The SIGN of ELECTRODE POTENTIAL CREIG S. HOYT Gmve City College, Grove City, Pennsylvania
0
NE of the more difficult tasks for the student of physical chemistry is the mastery of the group of conventions which determine the sign of the electromotive force in a galvanic cell. Part of this dif ficulty arises from the fact that the convention was reversed some years ago, assigning to the metals above hydrogen in the electromotive series a negative sign in place of the positive sign they had previously borne. Since some texts and charts still use the earlier convention, it is inevitable that some confusion should result. The system which is described has been in use in the author's classes for several years with some success. It has the advantage of being easily understood and of correlating with the thermodynamic derivation. CONVENTIONS IN THE WRITING OF GALVANIC CELLS
s~~~~~~ the cell
to be =itten
in the usual form
Zn I ZnSOa M/lOII KClsaturated II CuSOl M/10 I Su
(1)
The reaction occurring in a cell may be invariably had by taking as reactants the reducing or lower valence as written substance from the left-hand side of the and the oxidizing or higher valence substance from the right-hand side. Thus Zn
+ CUSOI+ZnSO, + Cu
In order for the left-hand or zinc electrode to forward the same reaction as the comer,. transfer of ion must occur in the opposite direction; i. e., from electrode to solution. Equation 4 applies to this reactiou also but since the transferis in the with the signs just reverse direction. The potential may be subtracting the potential of the lefthand electrode from that of the right-hand electrode. Thus,
..
E,a
E m
=
+ 2,302 RT -logeo.r.r nF
-:,E m - 2.302 RT -logam++ nF (5)
With the cell written in this fashion, it is indicated that the ordinary or spontaneous cell reaction will involve the solution of the zinc electrode to form zinc sulfate and the deposition of an equivalent amount of copper from the solution upon the copper ele@ode. For this reaction to be a spontaneous one, the cell reactiou must involve a loss in free energy content in the system, which loss is equal to the electrical work done by the cell when operating isothermally and reversibly. These conditions are attained when the cell delivers an infinitely small current against an infinite resistance a t constant temperature. The free energy loss is represented by the equation, - AF = nFE
The second term of this equation has no quantity which is characteristic of the particular solution about the electrode, or, if the electrode is properly prepared, of any particular electrode. This term is, therefore, a property of the system copper-copper ion and is a constant a t constant temperature. When both sides of the equation are divided by nF, the second term has the dimension of voltage and is represented by Eo, the standard potential.
(2)
since the activity coeficients of M / ~ O C ~ S and O, ~ 1 1 0
znso,are each approximately 0.16 E,a E.,e
+ 0.0591 log 0.016 -'(-0.7618) - 0.0591 log 0.016 (6) = 0.3441 - 0.0531 + 0.7618 + 0.0531 = 1.1059volts (7)
=
0.3441
Since the positive potential of the cell a loss in free energy, a cell reaction which gives a positive cell is one which occurs spontaneously, In such a cell a continuous passage oPelectrons from the righthand electrode to the solution is necessary to the deposition of ions at this point, The current, there. fore, flows from right to left in the cell. The procedure followed in the case above is directly applicable to every type of cell, necessitating only one equation and one method of treatment, To demonstratethe applicability of the convention, the following types of cells are considered,
where E is the cell potential, n is the number of Faraquantities in the required to convert the equation, and F is the number of coulombs per Faraday. Considering the right-hand electrode alone for the time, the free energy of transfer from metal ion to THE CELL REACTION IS NOT SPONTANEOUS metal lattice may be represented as occurring in two Suppose the cell were as follows: steps: (1) the transfer of the ion from its activity in the solution to unit activity, and (2) the transfer of the Cu I CuSO, M/10 /I KC1 (M) Hg& I Hg ion from unit activity to the normal unstrained lattice The cell reaction is of the pure metal. The equation is 530
E = Eo
The cell potential is E.m = 0.2805
- Em,
RT - 2.302 - log 0.016
nF
(8)
where 0.2805 is the potential of the normal calomel electrode. E..u = 0.2805 - 0.3441
+ 0.0531 = -0.0105
volt
(9)
23050 = -485 calories
(10)
aco++t+ + 2.302 nRT -log --F ace+++
It is apparent that the sign of the second term is invariably positive and that the ratio is that of the activity of the oxidant to the activity of the reductant. Since the left-hand electrode must react in reverse direction to carry on the cell reaction, the potential of the left-hand electrode is subtracted from that of the right-hand electrode as before.
The free energy is - AF = -0.0105
x2x
which indicates that the reaction as written is not spontaneous. In this case the right-hand electrode is negative and the current flows from left to right inside the cell. OXIDATION-REDUCTION CELLS
Following the rule previously formulated, the cell is written
At the right-hand electrode, the rea'ction is
- AF
=
nFE
=
2.302RT log
ac.++++.
+ 2.302RT log K
=
nFE
=
2.302RT log- a
RTEo(c.++++, a+++) - E o ( F ~ + +F+ L +,+ ) = 2.302 - log 1/K nF
(16)
where K is the equilibrium constant for the reaction. INVOLVING THE HYDROGEN ION
The Quinhydrone Electrode.-When quinone is brought into contact with a negative electrode in the presence of hydrogen ion, it is reduced to hydroquinone. This is one of the few organic oxidations and reductions which are reversible. We may assume as in the previous case that the oxidant is transferred from its initial activity to unit activity, reduced from qninone a t unit activity to hydroquinone a t unit activity and the hydroquinone transferred to its final activity. 'Now, in a solution saturated with +inhydrone, the activities of quinone and hydroquinone are equal and the only free energy terms are those involving the reduction of quinone a t unit activity and the transfer of two moles of hydrogen ion from the initial activity to unit activity.
+
+ 2.302RT log ace+++
acs+++
(15)
RT
E,,.,i, wrnrlnz = Ewlnhv,iron. 2 302 2 ~ l o g ( a ~ + ) 2(17)
+
Cancelling the exponent of the hydrogen-ion activity against the valence change in the denominator
(11)
This is done by assuming that the ceric ion is transferred from its activity in the solution to unit activity, converted to cerous ion a t unit activity, and the cerous ion transferred to its final activity in the solution. A rearrangement of this equation gives -AF
ape+++
-a~.++
Now
OXIDATION-REDUCTION
In certain instances, the electrode serves only as a carrier for the introduction of electrons into the solution or for their removal from the solution. Such an electrode furnishes no ions and is'referred to as an inert electrode. This designation is, perhaps, not altogether correct since the character of the electrode surface may have an effect upon the reversibility of the reaction. Among the electrodes which are employed in this way are gold, platinum, and carbon. Suppose that we have as the cell reaction
ce++++ + < = &+++
RT -Ea(a.+++. w + )- 2.302 -log nF
+ 2.302RT log K
(12)
The second term of this equation involves the free energy of reduction of the ceric ion a t unit activity which is a property of the ceric-cerons system and, therefore, constant a t constant temperature. The equation becomes
When. the left-hand electrode is the saturated calomel electrode, a t 25'C.,
CONCENTRATION CELLS
A cell may be constructed with two identical electrodes in contact with an electrolyte which has different concentrations in the two halves. Since this differs only in the activity of the ion in the electrolyte, such cells are called concentration cells. Similarly concentration cells may be constructed with electrodes having different activities of the metal but in contact with a common electrolyte.
Let us consider the cell: Ag
I Ag NOa,,, M/100 11
Ag Nosa2,M/lO
necessary to transport the metal in the electrode to the activity of the metal in the normal lattice before converting to lead ion; RT a, RT ox E,,u = 2.302 - log -- - 2.302 -log -
I Ag
Using our convention, E,zz = E u s
+ 0.059110ga~- E m - 0.0591 logal
(20)
Since the electrodes are identical, the standard potential cancels and
nF
a11
nF
ar
(22)
KT ar E,.n = 2.302 - log nF an CONCLUSION
Now for a cell of the opposite type, we have: Pb emal. Pb = er
I
PbSO, sat. Pb amal. Pb++ = a, Pb = a11
j
Using our convention, and remembering that i t is
A convention for the sign of the potential of a galvanic cell based on free energy changes a t the electrodes has been presented. The convention has the advantage of being independent of the direction of the cnrrent flow and of applying uniformly to all cases. A number of applications have been cited.
