Electrochemistry Chapter 18

Suggested reading: Sections 4.9−4.10, pages 170−177.

Oxidation States: the imaginary charges the atoms would have in a covalent compound if the shared e−’s were…

Ø  divided equally between identical atoms bonded to each other or, Ø  (for different atoms) all assigned to the atom in each bond that has the

greater electronegativity ²  For ionic compounds, oxidation states are equal to the ion

charges.

Review: Chapter 4

Review: Chapter 4

Example: Assign oxidation states to all atoms in CO2 and SF6.

Review: Chapter 4

Oxidation−Reduction (Redox) reactions involve the transfer of one or more electrons.

Review: Chapter 4

Oxidation−Reduction (Redox) reactions involve the transfer of one or more electrons.

Ø  Oxidation: an increase in oxidation state (a loss of electrons).

Ø  Reduction: a decrease in oxidation state (a gain of electrons).

Review: Chapter 4

Oxidation−Reduction (Redox) reactions involve the transfer of one or more electrons.

Ø  Redox with no ionic reactants or products: Look for O2 as a reactant or product.

For example: combustion

CH4(g) + 2 O2(g) ⟶ CO2(g) + 2 H2O(g)

Review: Chapter 4

Example: Balance the following reaction.

H+(aq) + Cl−(aq) + Sn(s) + NO3−(aq) ⟶ SnCl6

2−(aq) + NO2(g) + H2O(ℓ)

1.  Notice that it looks complex compared to a common chemical equation.

2.  Assign oxidation states to all atoms in reactants and products.

3.  Balance charge based on species that are oxidized ⁄ reduced.

4.  Balance the remainder of the equation by inspection.

Review: Chapter 4

Chapter 18: Balancing Redox Equations

The Half-Reaction Method Separate the reaction into two half-reactions: one involving oxidation and the other involving reduction.

Example 18.1, page 836 Potassium dichromate, K2Cr2O7, is a bright orange compound that can be reduced to a blue-violet solution of Cr3+ ions. Under certain conditions, K2Cr2O7 reacts with ethanol, C2H5OH, as shown below. Balance the chemical equation.

H+(aq) + Cr2O72−(aq) + C2H5OH(ℓ) ⟶ Cr3+(aq) + CO2(g) + H2O(ℓ)

Balancing Redox Equations

Example 18.1, page 836 Potassium dichromate, K2Cr2O7, is a bright orange compound that can be reduced to a blue-violet solution of Cr3+ ions. Under certain conditions, K2Cr2O7 reacts with ethanol, C2H5OH, as shown below. Balance the chemical equation.

__ H+(aq) + __ Cr2O72−(aq) + __ C2H5OH(ℓ) ⟶ __ Cr3+(aq) + __ CO2(g) + __ H2O(ℓ)

Galvanic Cells

Galvanic Cell: A device in which chemical energy is changed into electrical energy.

Consider the reaction between MnO4− and Fe2+.

8 H+(aq) + MnO4−(aq) + 5 Fe2+(aq) ⟶ Mn2+(aq) + 5 Fe3+(aq) + 4 H2O(ℓ)

Fe2+ is oxidized and MnO4− is reduced ∴ electrons are transferred from

Fe2+ to MnO4−.

Note: The terms reducing agent and oxidizing agent are no longer used on the AP exam.

Galvanic Cells

Consider the reaction between MnO4− and Fe2+.

8 H+(aq) + MnO4−(aq) + 5 Fe2+(aq) ⟶ Mn2+(aq) + 5 Fe3+(aq) + 4 H2O(ℓ)

Reduction half-reaction: 8 H+ + MnO4− + 5 e− ⟶ Mn2+ + 4 H2O

Oxidation half-reaction: 5 (Fe2+ ⟶ Fe3+ + e−)

Ø  Separate the two species, thus requiring the e− transfer to occur through a wire.

Ø  Problem: Current flows for an instant, then ceases due to charge buildups.

Ø  Solution: Use a salt bridge or porous disk, which allow ions to flow without extensive mixing of the solutions. Maintain electrical neutrality

Galvanic Cells

Ø  The electrode compartment in which oxidation occurs is called the anode.

Ø  The electrode compartment in which reduction occurs is called the cathode.

Note: Textbook shows a porous disk frequently, but on the AP exam it’s always a salt bridge.

Galvanic Cells

Salt Bridge: Needed to allow charge balance to occur in the solutions the electrodes are immersed in. In the absence of the salt bridge, ions cannot flow to balance the buildup of cations in the anode compartment and the buildup of anions in the cathode compartment.

Cell Potential

Ø  Galvanic cell consists of a substance being reduced that “pulls” electrons through a wire from a substance that is being oxidized in the other compartment.

Ø  The “pull,” or driving force, on the electrons is called the cell potential (Ecell) or the electromotive force (emf) of the cell.

²  Textbook uses symbol , but E ° is used on the AP exam. Note the superscript circle, °, meaning standard conditions or standard state (see page 265).

²  ² 

Cell Potential

A galvanic cell involving the reactions Zn → Zn2+ + 2 e− (at the anode) and 2 H+ + 2 e− → H2 (at the cathode) has a potential of 0.76 V.

The standard hydrogen electrode where H2(g) at 1 atm is passed over a platinum electrode in contact with 1 M H+ ions. This electrode process (assuming ideal behavior) is arbitrarily assigned a value of exactly zero volts.

Cell Potential

Zn(s) + Cu2+(aq) ⟶ Zn2+(aq) + Cu(s) Example: Consider the reaction shown above. The diagram below shows a galvanic cell based on the reaction. Assume that the temperature is 25°C.

Cell Potential

Zn(s) + Cu2+(aq) ⟶ Zn2+(aq) + Cu(s) Example: Consider the reaction shown above. The diagram below shows a galvanic cell based on the reaction. Assume that the temperature is 25°C.

What does the voltmeter read? 1)  The accepted convention is to give the potentials of half-reactions as

reduction processes. 2)  Standard reduction potentials are the E ° values corresponding to

reduction half-reactions with all solutes at 1 M and all gases at 1.00 atm.

3)  One of the reduction half-reactions must be reversed (since redox reactions must involve a substance being oxidized and a substance being reduced).

Cell Potential

Zn(s) + Cu2+(aq) ⟶ Zn2+(aq) + Cu(s) Example: Consider the reaction shown above. The diagram below shows a galvanic cell based on the reaction. Assume that the temperature is 25°C.

What does the voltmeter read? 4)  The half-reaction with the largest positive potential will run as written (as

a reduction). 5)  The other half-reaction will be forced to run in reverse (will be the

oxidation reaction).

6)  Number of electrons lost = number of electrons gained. However, the value of E ° does NOT change when a half-reaction is multiplied by an integer.

Cell Potential

Zn(s) + Cu2+(aq) ⟶ Zn2+(aq) + Cu(s) Example: Consider the reaction shown above. The diagram below shows a galvanic cell based on the reaction. Assume that the temperature is 25°C.

What does the voltmeter read?

Multiple Choice Example 1

. . . Zn(s) + . . . H+(aq) + . . . NO3−(aq) ⟶ . . . Zn2+(aq) + . . . NH4

+(aq) + . . . H2O(ℓ)

When the equation above is balanced and all coefficients are reduced to lowest whole number terms, the coefficient for Zn(s) is

(A) 2

(B) 4

(C) 10

(D) 14

Multiple Choice Example 2

Cu2+(aq) + 2 e− → Cu(s) E° = 0.34 V

Cr3+(aq) + e− → Cr2+(aq) E° = −0.41 V

According to the half-reactions represented above, which of the following occurs in aqueous solutions under standard conditions?

(A) Cu2+(aq) + Cr3+(aq) → Cu(s) + Cr2+(aq)

(B) Cu2+(aq) + 2 Cr2+(aq) → Cu(s) + 2 Cr3+(aq)

(C) Cu(s) + 2 Cr3+(aq) → Cu2+(aq) + 2 Cr2+(aq)

(D) Cu(s) + Cr3+(aq) → Cu2+(aq) + Cr2+(aq)

Multiple Choice Example 3

Al3+(aq) + 3 e− → Al(s) E° = −1.66 V

Ag+(aq) + e− → Ag(s) E° = +0.80 V

According to the standard reduction potentials given above, what is the standard cell potential for the reaction represented below?

3 Ag+(aq) + Al(s) → 3 Ag(s) + Al3+(aq)

(A) −0.74 V

(B) +0.74 V

(C) +2.46 V

(D) +4.06 V

Electrochemistry and Thermodynamics

Ø  Based on previous discussions: E°cell > 0 ⟹ reaction is spontaneous (galvanic cell) E°cell < 0 ⟹ reaction is nonspontaneous

Ø  The maximum cell potential is directly related to the free energy difference between the reactants and the products in the cell:

ΔG° = −nFE° n = moles of e− F = Faraday’s constant

= 96,485 coulombs per mole of e−

Dependence of Cell Potential on Concentration

Ø  Recall: Under standard conditions, all concentrations are 1 M. Ø  Use Le Châtelier’s principle for qualitative understanding. Ø  Quantitative understanding is beyond the scope of the AP exam.

Ø  “The Nernst equation (pages 854−856) is beyond the scope of this course and the AP exam. Qualitative reasoning about the effects of concentration on cell potential is part of the course. However, inclusion of algorithmic calculations was not viewed as the best way to deepen understanding of the big ideas.” —The College Board

Dependence of Cell Potential on Concentration

Example 18.7, page 853: 2 Al(s) + 3 Mn2+(aq) ⟶ 2 Al3+(aq) + 3 Mn(s) E°cell = 0.48 V

For the cell reaction shown above, predict whether Ecell is greater than, less than, or equal to E°cell for the following cases. (a) [Al3+] = 2.0 M, [Mn2+] = 1.0 M

(b) [Al3+] = 1.0 M, [Mn2+] = 3.0 M

Problem 36, page 879:

Consider the galvanic cell shown above.

(a) Identify the species that is oxidized in the reaction. ________

(b) Identify the species that is reduced in the reaction. ________

(c) On the diagram, indicate the direction of electron flow in the wire.

Problem 36, page 879 (continued): (d) Determine the value of the standard voltage, E°, for the cell.

(e) Which electrode increases in mass as the reaction proceeds, and which electrode decreases in mass? Explain.

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Problem 78, page 881:

Consider the galvanic cell based on the following half-reactions:

Au3+ + 3 e− → Au E° = +1.50 V

Tl+ + e− → Tl E° = −0.34 V

(a) Write the balanced chemical equation for the overall cell reaction.

(b) Calculate the standard potential for the cell at 298 K.

(c) Calculate ΔG° for the cell at 298 K.

(d) Calculate the equilibrium constant, Kc, for the cell reaction at 298 K.

Electric Current Current: Flow of charge per unit time. AP questions that involve current can be solve using dimensional analysis.

I = qt

Symbol Definition Unit

Electrolysis (Electrolytic Cells)

Ø  Recall: A galvanic cell produces current when a redox reaction proceeds spontaneously.

Ø  A similar apparatus, an electrolytic cell, uses electrical energy to produce chemical change. The process of electrolysis involves forcing a current through a cell to produce a chemical change for which the cell potential is negative; that is, electrical work causes an otherwise nonspontaneous chemical reaction to occur.

Example 18.11, page 866: How long must a current of 5.00 amps be applied to a solution of Ag+ to produce 10.5 g of silver metal? Express your answer in minutes.

Electrolysis (Electrolytic Cells)

Problem 108, page 883: Copper can be plated onto a spoon by placing the spoon in an acidic solution of CuSO4(aq) and connecting it to a copper strip via a power source, as illustrated.

(a) On the diagram, label the anode and cathode.

(b) On the diagram, indicate the direction of electron flow in the wire.

(c) Write the half-reactions that occur at each electrode.

Electrolysis (Electrolytic Cells)