# Lecture 14: Galvanic Cells and Standard Reduction Potentials

## General Chemistry II

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## Learning Objectives

By the end of this lecture, students will be able to:

1. Describe the components and operation of a galvanic (voltaic) cell
2. Use cell notation (line notation) to represent electrochemical cells
3. Define standard reduction potential and use the standard hydrogen electrode as a reference
4. Calculate standard cell potential (E^0_cell) from standard reduction potentials
5. Use E^0_cell to predict spontaneity of redox reactions
6. Relate E^0_cell to Delta G^0 and K

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## Lecture Content

### I. Galvanic (Voltaic) Cells

A galvanic cell converts the chemical energy of a spontaneous redox reaction into electrical energy. The cell consists of two half-cells, each containing an electrode immersed in an electrolyte solution. The anode is the electrode where oxidation occurs and serves as the negative terminal in a galvanic cell. The cathode is where reduction occurs and serves as the positive terminal. The mnemonic "An Ox, Red Cat" (Anode = Oxidation, Reduction = Cathode) is a useful reminder.

A salt bridge connects the two half-cell solutions and allows ion flow to maintain electrical neutrality. Without it, charge would rapidly build up in each half-cell and the reaction would stop. Anions flow through the salt bridge toward the anode, while cations flow toward the cathode. An external wire connects the two electrodes, and electrons flow from the anode to the cathode through this external circuit, doing useful electrical work along the way.

<image>A detailed diagram of a Zn-Cu galvanic cell. The left half-cell contains a zinc strip (anode) immersed in ZnSO4 solution. The right half-cell contains a copper strip (cathode) immersed in CuSO4 solution (blue). A salt bridge (containing KNO3 or NaCl in gel) connects the two solutions. An external wire connects the electrodes through a voltmeter reading +1.10 V. Arrows show: electrons flowing from Zn to Cu through the wire; Zn dissolving into solution (Zn -> Zn^2+ + 2e-); Cu^2+ depositing as Cu metal (Cu^2+ + 2e- -> Cu); anions (NO3- or Cl-) migrating through the salt bridge toward the anode; cations (K+ or Na+) migrating toward the cathode. Labels identify anode (-), cathode (+), oxidation and reduction half-reactions.</image>

### II. Cell Notation (Line Notation)

Cell notation provides a shorthand representation of a galvanic cell. By convention, the anode (oxidation) is written on the left and the cathode (reduction) on the right: anode | anode solution || cathode solution | cathode. A single vertical line represents a phase boundary, and a double vertical line represents the salt bridge. For the zinc-copper cell, the notation is Zn(s) | Zn^2+(aq) || Cu^2+(aq) | Cu(s). Concentrations can be specified in parentheses: Zn(s) | Zn^2+(1.0 M) || Cu^2+(1.0 M) | Cu(s). When a half-cell involves species in the same phase and requires an inert electrode to provide a surface for electron transfer, platinum is used: Fe^2+(aq), Fe^3+(aq) | Pt(s).

### III. Standard Reduction Potentials (E^0)

The standard reduction potential measures the tendency of a half-reaction to proceed as a reduction under standard conditions (1 M concentrations, 1 atm, 25 degrees C), relative to the standard hydrogen electrode (SHE). The SHE, defined as 2H+(aq, 1 M) + 2e- -> H2(g, 1 atm) with E^0 = 0.00 V, serves as the universal reference.

Standard reduction potentials are tabulated exclusively as reduction reactions. A more positive E^0 indicates a greater tendency to be reduced, making the species a stronger oxidizing agent. A more negative E^0 indicates a greater tendency to be oxidized (in the reverse direction), making the species a stronger reducing agent. Key values span from F2/F- at +2.87 V (the strongest common oxidizing agent) through Ag+/Ag at +0.80 V, Cu^2+/Cu at +0.34 V, and the SHE at 0.00 V, down to Zn^2+/Zn at -0.76 V and Li+/Li at -3.04 V (the strongest common reducing agent).

### IV. Calculating Standard Cell Potential

The standard cell potential is calculated as E^0_cell = E^0_cathode - E^0_anode, where both values are looked up as reduction potentials directly from the table. There is no need to change the sign when looking up the anode value; the subtraction in the formula handles it. An equivalent formulation is E^0_cell = E^0_reduction + E^0_oxidation, where E^0_oxidation is the negative of the standard reduction potential for the anode reaction.

A critical point is that E^0 values are not multiplied by stoichiometric coefficients. Cell potential is an intensive property, meaning it does not depend on the amount of substance involved. For the zinc-copper cell, with cathode Cu^2+ + 2e- -> Cu at E^0 = +0.34 V and anode Zn -> Zn^2+ + 2e- at E^0_red = -0.76 V, the cell potential is E^0_cell = 0.34 - (-0.76) = +1.10 V.

### V. Predicting Spontaneity from E^0_cell

The sign of E^0_cell directly indicates spontaneity. A positive E^0_cell means the reaction is spontaneous as written (Delta G^0 < 0). A negative E^0_cell means the reaction is nonspontaneous (Delta G^0 > 0). An E^0_cell of zero means the system is at equilibrium. Using the reduction potential table, any species higher in the table (more positive E^0) will spontaneously oxidize a species lower in the table (more negative E^0). In other words, for a spontaneous cell, the cathode reaction should appear above the anode reaction in the table.

<image>A partial standard reduction potential table arranged vertically with E^0 values on the right. The top of the table (most positive E^0) includes F2/F- (+2.87 V), Au^3+/Au (+1.50 V), Ag+/Ag (+0.80 V). The middle includes Cu^2+/Cu (+0.34 V), SHE (0.00 V). The bottom (most negative E^0) includes Zn^2+/Zn (-0.76 V), Al^3+/Al (-1.66 V), Li+/Li (-3.04 V). Arrows on the left indicate "Increasing strength as oxidizing agent" pointing upward and "Increasing strength as reducing agent" pointing downward. A diagonal arrow shows that F2 (top left) can oxidize Li (bottom right), representing the largest possible E^0_cell.</image>

### VI. Relationship Between E^0_cell, Delta G^0, and K

Three fundamental quantities are connected by the equation Delta G^0 = -nFE^0_cell, where n is the number of moles of electrons transferred in the balanced equation and F is Faraday's constant (96,485 C/mol e-). Since Delta G^0 also equals -RT ln(K), these two relationships can be combined: -nFE^0_cell = -RT ln(K), which rearranges to ln(K) = nFE^0_cell / (RT). At 25 degrees C, this simplifies to log(K) = nE^0_cell / 0.0592.

The three quantities are mutually consistent in their predictions. A positive E^0_cell corresponds to a negative Delta G^0 and a K greater than 1, all indicating a spontaneous reaction that favors products at equilibrium. A negative E^0_cell corresponds to a positive Delta G^0 and a K less than 1. An E^0_cell of zero corresponds to Delta G^0 = 0 and K = 1, the equilibrium condition.

<image>A triangle diagram showing the relationships among E^0_cell, Delta G^0, and K. At the three vertices of the triangle are: "E^0_cell" (top), "Delta G^0" (bottom left), and "K" (bottom right). Along each edge, the conversion equation is written: between E^0_cell and Delta G^0: "Delta G^0 = -nFE^0_cell"; between E^0_cell and K: "E^0_cell = (RT/nF) ln K"; between Delta G^0 and K: "Delta G^0 = -RT ln K." Inside the triangle, a table shows the three cases: E^0 > 0 / Delta G^0 < 0 / K > 1 (spontaneous), E^0 = 0 / Delta G^0 = 0 / K = 1 (equilibrium), E^0 < 0 / Delta G^0 > 0 / K < 1 (nonspontaneous).</image>

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