Module 7.4: Redox Reactions

7.4.1 Fundamentals

I Oxidation: the process of losing one or more electrons.

1. Oxidation is often related to the process of gaining oxygen or losing hydrogen atoms.

2. Oxidizing reagent (oxidant): the compound that is being reduced.

II Reduction: the process of gaining one or more electrons.

1. Reduction is often related to the process of losing oxygen or gaining hydrogen atoms.

2. Reducing reagent (reductant): the compound that is being oxidized.

III Both oxidation and reduction must occur at the same time (conservation of charge).

1. Something must be reduced in order for something to be oxidized.
2. Something must be oxidized in order for something to be reduced.

7.4.2 Electrochemistry and Electrolysis

IV electrolytic cell: a nonspontaneous redox reaction is forced to occur by applying work.

1. this work is done by the surroundings as electric work.

V galvanic cell: a spontaneous redox reaction occurs and generates an electrical current.

1. in the galvanic cell, the electric work is done by the system.

VI anode (-): the electrode at which oxidation takes place; electrons are released.

VII cathode (+): the electrode at which reduction takes place; electrons are accepted.

VIII electrolyte: ionically conducting medium, which carries an electric current (electrons)

IX electrodes: metallic conductors that are in contact with an electrolyte.

X cell potential ($\textrm{E}_{cell}$): The potential difference associated with a galvanic cell that is working reversibly

1. the cell potential illustrates how much work a galvanic cell can do

2. a negative cell potential will illustrate that work would have to be done on the surroundings for the reaction to proceed (as it corresponds to a positive $\Delta \textrm{G}$)

3. If the chemical equation is multiplied by a factor, $\textrm{E}_{cell}$ is not affected

4. the standard cell potential ($\textrm{E}_{cell}\degree$) is defined by the standard Gibbs free energy of the reaction $\Delta \textrm{G} = -\textrm {nFE}_{cell}$ (Eq. 120)

   1. similar to $\Delta \textrm{G}$, $\textrm{E}_{cell}$ illustrates the cell potential between the products and reactants that they have at an intermediate stage of the reaction and have many possible values ($\Delta \textrm{G} = \Delta \textrm{G}\degree + \textrm{RT} \textrm{ln} (\textrm{Q})$)

   2. similar to $\Delta \textrm{G}\degree$, $\textrm{E}_{cell}\degree$ illustrates the cell potential between isolated products and reactants in their standard states and only has one unique value per reaction.

XI The equilibrium constant of redox reactions can be calculated through $\Delta \textrm{G}_{r}\degree = -\textrm{RT}\textrm{ln}(\textrm{K})$:

$\textrm{ln}(\textrm{K}) = \frac{\textrm{n}_{r}\textrm{FE}_{cell}\degree}{\textrm{RT}}$ (Eq. 121)

1. An extremely useful equation, illustrates that:

   1. a reaction with a large, positive $\textrm{E}_{cell}\degree$ will result in a large K

   2. a reaction with a large, negative $\textrm{E}_{cell}\degree$ will result in a small K

XII Electrochemical series illustrates the reactivity of species in order of their standard potentials

1. If the standard potential of a reduction half-reaction is very positive, its oxidized form is strongly oxidizing

2. If the standard potential of a reduction half-reaction is very negative, its reduced form is strongly reducing

XIII In a galvanic cell, oxidation will occur at the anode, pushing electrons into the cathode, where reduction will occur (Ref. Figure 80)

1. a porous wall prevents any charge buildup from occurring by allowing electrolyte solutions to move between the two compartments

   1. without it, charge buildup will cause the reaction to cease

2. salt bridge: similar to a porous wall, a gel containing a concentrated aqueous salt solution in an inverted U-tube that allows a flow of ions (completing the circuit)

3. each “compartment” with an electrode is formally known as a half-cell

XIV cell diagram: a notation that expresses the structure of a cell

1. an example for the Daniell cell is given below: $\textrm{Zn}$ (s) | $\textrm{Zn}^{2+}$ (aq) || $\textrm{Cu}^{2+}$ (aq) | $\textrm{Cu}$ (s)

   1. a salt bridge is illustrated with a double vertical line (||)

2. When gases are involved in a redox reaction, platinum or any other inert electrode is utilized. An example is $\textrm{H}_{2}$(g).

3. Any inert metallic component of an electrode is written as the outermost component of that electrode in the cell diagram

4. commonly, the right-hand electrode in the diagram usually represents to be the site of reduction (cathode) and the left-hand electrode is the site of oxidation (anode).

XV the standard potential ($\textrm{E}\degree$) is the difference between the standard potentials of the two electrodes

$\textrm{E}_{cell}\degree = \textrm{E}_{R}\degree - \textrm{E}_{L}\degree$ (Eq. 122)

1. R stands for the right hand of the cell diagram (cathode), L stands for left

2. the contribution of a single half-cell can be calculated with respect to a standard hydrogen electrode (SHE), which

   $\textrm{E}\degree$ ($\frac{\textrm{H}^{+}}{\textrm{H}_{2}}) = 0$ at all temperatures

3. for example, when measuring the standard potential of copper:

   $\textrm{Cu}^{2+}(\textrm{aq}) + \textrm{H}_{2}(\textrm{g}) \rightarrow \textrm{Cu}(\textrm{s}) + 2 \textrm{H}^{+}(\textrm{aq})$

   $\textrm{E}_{cell}\degree = \textrm{E}_{R}\degree - \textrm{E}_{L}\degree = \textrm{E}_{R}\degree$

4. caution for using Eq. 122: when different numbers of electrons are involved in half- reactions for the same element, you must combine the values of $\Delta \textrm{G}\degree$ instead of adding the cell potential together

   1. in fact, Eq. 122 is derived using the additive properties of Gibbs free energy

XVII Nernst equation: an equation that illustrates the cell potential at nonstandard conditions

$\textrm{E}_{cell} = \textrm{E}_{cell}\degree - \frac{\textrm{RT}}{\textrm{n}_{r}\textrm{F}} \textrm{ln}(\textrm{Q})$ (Eq. 123)

1. $\textrm{F}$ is Faraday's constant; $\textrm{n}_{r}$ stands for the number of moles of electrons involved in the reaction; $\textrm{Q}$ is the reaction quotient.

2. When $\textrm{E}_{cell} = 0$ in which the system has reached equilibrium, $\textrm{Q} = \textrm{K}$.

3. Used to illustrate the cell potential at a given composition of the reaction mixture

XX In an electrolytic cell, a current must be supplied externally and forces oxidation to occur at the anode and reduction to occur at the cathode.

1. overpotential is required, which is experimentally determined and greater than the calculated cell potential, to achieve a significant rate of product formation in electrolysis

2. the number of electrons (in moles) from an external current can be calculated by: $\textrm{n} = \frac{\textrm{It}}{\textrm{F}}$ (Eq. 124)

3. I stand for current (in Amperes), t stands for time (in seconds), and F is a constant