Page 180 - Physical Chemistry

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Standard Entropy of Reaction Section 5.8
For a reaction with stoichiometric numbers n , the standard entropy change is Standard Gibbs Energy of Reaction
i
¢S° a n S° m,T,i (5.36)
T
i
i
which is similar to H° n H° [Eq. (5.3)]. Using (5.36), we can calculate S°
i i m,i 298
from tabulated conventional entropies S° .
m,298
Differentiation of (5.36) with respect to T and use of (
S /
T) C /T
i P P,i
[Eq. (4.49)], followed by integration, give (Prob. 5.38)
T 1
¢S° ¢S° T 2 ¢C° P dT (5.37)
T
T 2
T 1
which enables S° at any T to be calculated from S° . Note that (5.37) and (5.19)
298
apply only if no species undergoes a phase change in the temperature interval.
EXAMPLE 5.8 S°for a reaction
Use data in the Appendix to find S° for the reaction 4NH (g) 3O (g) →
298 3 2
2N (g) 6H O(l).
2 2
Substitution of Appendix S° values into (5.36) gives
m,298
¢S° >3J>1mol K24 21191.612 6169.912 41192.452 31205.1382
298
582.53
Gases tend to have higher entropies than liquids, and the very negative S° for
this reaction results from the decrease of 5 moles of gases in the reaction.
Exercise
1
Find S° for 2CO(g) O (g) → 2CO (g). (Answer: 173.01 J mol 1 K .)
298 2 2

5.8 STANDARD GIBBS ENERGY OF REACTION
The standard Gibbs energy (change) G° for a chemical reaction is the change in
T
G for converting stoichiometric numbers of moles of the separated pure reactants, each
in its standard state at T, into the separated pure products in their standard states at T.
Similar to H° n H° [Eq. (5.3)], we have
T i i m,T,i
¢G° a n G° m,T,i (5.38)
T
i
i
If the reaction is one of formation of a substance from its elements in their reference
forms, then G° is the standard Gibbs energy of formation G° of the substance.
T f T
For an element in its reference form at T, G° is zero, since formation of an element
f T
from itself is no change at all. Recall from Sec. 4.5 that G is physically meaningful
only for processes with T 0. The same reasoning that gave H° n H°
T i i f T,i
[Eq. (5.6)] shows that
¢G° a n ¢ G° T,i (5.39)*
i
T
f
i
How do we get G°values? From G H TS, we have G H T S for
f
an isothermal process. If the process is the formation reaction for substance i, then
¢ G° ¢ H° T ¢ S° T,i (5.40)
f
f
T,i
T,i
f