Page 51 - Bruno Linder Elementary Physical Chemistry

August 18, 2010 11:36 9in x 6in b985-ch05 Elementary Physical Chemistry

36 Elementary Physical Chemistry

etc. and thus the dimensions are the dimensions of energy or Joules
per mole. Any combination with stoichiometric coefficients, as in the
reaction free energies or enthalpies, will produce values of units J/mol.
To obtain the real dimensions of free energies or enthalpies, one should
usemolenumbers, n i , instead of stoichiometric numbers, such as
0
0
ν i. Considering that n i = ν I mol ,where mol is the unit mol, it
follows that to obtain energy dimensions in J, all that is needed is
multiplication of the final molar quantities by the unit mol.

The standard free energy can be obtained from the standard enthalpy
o o
of formation, ∆H , and the standard entropy, S , or from the standard free
f
o
energy of formation,∆G , listed in many handbooks.
f
o
Example 5.1. Find ∆G for the reaction
3O 2 (g) → 2O 3 (g)at298.15 K. (5.11)
o
o
1) From ∆H and S ,
o
o
o
∆H =2∆H (O 3) − 3∆H (O 2 ) (5.12a)
f f
=2 × 142.7 − 3 × 0 = 285.4kJ
o
o
o
∆S =2S (O 3) − 3S (O 2) (5.12b)
=2 × 238.93 − 3 × 205.14 = −137.56 JK −1
o
o
∆G =∆H − T ∆S o (5.12c)
= 285.4 kJ + 298.15 × 137.56/1000 kJ
= (285.4+ 41.0) kJ = 326.4kJ
2) From ∆G o
f
o o o
∆G =2∆G (O 3 ) − 3∆G (O 2) (5.13)
f
f
f
=(2 × 163.2 − 0) = 326.4kJ
Note that the sign of ∆G is positive, and according to what was said
before, the reaction as written cannot proceed spontaneously. The reverse
reaction, O 3 → O 2 , on the other hand, has a negative ∆G and can proceed
spontaneously. This is indeed happening in the upper atmosphere, where
ozone is converted to oxygen.