282
Electrochemistry I: Batteries and Free Energy
AG° = -2.3QRTlogK e
(17-14)
= -4.57 T \ogK e cal/mole
(17-15)
where T is the temperature at which the equilibrium constant is known. With this
last expression, you can see that the concept of electron-transfer has been
eliminated ("« " is no longer involved), and you see that the change in standard
free energy for a reaction is associated with its equilibrium constant. In other
words, for any chemical reaction, regardless of whether it involves electrontransfer, it is possible to calculate the change in standard free energy at a given
temperature if its equilibrium constant is known for that temperature. In
eliminating "«" to obtain Equation 17-14, we must not overlook the fact that
the value of AG° still depends on the amount of material used and the way the
chemical equation is written. For the reaction written as 20 H 2 + 10 O 2 <=*
20 H 2 O, the value of the equilibrium constant is (/£ e )
10 , compared with K e for
the same reaction written as 2H 2 + O 2 +* 2H 2 O; the value of AG° for the first
is 10 times that for the second, as expected from Equation 17-14.
The values of K e used in Equations 17-6 or 17-7 and 17-14 or 17-15 must
correspond to K c (see p 255), where concentrations are expressed in moles/liter.
Values of K p with concentrations expressed in atm or torr can be converted to
K c by means of Equation 16-4.
Because no reversible reaction, in principle, ever goes to completion, we
need an expression that indicates our expectation of whether the reaction
"goes" (with the final equilibrium more to the right), or "doesn't go" (with the
final equilibrium more to the left). We summarize all this in one word, "spontaneous." We say that a reaction is spontaneous if AG° is negative, corresponding to a value of K e greater than one and an equilibrium position that is more to
the right than to the left. All of this is consistent with Equation 17-14. If AG° is
positive, we say that the reaction is not spontaneous. The reaction between Zn
and Cu
2+ is very spontaneous.
It is not always easy to harness non-electron-transfer reactions to do useful
work, but the potential to do the work is still present. To see how this wider
concept ties in with other equilibrium reactions studied in this book, consider
the following examples.
1. At 25.0°C for the reaction (p 351)
HN0 2 ?± H+ + NO 2 -
AG° = -(4.57)(298)log K e = -(4.57)(298)log(4.5 x 10~
4
)
= +4550 cal/mole
Electrochemistry I: Batteries and Free Energy
AG° = -2.3QRTlogK e
(17-14)
= -4.57 T \ogK e cal/mole
(17-15)
where T is the temperature at which the equilibrium constant is known. With this
last expression, you can see that the concept of electron-transfer has been
eliminated ("« " is no longer involved), and you see that the change in standard
free energy for a reaction is associated with its equilibrium constant. In other
words, for any chemical reaction, regardless of whether it involves electrontransfer, it is possible to calculate the change in standard free energy at a given
temperature if its equilibrium constant is known for that temperature. In
eliminating "«" to obtain Equation 17-14, we must not overlook the fact that
the value of AG° still depends on the amount of material used and the way the
chemical equation is written. For the reaction written as 20 H 2 + 10 O 2 <=*
20 H 2 O, the value of the equilibrium constant is (/£ e )
10 , compared with K e for
the same reaction written as 2H 2 + O 2 +* 2H 2 O; the value of AG° for the first
is 10 times that for the second, as expected from Equation 17-14.
The values of K e used in Equations 17-6 or 17-7 and 17-14 or 17-15 must
correspond to K c (see p 255), where concentrations are expressed in moles/liter.
Values of K p with concentrations expressed in atm or torr can be converted to
K c by means of Equation 16-4.
Because no reversible reaction, in principle, ever goes to completion, we
need an expression that indicates our expectation of whether the reaction
"goes" (with the final equilibrium more to the right), or "doesn't go" (with the
final equilibrium more to the left). We summarize all this in one word, "spontaneous." We say that a reaction is spontaneous if AG° is negative, corresponding to a value of K e greater than one and an equilibrium position that is more to
the right than to the left. All of this is consistent with Equation 17-14. If AG° is
positive, we say that the reaction is not spontaneous. The reaction between Zn
and Cu
2+ is very spontaneous.
It is not always easy to harness non-electron-transfer reactions to do useful
work, but the potential to do the work is still present. To see how this wider
concept ties in with other equilibrium reactions studied in this book, consider
the following examples.
1. At 25.0°C for the reaction (p 351)
HN0 2 ?± H+ + NO 2 -
AG° = -(4.57)(298)log K e = -(4.57)(298)log(4.5 x 10~
4
)
= +4550 cal/mole