CONVENTION OF SIGNS AND CALCULATION OF E MF

3.5 CONVENTION OF SIGNS AND CALCULATION OF E MF

In accord with the foregoing discussion, the standard potential of zinc, which is not separately measurable, refers to the emf of a cell with two electrodes — zinc and the standard hydrogen electrode:

26 THERMODYNAMICS: CORROSION TENDENCY AND ELEC TRODE POTENTIALS

Pt; H , H , Zn + 2 2 + ; Zn (3.11) The corresponding reaction, somewhat simplifi ed, is written arbitrarily subtract-

ing the left - hand reduction reaction from the right - hand reduction reaction, or

standard emf =−. 0 763 V (3.12) The free - energy change, Δ G ° , equals 0.763 × 2 F joules; the positive value indicates

Zn 2 + + H 2 + → Zn 2H +

that the reaction is not thermodynamically possible as written, for products and reactants in their standard states. On the other hand, for the cell

Zn; Zn , H , H Pt 2 + + 2 ;

Standard emf = . 0 763 V (3.13)

+ H 2 , the standard emf is positive, and Δ G ° is negative, indicating that the reaction is thermodynamically possible. Clearly, the standard reduction potential for zinc is opposite in sign to the standard oxidation potential for zinc. It was agreed at the 1953 meeting of the International Union of Pure and Applied Chemistry that the reduction potential for any half - cell electrode reac- tion would be called the potential . This designation of sign has the advantage of conforming to the physicist ’ s concept of potential defi ned as the work necessary to bring unit positive charge to the point at which the potential is given. It also has the advantage of corresponding in sign to the polarity of a voltmeter or potentiometer to which an electrode may be connected. Thus, zinc has a negative reduction potential and is also the negative pole of a galvanic cell of which the standard hydrogen electrode is the other electrode. It is said to be negative to the hydrogen electrode.

the corresponding reaction is Zn + 2H + → Zn 2+

In setting up the emf of a cell, the foregoing conventions of sign dictate the direction regarding spontaneous fl ow of electricity. If, on short - circuiting a cell, positive current through the electrolyte within the cell fl ows from left to right, then the emf is positive, and, correspondingly, the left electrode is anode and the right electrode is cathode. If current fl ows within the cell from right to left, the emf is negative.

To calculate the emf of the cell shown in Fig. 3.2 , Cu; Cu 2+ , Zn 2+ ; Zn, we can fi rst write the reduction reaction of the left electrode, Cu, as if it were cathode (whether it is or not is clarifi ed later):

Figure 3.2. Copper – zinc cell.

CONVENTION OF SIGNS AND C ALCUL ATION OF EMF

= . 0 337 V (3.14) and

The reduction reaction for the right electrode is

=− . 0 763 V (3.16) and

Reaction (3.14) is subtracted from (3.16) , multiplying, if necessary, by a numerical factor so that the total electrons are canceled out. This results in the tentative reaction for the cell,

Cu Zn + 2 + → Cu 2 + + Zn (3.18) * The emf is obtained by adding, algebraically, the corresponding half - cell poten-

tials, (3.15) and (3.17) . Although reversing a reaction changes the sign of poten- tial, multiplying by any factor has no effect on either emf or φ ° values, since the

tendency for a reaction to go is independent of the amount of substance reacting (in contrast to the total free - energy change, which does depend on amount of substance reacting):

(Cu 2 + ) emf = φ Zn − φ Cu =− . 1 100 −

2 ( Zn 2 + ) If the activities of Cu 2+ and Zn 2+ are chosen to be the same, the emf E is − 1.100 V.

log

Since the emf is negative, current fl ows spontaneously from right to left within the cell. This fi xes the true polarity of the cell, with the left electrode, Cu, as posi- tive (cathode) and the right electrode, Zn, as negative (anode). From the relation Δ G = − nFE , the free - energy change of (3.18) is positive, and the reaction is, therefore, not spontaneous as written, but goes instead in the opposite direction. In other words, when current is drawn from the cell, Cu 2+ plates out on the copper

electrode, and the zinc electrode corrodes.

* Reaction (3.18) is a simplifi cation of the actual reaction. A more exact approach would include cal- culation of the liquid - junction potential between CuSO 4 and ZnSO 4 and elimination of single - ion activities, for which values are not measurable.

28 THERMODYNAMICS: CORROSION TENDENCY AND ELEC TRODE POTENTIALS

Similarly, the emf, polarity, and spontaneous reaction can be determined for any cell for which half - cell reactions and standard potentials are known.