Spontaneity of Redox Reactions

A positive voltage that forms across the electrodes of a voltaic cell indicates that the oxidation-reduction reaction is a spontaneous reaction for reduction at the cathode and oxidation at the anode.

• Conversely, if the potentials of the half-cells are known, then it is possible to predict whether a given redox reaction will be spontaneous (i.e. result in a positive voltage)
• A negative voltage indicates that the reverse reaction is spontaneous (i.e. oxidation at the cathode, and reduction at the anode; by convention you would need to swap the labels on the electrodes)
• Basically, any current flow indicates that there is a spontaneous redox reaction occurring in a voltaic cell. The sign of the voltage indicates at which electrode the reduction or oxidation is occurring. (electrons flow towards the half-cell where reduction is occurring - by convention, the cathode)

As long as we can identify the actual reduction and oxidation processes that will occur in a redox reaction, the general description of the standard reduction potential for any redox reaction (and not just one occurring in a voltaic cell) would be:

• Thus, E⁰ will be positive for the case where the reaction is spontaneous
• E⁰ will be zero for a redox reaction at equilibrium
• E⁰ will be negative for the case where the reaction is spontaneous in the reverse direction
• Note that there is no reference here to what is the cathode and what is the anode

Cu(s) + 2H⁺(aq) ® Cu²⁺(aq) + H₂(g)

Oxidation: Cu(s) ® Cu²⁺(aq) + 2e^-

Reduction: 2H⁺(aq) + 2e^- ® H₂(g)

2H⁺(aq) + 2e^- ® H₂(g) E⁰_red = 0 V

• What about the oxidation reaction? The standard reduction potential for copper is listed in tables as copper ion combining with electrons to yield copper metal:

Cu²⁺(aq) + 2e^-® Cu(s) E⁰_red = +0.34

• In the oxidation reaction we have copper metal oxidizing to yield copper ion plus electrons. The key point here is that the reverse reaction will have the same voltage magnitude, just an opposite sign. In any case, the expression for the standard reduction potential for the redox reaction requires the reduction potentials for the half reactions. Notice that for the oxidation half-reaction, the sign is swapped in this equation:

• The standard reduction potential for this reaction is:

Since this value is negative, this redox reaction is not spontaneous as written. The reverse reaction (reduction of copper ion by hydrogen gas) is spontaneous

Activity Series of Metals

The activity series of metals lists the metals in decreasing order of their relative ease of oxidation:

The Standard Reduction Potential list compounds in decreasing order of the electron potential associated with reduction (in other words, the potential for reduction is high for those atoms at the top of the list):

Standard Reduction Potential, (E0red) in Volts	Reduction Half-Reaction
0.80	Ag+(aq) + e- ® Ag(s)
0.34	Cu2+(aq) + 2e- ® Cu(s)
0	2H+(aq) + 2e- ® H2(g)
-0.28	Ni2+(aq) + 2e- ® Ni(s)
-0.76	Zn2+(aq) + 2e- ® Zn(s)
-3.05	Li+(aq) + e- ® Li(s)

Thus, the basis of the activity series lies in the relative reduction potential:

• The stronger the reduction potential, the more difficult it is to oxidize the compound.
• The weaker the reduction potential, the easier it is to oxidize the compound

Free energy change, DG, is a measure of the spontaneity of a chemical reaction or process. Likewise, the standard reduction potential (E⁰_cell) for a redox reaction is also a measure of the spontaneity of a redox reaction. What is the relationship between these two values?

• DG has units of J/mole
• Reduction potential (electromotive force, E) has units of Volts. 1 Volt describes the potential difference necessary to impart 1J of energy to a charge of 1 coulomb (6.24 x 10¹⁸ electrons)
• We need some way to relate charge in Coulombs (a collection of electrons) to moles of electrons (another collection of electrons)

• n = number of moles of electrons transferred in the reaction
• F = the quantity of electrical charge (in coulombs) that is contained in 1 mole of electrons (this is the Faraday constant). One Faraday is equal to 96,500 coulombs/mole of e-. Since 1 volt = 1Joule/coulomb, one Faraday also equals 96,500 J/volt*mole e-

Joules/mol = -(electrons)* (coulombs/mol of electrons) * (Joules/coulomb)

• F, and n, are positive values. Therefore, a positive value of E (which indicates spontaneity) is a negative value for DG (which also indicates spontaneity)

If everything is in the standard state: