X(-56 x 4.184) = -117 kJ/mole AGYo = ><(-88 x 4.184) = -184 kJ/mole
The factor of V2 accounts for the fact that the Ellingham diagram gives free energies of formation per mole of O2 while reactions (10.2a) and (10.2b) are written for one mole of oxide. Combining the above values gives AG° = AGyo" AGXo = "67 kJ/mole, and Eq (10.5b) with z = 2 gives a cell EMF of:
The couples in the half-cells are not restricted to metals and their oxides. Problem 10.7 analyzes a cell in which one electrode contains two oxides of the same metal. However, all components of the cell are pure, and are thus in standard states. Nonstandard variants of the solid-state electrochemical cell are presented in the following section.
Reactions (10.2) suggest an alternate interpretation of the electrochemical cell based on Reaction (10.1). Each half cell of Eq (10.4) is a MO/M couple with a characteristic oxygen pressure (po2 )MO)/m (see
Digression 2 in Sect. 9.9.1). The electrochemical cell of Equation (10.4) could equally well be written as:
(O2)xo/x ||electrolyte||(O2)yo/y In place of reactions (10.3), the half-cell reactions are:
Instead of Equation (10.5b), the cell EMF is:
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