Burdge/Overby, Chemistry: Atoms First, 2e Ch14 | Page 20
SEC TION 14.5 ? Predicting Spontaneity
Ta b le 1 4 .4
589
Predicting the Sign of ?G Using Equation 14.10 and the Signs of ?H and ?S
When ????H is
And ????S is
????G will be
And the process is
Example
Negative
Positive
Negative
Always spontaneous
Positive
Negative
Positive
Always nonspontaneous
3O2(g)
Negative
Negative
Negative when T?S < ?H
Positive when T?S > ?H
Spontaneous at low T
Nonspontaneous at high T
H2O(l)
Positive
Positive
Negative when T?S > ?H
Positive when T?S < ?H
Spontaneous at high T
Nonspontaneous at low T
2HgO(s)
2H2O2(aq)
2H2O(l) + O2(g)
2O3(g)
H2O(s)
(freezing of water)
2Hg(l) + O2(g)
Water freezes spontaneously at temperatures below 0°C, and ice melts spontaneously at temperatures above 0°C. At 0°C, a system of ice and water is at equilibrium. The temperature that divides
“high” from “low” depends, though, on the individual reaction. To determine that temperature, we
must set ?G equal to 0 in Equation 14.10 (i.e., the equilibrium condition):
0 = ?H ? T?S
Rearranging to solve for T yields
?H
T = ___??
?? ?
?S
The temperature that divides high from low for a particular reaction can now be calculated if the
values of ?H and ?S are known.
Worked Example 14.5 demonstrates the use ? \?\ ??X? ??????Y^[\H M ?B?X???[?? ?X?H M ? H ?XX?[? ?[?H ??[?[?\?? H]Y? [\\?] \?\?Y???8?!?[???!??\?H ??]]?K???H ?XX?[?[? ?X?8?!?H NNK?H??[?[?8?!??H
????8?&H[? ]\?Z[?H B?[\\?] \?H
[?0??HX??H ?X? H ?XX?[?\? ??[?[?\???? ?]Y?HH [\\?] \?H ]]?Y\?Y????H??\? H [\\?] \?H] ?X?8?!?H8?!??8?!??H
K?\?Y??K ?H \?H\]X][? M ?L ?X??] ][?? ??8?!??[? ?? ?[???? ?]\?Z[?B?[\\?] \?H[??[ ?[??? ?H [????\? ?Y?Y\??[ ?]\???] \8? ???? ][?? ???8?+??H
8?+??B??
???H???!??H8?"?????????+??"??+??+????????+??"??+??+? ?
????8?&H[???"??+¸?+??"?8?"?8?"??+¸?+??"?B??8?&H[? L ???NNK?H??[???!???????????????UH????+??"??+?H8?+??+¸?"??+¸?"??+?8?+??+¸?+??"?H
NH? ?
????8?&H[???!??OH
NH8?$? ???HH M
????[??X??]]????[?Z] H\??]??Y?HH ?[X\?H?[?\??H
8?!??Z[???Y?]]?JH[??H[?[??X\?H[?[? ?? H
8?!???Z[????]]?JK??[??? ]X[?]Y\?\?H ??]]?K\?[? \??\?K? H H[? ?? H?[??H?]??? ??[?Z] K????[?[??\?ZX? ???\?? ?X?\? \? ?X? ?\]Z\?\? H[? ]?X] ] ??[XZ?H ?[??H ]?Y[??[?HX]?H[??X\?[?? H [\\?] \?H ?[ ?Y? H\]Z[X??][H ? H ?Y? \?XZ?[??]??'[?H ??[?[?\??'B? ?X?X?H ??[HH HH 8? ?H ?XX?[? ?[?H ??[?[?\?? H]?? [\\?] \?\?Y?????!?[?8?!??\?H?Y?]]?K???H ?XX?[?[? ?X?8?!?H8?$?? ?H??[?[?8?!??H8?$?MK? ???8?&H[? ?]\?Z[?H H [\\?] \?H
[?0??H?[?? ?X? H ?XX?[?\? ??[?[?\?? ?X?X?H ??[H? HH8? ??]?[? ] H ?XX?[?
?J ?H
? ???H
?
? ??
B??J?
L? ?H\? ??[?[?\?] [\\?] \?\??[?? NML0??\?[X]H H ?[?\?[? ?? H???J?
L? ?K????[?YY??^ Y?JB???\?LLN
?? M?M? M? ?[?
NB??K?L ?L? L?? HB??