Physical Chemistry , 1st ed.

we make the approximation that His constant over small temperature ranges,
we can use equation 4.44 to approximate Gat different temperatures, as the
following example illustrates.

Example 4.11

By approximating equation 4.44 as



TG

p^ H

T

(^1) 
predict the value ofG(100°C, 1 atm) of the reaction
2H 2 (g) O 2 (g) →2H 2 O ()
given that G(25°C, 1 atm) 474.36 kJ and H571.66 kJ. Assume
constant pressure and H.
Solution
First, we should evaluate (1/T). Converting the temperatures to kelvins, we
find that

T

1



37

1

3K



29

1

8K

0.000674/K

Using the approximated form of equation 4.44:

p^ 571.66 kJ





T

G

0.386 

k

K

J



Writing (G/T) as (G/T)final(G/T)initial, we can use the conditions

given to get the following expression:

 37



3

G

K



final



 4

2

7

9

4

8

.3

K

6kJ



initial

0.386 

k

K

J



GfinalG(100°C)450. kJ

This compares to a value of439.2 kJ obtained by recalculating H(100°C)

and S(100°C) using a Hess’s-law type of approach. The Gibbs-Helmholtz

equation makes fewer approximations and would be expected to produce

more accurate values ofG.

What is the relationship between pressure and G? Again, we can get an ini-
tial answer from the natural variable equations:



G

p



T

V

We can rewrite this by assuming an isothermal change. The partial derivative
can be rearranged as
dGV dp

We integrate both sides of the equation. Because Gis a state function, the in-
tegral ofdGis G:

G

pi

pf

V dp

TG



0.000674/K

4.7 Focus on G 107