Humboldt State University ® Department of Chemistry

Richard A. Paselk

Chem 110	General Chemistry	Fall 2003
Lecture Notes::Lec 13_24 September	© R. Paselk 2003
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Galvanic Cells

Last time we looked at the two half cells required to create a galvanic cell. We then connected them with a wire, discovering that there was only an instantaneous flow of currrent. So what can we do to allow the flow of electrons to continue? What we need to do is connect the solutions in the beakers so that the charges can be neutralized with a counter flow of ions. The connecting ionic fluid is referred to as a salt-bridge, as seen in the figure. Other arrangements are possible such as semi-permeable membranes etc. Such an arrangement is called a Galvanic cell.

Galvanic cells (or Voltaic cells) are cells in which the overall redox reactions occur spontaneously (equilibrium favors products) as written. They can serve as a source of electric power (as a battery).

Anodes vs. Cathodes.

• Anode: the electrode at which the oxidation half reaction occurs - electrons are taken up from the reaction at this electrode. Thus at the zinc electrode Zn(II) ions would be released, leaving two electrons behind for each ion. Note that this electrode should have a negative charge! (The chemistry is putting excess electrons into the electrode.)
• Cathode: the electrode at which the reduction half reaction takes place - electrons are released to the reaction at this electrode. (Think cathode ray tube, CRT, shooting electrons.) Note that the chemical reaction is taking electrons from this electrode so it will be positive! Thus a copper electrode would provide electrons to Ag(I) ions to plate out silver metal.

Electrodes and Electrode Potentials

Reference Electrodes: there is no absolute standard for potential--it must always be defined in reference to something (think about gravitational potential or field), potential can be positive or negative. Thus arbitrarily chose a particular cell as the standard, define its potential, and compare everything else to it.

 

• The Standard Hydrogen Electrode (SHE) has been defined as the standard. It has a potential of 0.000 V at all temperatures. The electrode compares the voltage of an electrode with hydrogen gas at exactly 1 atm bubbling over a Pt electrode immersed in a solution with hydronium ion activity = 1.000 (1 M). Commonly use a platinized platinum electrode (platinum coated with finely divided platinum (platinum black) to maximize surface area and catalyze the reaction.

Standard Reduction Potentials

Let's look again at a Galvanic Cell (note that Zumdahl's illustrations assumes a porous disk connection)

The Galvanic cell consists of two half cells. In each cell the reaction, by convention, is written as a half-reaction, which is in fact the chemistry taking place in the half cells.

Note that in tables of Reduction Potentials the reactions are written as reduction half reactions, with the potentials those which would occur if the half-cell were connected into a galvanic cell with a SHE.

For the Zn, Cu, system we then have

Zn half cell:

But of course in our cell, this goes backwards:

Cu Half Cell:

CELL :

But recall we also stated that these half-cell potentials are always related to the SHE, which is defined as 0.00 V at all temperatures.

The voltages of half cells determined relative to SHE are the Standard Reduction Potentials for these half cells (1M [more properly, at an activity of 1], 1 ATM)

So how do we determine the V of a Galvanic Cell from half-cell voltages?

1. Electrons will flow from less positive to more positive cell.

Consider a Galvanic Cell of Ag⁺/Ag and Cu²⁺/Cu

What will the reaction be?

Ag⁺ + e ^- Æ Ag⁰ E° = +0.80 V

Cu²⁺ + 2e ^- Æ Cu⁰ E° = +0.34 V

Since e^- flow toward the more positive half cell, then Ag⁺/Ag cell is cathode (reduction at cathode) and Cu²⁺/ Cu will be reversed.

Now we need to balance electrons so

2 (Ag⁺ + e ^- Æ Ag⁰) E° = +0.80 V

Cu⁰ Æ Cu²⁺ + 2e ^- E° = -0.34 V

---

2 Ag⁺ + Cu⁰ Æ 2 Ag⁰ + Cu²⁺ E° = + 0.46 V

Cell Diagrams

Instead of drawing cells we often draw a cell diagram using what your author refers to as "Line Notation." It is conventional to start with the anode on left. The cell diagram for the Zn/ Cu Galvanic Cell will then be represented as:

Both of these describe cells with a liquid junction, such as a porous disk. What do Lines represent? Changes in phase or boundaries. With a salt bridge we see:

Note the two lines in the center representing the salt bridge. We need two lines because there is a boundary between each end of the salt bridge and its respective half cell.

So the complete description of our cell includes:

1. The cell potential (= 1.10 V).
2. The electron flow direction.
3. Designation of Anode and Cathode. (Note that these terms can refer to the metal probe or the half cell. Note also that the term electrode often refers to the entire half cell.)
4. The nature of each electrode, and the solution in each half cell.

Cell Potential and DG

If we think physics, then the work done by a system is:

Where E = potential difference and q = charge.

So for the system or reaction:

and

If we consider a system doing the maximum possible work (no currrent flow - so takes forever), then work equals free energy, or:

For standard conditions @ equilibrium:

Substituting -nFE for DG:

Dividing by -nF:

This is called the Nernst Equation, which relates the voltage produced by a cell to the concentrations of reactants and products in a system. Note that this is the electrochemical version of the equation for free energy in a non-equilibrium system.

© R A Paselk

Last modified 25 September 2003