Cell EMF

 Here is a summary of a voltaic cell:

A key question is: what causes the electrons to flow from the anode to the cathode?

• The electrons flow from the anode to the cathode because of a difference in the potential energy of the electrons at the anode compared to the cathode
• In particular, the potential energy of the electrons is higher at the anode than at the cathode
• Like water molecules in a waterfall, the electrons move in a direction from high potential energy to low potential energy (i.e. "downhill" in an energy landscape)

The potential difference between two electrodes is measured in Volts (V)

• One volt is the potential difference, between an anode and a cathode, that would be required in order to impart 1 Joule of energy to a charge of 1 coulomb (note: 1 coulomb is the charge of a collection of 6.24 x 10¹⁸ electrons)

• The potential difference between two electrodes is called the electromotive force, or emf
• The emf of a voltaic cell is called the cell potential, or the cell voltage
• The cell voltage of a voltaic cell will be positive value

The cell voltage will depend upon the specific half-reactions, concentrations of ions, and temperature

• Common tabulations of cell voltages are performed at 25°C and standard conditions of concentrations of liquid (i.e. 1M) and gas components (i.e. 1 atm)
• Under standard conditions, the emf of a voltaic cell is called the standard emf or the standard cell potential (E⁰_cell)
• By convention, the potential associate with an electrode is the potential for reduction
• The standard cell potential is given by the standard reduction potential of the cathode, minus the standard reduction potential of the anode

The cell potential of a voltaic cell depends upon the two redox half-reactions that comprise the functioning cell

• There are many different combinations of redox half-reactions. Do we need to tabulate all possible unique combinations?
• As you might have guessed, the answer is no, we don't. In principle, we could assign a unique standard potential to each half-reaction and by comparing these values determine the cell potential for any combination of half-reactions

There is one problem, however: we have seen that an isolated half-reaction doesn't result in reduction or oxidation or electron flow. Therefore, how are we going to assign a standard potential to a half-reaction?

• We are going to use a generally agreed upon reduction reaction as the reference half-reaction against which to compare and tabulate all possible half-reactions
• The reference reaction is the reduction of H⁺(aq) ions to produce H₂(g):

2H⁺(aq, 1M) + 2e^- ® H₂(g, 1 atm) E⁰_red = 0.0V

How do we use this SHE to determine the standard reduction potential, E⁰_red, for some redox half-reaction?

• Let's say we are interested in determining the standard reduction potential for Zn²⁺
• We would set up a voltaic cell using a SHE as one half-cell, and a Zinc electrode as the other half-cell

• The half-cell reactions are:

Zn(s) ® Zn²⁺(aq) + 2e^- (Zinc electrode)

2H⁺(aq) + 2e^- ® H₂(g) (SHE)

• The overall cell reaction:

Zn(s) + 2H⁺(aq) ® Zn²⁺(aq) + H₂(g)

• Note: this is performed under Standard Conditions, where concentrations = 1.0M, and p = 1 atm

• For the reaction as shown, the zinc electrode is the anode (oxidation), and the SHE is the cathode (reduction)
• The voltage for the overall cell is measured at 0.76 Volts (i.e. this is the standard cell potential)
• From the previous definition of the standard cell potential:

• We know the value for the standard cell potential, it is +0.76V. We also know the value for the reduction potential for the SHE, it is 0V. Thus,

• In other words, in reference to the SHE, the standard reduction potential for the zinc electrode is determined to be -0.76V.

This may seem a little strange because the cell reads +0.76V and yet the determined reduction potential for the zinc electrode is -0.76V.

• The key here is that the original definition of the standard cell potential is set up such that each cell is referenced as a reduction reaction.
• In other words what we have actually determined is the half-cell potential (in reference to the SHE) for the reduction of zinc:

Zn²⁺(aq) + 2e^- ® Zn(s) E⁰_red = -0.76V

• Thus, in reference to the SHE, the oxidation of Zn(s) is associated with a half-cell potential of +0.76V (this is the spontaneous direction for the reaction; the reduction of Zn²⁺ and the oxidation of H₂(g) is not spontaneous)

The standard cell potential (Voltage) describes the potential per unit charge that the reaction produces

• This value of the potential per unit charge (i.e. electron) is a constant that is a property of the two half-reactions that are reacting in the cell. It is independent of the stoichiometry or amount of the reactants in the cell

Some standard reduction potentials at 25°C:

• The more positive the value of E⁰_red the greater the driving force for reduction
• In reference to H⁺/H₂(g) , Ag⁺ will preferentially be reduced to Ag(s) and H₂(g) will be oxidized to H⁺(aq). In reference to H⁺/H₂(g) , Zn(s) will preferentially be oxidized and H⁺ will be reduced to H₂(g).
• The cathode is the electrode where reduction occurs, therefore, in order for a cell to operate spontaneously, the half-reaction at the cathode must have a more positive value of E⁰_red than the half-reaction at the anode
• The greater driving force for reduction at the cathode can force the reaction at the anode to operate "in reverse" - i.e. to undergo the oxidation reaction
• The difference between the standard reduction potentials of the two reactions, E⁰_red (cathode) - E⁰_red (anode), is the excess potential that can be used to drive electrons through the cell, E⁰_cell

A silver-lithium battery is a voltaic cell with a silver cathode and a lithium anode. What is the voltage of this voltaic cell?

What will happen if a science project on batteries suggests that a cathode be made out of Zinc and the anode of Copper?

In the above discussion of reduction potentials and their relationship to one another in half-reactions, we can predict which direction current will flow in a voltaic cell. In other words, we can predict which reactant will be oxidized and which will be reduced

• The same information can be used for redox reactions where the compounds are in direct contact, and not separated into half-cells.
• For example, from the example above, we would predict that silver ion will oxidize lithium metal as a spontaneous redox reaction. Alternatively, we would predict that the reduction of lithium ion by silver metal is not a spontaneous reaction (and would require the input of energy to drive)

• Substances that are strong oxidizing agents are subsequently weak reducing agents. Likewise, substances that are strong reducing agents are weak oxidizing agents.