
T
Similar relations can be derived from Eq. (10.44) for S° and H° (Prob. 10.54):
f

S°3i1aq24 n S° n S° (10.92)

¢ H°3i1aq24 n ¢ H° n ¢ H° (10.93)

f

f

f

q
q
The relation V i n V n V (equivalent to V° i n V° n V° ) was used in
q

Prob. 9.16. In these equations, the standard state for an ion is the fictitious state with
m/m° and g of that ion equal to 1.
m
The properties of the electrolyte i on the left sides of Eqs. (10.91) to (10.93) can
be found experimentally. Observations on the electrolyte H X (aq) together with the
n n

H (aq) conventions give the thermodynamic properties of X (aq) relative to those of
z

H (aq). Observations on M X (aq) then give the properties of M (aq). For exam-
z
n n
ples, see Probs. 10.57 and 10.58.