Humboldt State University ® Department of Chemistry

Richard A. Paselk

Chem 110	General Chemistry	Fall 2003
Lecture Notes::Lec 14_26 September	© R. Paselk 2003
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Cell Potential and DG

Last time we finished with a derivation of the Nernst Equation which relates cell potential, E, the standard cell potential, E°, and the mass action potential, Q:

or, substituting values for R, T, and F at 25°C:

We also noted the relationship between free energy and voltage under standard conditions:

So let's use this relationship is a typical problem.

Example: Calculate the voltage for the cell:

Standard potentials for the half reactions are:

Electrons will flow to the more positive half cell, where reduction takes place. Therefore the Ag ⁺/Ag half cell is the cathode, and the Sn²⁺/Sn half cell must be reversed to become the anode:

Sn_(s) Æ Sn²⁺_(aq) + 2e ^- E°= +0.14 V

2(Ag⁺_(aq) + 2e ^- Æ Ag_(s)) E°= + 0.80 V

---

2 Ag⁺_(aq) + Sn_(s) Æ Ag_(s) + Sn²⁺_(aq) E°= + 0.94 V

For this reaction the mass action expression, Q, is Q = [Sn²⁺]/[Ag⁺]².

Substituting into the Nernst equation:

E = E° - (RT/nF) ln Q

E = 0.94 V - (0.0257/2) ln [0.15]/[0.30]²

E = 0.94 - 0.006564 = 0.947 V = 0.95 V

 

Concentration Cells

Concentration cells are cells where the components in the two half cells are identical, but the concentrations differ. So what will the voltage of such a cell be? Consider a cell made up with 0.10 M Ag⁺ on one side and 1.0 M Ag⁺ on the other.

Notice that the E° values cancel to give a standard potential of 0.00 V. The question is, which is the anode and which is the cathode?

Let's look at the system qualitatively and see if we can reason which half cell is which.

• First we note that both half cells use solid silver as electrodes, as we've seen in equilibrium systems the activity of the solid is one, so there is no difference between the half cells in this respect.
• On the other hand the concentrations of silver ion are quite different. To predict the electrochemistry we can look at the system and ask ourselves what would happen if we connected the half cells with a channel. Of course the two sides would mix until the silver concentrations were identical. Since the electrochemical system is just another arrangement to accomplish the same reaction, we should expect the same result!
• So the question becomes, how can we bring the two half cells to the same concentration of silver ion simply by transferring electrons?
  • First, note that if electrons flow from the half cell silver will be converted to silver ions, increasing the concentration of Ag⁺. The opposite will occur in the cell electron flow to.
  • Thus the electrons will flow from the low concentration to the high concentration.

So the system should be written as:

or, as a cell diagram, with the anode on the left:

We can now use the Nernst equation to calculate the voltage:

E = E° - (RT/nF) ln Q

Note that V is very small (59 mV for a change in concentration of 10). We can use such changes of voltage with concentration as a way of determining concentration called potentiometry.

Potentiometry

Potentiometry refers to the use of potential differences to determine concentration differences. The most common and familiar use of potentiometry is in pH meters.

Let's look a bit at how we might determine pH (that is [H⁺]) by potentiometry.

• We might try determining [H⁺] with a concentration cell with a SHE as one half cell and the non-standard hydrogen half cell as the other. Of course these are rather inconvenient and the SHE is difficult to set up and maintain properly.
• So we would like some kind of reference electrode (reference half cell) of known potential to substitute for the SHE.

Reference Electrodes

Calomel (SCE). One of the most common reference electrodes is the so called calomel electrode (named for the calomel filling = Hg₂Cl₂)

Diagram (note the diagram is for the half cell only):

for the half-reaction:

Note that there is only one variable contributing to the Nernst equation, the concentration (activity) of chloride ion, since calomel and mercury are in the pure states and thus have activities of 1! Thus the potential is:

for the saturated version of the Standard Calomel Electrode (SCE). The SCE is very common because its easy to prepare and very stable, and it has a well defined potential.

The calomel electrode has lost some popularity due to its mercury content. The most common alternate electrode is the Ag/AgCl reference electrode, which we will not discuss.

So now we have a reference electrode, what about the electrode for measuring hydrogen ion? Again the SHE type electrode is difficult to work with and is very rarely used.

The most common electrode for measuring pH is the glass electrode. (overhead - see figure in text)

The Glass Electrode

Let's look at the construction of this electrode (overhead - see figure in text). It can be diagramed, for example, as:

Note the two parts to this electrode: an internal reference electrode (in this case AgCl/Ag, but can also be calomel), and a glass membrane. The two parts are connected by a solution of fixed hydronium activity. Each of these components generates a potential, which generates the overall electrode potential. In making a pH measurement the entire cell, including the reference and indicating electrodes, may be diagramed as:

So how does the electrode work?

• Glass structure: silicon dioxide lattice (each silicon bonded to 4 oxygens, each oxygen bonded to 2 silicons) with monovalent counter ions such as sodium, hydronium etc.
• Hygroscopicity: glass must be hygroscopic in order for ion exchange to take place, and for electrode to function: H⁺ + Glass^- ´ H⁺Glass^-. This exchange takes place on both surfaces of glass membrane. Sodium ions in the glass serve as mobile charge carriers within the glass. The net effect is a boundary potential across the membrane which is dependent on external [H⁺] (internal [H⁺] is fixed).

© R A Paselk

Last modified 26 September 2003