G. P. Haight, Jr. School of Chemical Sciences
University of Illinois Urbana, 61801
II
Absolute Scales for Temperature and Reduction Potentials
In the historvof phvsical science i t has happened on occasim that a usefill in;e"sive property of mattermust be defined by means of a scale which evolves from a definition of arbitrary reference points. Later on a fixed point becomes definable, making estahlishment of an absolute scale possible. An obvious example is the temperature scale. Newton proposed a scale based on zero a t the temperature of freezing water, 12 as hodv temoerature: 17. the hottest water in which one may hold his hand; and 2 4 , t h e temperature of boiling wate;. Fahrenheit eave a value of zero to what he thought was the lowest obtaXable temperature; 32, the melting point of ice; 96, body temperature; and 212, the temperature of boiling water. The Celsius, or centigrade scale, made the freezing point of water zero and the boiling point 100. All these scales were proposed in the early 1700's. A hundred years later in 1848,Lord Kelvin translated Charles' Law, V = k ( T 273), into a definition of an absolute scale of temperature with zero set at -273' on the Celsius scale. Even though the appearance of temperature in formulations of physical laws is now always taken to mean the absolute temperature, we still commonly measure temnerature on the arhitrarv Celsius scale. Such practice requires an extra operation (converting to absolute temnerature) to Drocesses of recording and calculation. The familiar to allow aioption of the far more arbilrary scale is convenient absolute scale. It is interesting that the United States of America is now going,through the agony of convertine from the arbitrarv Fahrenheit to the arbitrary Celsius scale, Tollowing ~ n ~ l a n dconversion 's of a few years ago. An o~portunitvto adopt an absolute scale has been lost. It seems to ihe authbr that idoption of a new arhitrary scale is actually more trouble with far less practical purpose than conversion of the old scale to an absolute scale as is already done in scientific work. A similar situation is now developing with electrode potentials or reduction potentials. This property-the relative ability of an electron acceptor a t unit activity to be reduced in the presence of its reduction product also a t unit activity at an electrode immersed in aaueous medium-is measured against the reduction potentiai for 1M hydrogen ions in the presence of 1atm of Hz at a platinum electrode. The potential e- e KHz has been arbitrarily set a t zero. for H+(.,, Several years ago the author pointed out a difficulty arising from this arbitrary selection of zero for the potential of the H+/Hz half cell.' Energy cycles which break the property of potential down to its components of dissociation of hydrogen molecules, ionization of hydrogen atoms, and hydration of hydrogen ion had led thermodynamicists to assign AGh for hydration of H+ a value of 362 kcal (given in NBS circular 500.) Since the electron was not considered a reagent, its stmdard state was not defined. However, AGh for H+ was later calculated to he about 251 kcallmole. leavine about 110 kcal to be assigned to processes involving gaseous electrons enterinr condensed ohases. A similar cvcle involvine CI? + 2e2 ~ 1 'gives -113.5 kcal for changes in state for t i e electron. In the nrevious article it was sueeested that the 110 kcal could he assigned to the energy of put%g a mole of gaseous electrons into the electrode material. Plane and Hester2 chose to define the 110-117 kcal found in many cycles as the difference in energy between electrons in their "standard atate" and in the gas phase. This could lead to a definition of the H+/Hz Potential as +5.08 V and that the "truezero"of potential should
Srandard "Rational' Pofenfisl
Reduction Potential
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+
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he 5.08 V below H+/H.. Such azero would cause all reduction potenrials to be positive and all oxidation potentials negative. However, the 508 voluor 110 kcal must include the hydration energy of the electron. Pulsed radiolvsis has now provided us with a source of hydrated electron;, making it pbssible to study the kinetics and e-. KH2.3 The symbol enereetics of the reaction H+.. ecaqUdefineselectrons as reagentsEapable of existing in aqueous solution. The standard state may be taken to be solvated electrons at unit activity. The hydration energy of H+ has now been calculated to be 260 kcal; Iea\.ing -10i~kcal to be accounted for in electron processes. The hydration energy for electrons is calculated ta he 1.72 ?couole - - - V or -40 kcal.4 flu for the H 7 H. as determined experimentally is +S 2.67 V or -61 kcaL3.'Thus, a rational zero for a scale of reduction potentials is about 2.67 V below the present arbitrary zero for the H+/Hz couple. It is now nossible to "use" electrons as reagents, . estimate their solvation energy, and measure free energies (and thence notentials) for reactions of solvated electrons with many oxidants, and thus define a rational potential scale whichdoes not contain an arbitrary reference zero. Single electrode potentials are now implicitly those for cells consisting of the electrodes in question paired with a standard hydrogen electrode. With a new rational scale such potentials would be absolute for the half reactions in question, defined by measured (or calculated) energy states for all participants, including electrons, in the half reaction. The ahsolute zero of temperature has physical meaning, theoretical significance (cessation of molecular motion), and nractical utilitv in definine an ahsolute scale for use in calculations, yet has not been adopted for direct measurement by mankind. Unless some special significance, other than the possibility of defining it, is deduced for the "measured zero" or rational zero of potential, it is unlikely that we shall bother
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' Haight, Jr., G. P., J. CHEM. EDUC.,45,420 (1968).
Plane, Robert A,, and Hester, Ronald E., "Elements of Inorganic Chemistry,3W, A, Benjamin, New York, 1965, Matteson, Max S., in "The Salvated Electron," (Editor: Gould, Robert F.),American Chemical Society, Washington, 1965. Baxendale, J. H., Rad. Res. Suppl., 4,139 (1964).
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Volume 53. Number 11, November 1976 / 693
to change from the arbitrary scale first defined by potentials of redox couples 6 (H+&) =zero for unit activities of H+and H2. Here the measured zero of ootential is not an extremum or limit. The "rational" scale wehave defined is compared with some standard reduction potentials in the table. In a practical sense, there are oxidants which are too weak to oxidize the solvated electron-not manv hut a few--so the measured zero is within the scale and values of 8 may still he both positive and negative.
694 / Journal of Chemical Education
The solvated electron is not a practical concept in many solvents. Electrons solvated by liquid ammonia are well known. However, electrons solvated by molten Li+Cl- are difficult to imagine and a standard state for electrons difficult to define. The result of this exercise is thus an accounting for the "lost" -100 kcal of energy associated with states for the electron in aqueous electrode systems, and a not very compelling redefinition of the electrode potential scale.
