edited b y
J. DUDLEY HERRON Purdue Un8veniIy West L.fayene, Indiana 47907
-
Fe Fe3++ 3eresults in a AGO that is the simple sum
Oxidation-Reduction Potentials and Hess' Law Kenneth L. Stevenson Indiana-Purdue University a t Ft. Wayne Ft. Wayne, Indiana 46805 High school, as well as college, chemistry students often have difficulty with the concept of additivity of oxidation and reduction potentials. One problem is that they believe F values conform to Hess' Law in the same way as AH, AG, or AS values. And so, for example, when adding together the two half-reactions Fe
-
Fe3++ 3e-
and
rOx0 = 0.036 V
+ AGsO = AGIO
AG,O
But, using the relation between AGO and 8 , above, we get
(1)
-
(2) Ph2++ 2e- Ph c,dO = -0.126 V t h e student often incorrectly multiplies 2 X ro,Oand adds to 3 X r,do since this is the procedure for the other thermodynamic functions when arriving at the halanced redox reaction
-
(3) 2Fe + 3Pb2+ 2Fe3++ 3Pb After awhile, however, the student can accept the fact that the correct r d - 0 is the simple sum,Oc, +d', i.e., -0.090 V. This principle is often explained away by noting that an emf is a "tendency" of a reaction to occur, and the fact that a halfreaction is doubled or tripled in the balancing process does not mean that the "tendency" is doubled or tripled; the "tendency" is the same no matter how many moles of oxidant or reductant are involved. This explanation suffices for the addition of half-reactions to yield balanced redox reactions, but if the student applies this idea to the formation of a third half-reaction by adding two together he will get into real trouble. Thus, if the two half-reactions below are added
+
-nfie~O- ngFcso = -n#e~O or Zed0
+ *so = 3q0
and 2 q 0 + rsO -
(,0 =
3 In other words, the 60 for the summed reaction is a weighted averaee between the half-reaction 8's. with the weiehtine .. .. facto;sequal to the numberofelecrronsin each half.reacrion. This ran he explained to the students simply by saying that since en is the energy per unit charge, the twosummed halfreacrions must be multiplied by the numher of units of charge (two and one, respectively I before adding, and the sum must hedivided bv the number of units of charee in there- (three, . sulting half-ieaction. Gettine back to the combination of half-reactions to vield balanced-redox reactions, the question is, does this same procedure work? Of course it does, but most people do not go through the process of finding the weighted average since the weighting factors of the two half-reactions and the balanced redox reaction are all identical. Thus, when reactions one and two are added, they are first multiplied by two and three, respectively, so that six electrons show up in both equations. The redox reaction involves those same six electrons, although they are not showri in the balanced equation. Nevertheless, the r..dOxo is computed as 6 q 0 + 6rz0 6
or
-
+
Fe3+ 3e-, the student is to yield the half-reaction, Fe surprised to find out that the resulting 8 is not simply r.8 + rso, hut rather (2Q cs0)/3 or 0.036 V! The reason why Hess' Law does not seem to work is because an emf is not a quantity of energy as is AG or AH, but rather an amount of energy per unit charge. This is made clear in the relationship
+
no .
This happens every time a balanced redox equation is formed from half-reactions, and the resulting process is a simple ad+ c,d0. dition of sXo To test what you have learned from this discussion, find the P for the half-reaction
-
6"
= -0.851 V for
Hg
or
-nF which shows that 1V is the neeative of the Gihhs free enerev ..change in joulesdivided by the number ot'coulombsof charge ( rt moles electrons x 96500 Clmole e - ) . Since IC:does ohey ~ e s sLaw ' one can see that adding half-reactions (4) and ( 5 ) to give
-
2Hg2++ 2e-
Hg2+ given that
( = -AG
+ no .
-
Hg"
+ 22-
and eo =
for 2Hg Do you get -0.906 V?
-
-0.796 V Hgz2++ 2e-
Volume 53. Number 7. July 1976 / 453
