chapter 20. · pdf fileap chemistry chapter 20 electrochemistry - 5 - practice exercise 2...

AP Chemistry Chapter 20 Electrochemistry

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Chapter 20. Electrochemistry

20.1 Oxidation-Reduction Reactions

• Oxidation-reduction reactions = chemical reactions in which the oxidation state of one or more substance changes (redox reactions). • Recall: Oxidation involves loss of electrons (OIL). Reduction involves gain of electrons (RIG). • Consider the spontaneous reaction that occurs when Zn is added to HCl. Zn(s) + 2H+(aq) Zn2+(aq) + H2(g) • The oxidation number of Zn has ↑from 0 to +2. • The oxidation number of H has ↓ from +1 to 0. Zn is oxidized to Zn2+ while H+ is reduced to H2. • H+ causes Zn to be oxidized.

H+ is the oxidizing agent or oxidant. Examples of good oxidizing agents: H2O2, MnO4

-, Cr2O72-, Ce4+, O3, and the halogens.

• Zn causes H+ to be reduced. Zn is the reducing agent or reductant. Examples of good reducing agents:

alkali and alkaline earth metals. • Note: the reducing agent is oxidized and the oxidizing agent is reduced.

Sample Exercise 20.1 (p. 859) The nickel-cadmium (nicad) battery, a rechargeable “dry cell” used in battery-operated devices, uses the following redox reaction to generate electricity: Cd(s) + NiO2(s) + 2 H2O(l) Cd(OH)2(s) + Ni(OH)2(s) Identify the substances that are oxidized and reduced. .


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Practice Exercise 1 (20.1)

What is the reducing agent in the following reaction? i.e. What is oxidized? 2 Br-

(aq) + H2O2(aq) + 2 H+(aq) Br2(aq) + 2 H2O(l)

a) Br-

(aq) b) H2O2(aq) c) H+

(aq) d) Br2(aq) e) Na+

(aq)


Identify the oxidizing (that which is reduced) and reducing agents (that which is oxidized) in the following oxidation-reduction equation: 2 H2O(l) + Al(s) + MnO4

-(aq) Al(OH)4

-(aq) + MnO2(s)

20.2 Balancing Oxidation-Reduction Equations • Conservation of mass: The amount of each element present at the beginning of the reaction must be present

at the end. • Conservation of charge: Electrons are not lost in a chemical reaction.

Half-Reactions • Half-reactions are a convenient way of separating oxidation and reduction reactions.

Sn2+(aq) + 2Fe3+(aq) Sn4+(aq) + 2Fe2+(aq) Oxidation half-reaction: Sn2+(aq) Sn4+(aq) +2e– (electrons are a product) Reduction half-reaction: 2Fe3+(aq) + 2e– 2Fe2+(aq) (electrons are a reactant) Practice:

Write half-reactions for a reaction between Cu2+ and Zn metal.

Overall:

Oxidation:

Reduction:


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Balancing Equations by the Method of Half-Reactions

1. Write the overall unbalanced reaction (if available). 2. (i) Identify oxidized and reduced substances

(ii) Write down the two incomplete half reactions. 3. Balance each half reaction: (a) First, balance elements other than H and O. (b) Then balance O atoms by adding water on side deficient in O atoms. (c) Then balance H by adding H+ for acidic solutions (or OH- for alkaline solutions). (d) Finish by balancing charge by adding electrons. 4. Multiply each half-reaction by the appropriate factors so that the number of electrons gained equals electrons lost. 5. Now add the reactions and simplify.

Sample Exercise 20.2 (p. 862) Complete and balance the following equation by the method of half-reactions: Cr2O7

2-(aq) + Cl-

(aq) Cr3+(aq) + Cl2(g) (acidic solution)

Practice Exercise 1 (20.2) If you complete and balance the following equation in acidic solution Mn2+

(aq) + NaBiO3(s) Bi3+(aq) + MnO4

-(aq) + Na+

(aq) how many water molecules are there in the balanced equation (for the reaction balanced with the smallest whole-number coefficients)?

a) Four on the reactants side b) Three on the product side c) One on the reactant side d) Seven on the product side e) Two on the product side


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Practice Exercise 2 (20.2) Complete and balance the following equation in acidic solution using the method of half-reactions.

Cu(s) + NO3-(aq) Cu2+

(aq) + NO2(g)

Balancing Equations for Reactions Occurring in Basic Solution • The same method as above is used, but OH– is added to “neutralize” the H+ used. • The equation must again be simplified by canceling like terms on both sides of the equation.

Sample Exercise 20.3 (p. 864) Complete and balance this equation for a redox reaction that takes place in basic solution: CN-

(aq) + MnO4-(aq) CNO-

(aq) + MnO2(s) (basic solution)

Practice Exercise 1 (20.3) If you complete and balance the following oxidation-reduction reaction in basic solution NO2

-(aq) + Al(s) NH3(aq) + Al(OH)4

-(aq)

how many hydroxide ions are there in the balanced equation (for the reaction balanced with the smallest whole-number coefficients)?

a) One on the reactant side b) One on the product side c) Four on the reactant side d) Seven on the product side e) none


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Complete and balance the following oxidation-reduction reaction in basic solution:

Cr(OH)3(s) + ClO-(aq) CrO4

2-(aq) + Cl2(g)


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20.3 Voltaic (Galvanic) Cells

• generates electrical energy from a spontaneous redox reaction • can be used to do work IF the half reactions are kept separate • electron transfer occurs via an external circuit • must provide a conductor for transfer of electrons plus a salt bridge to keep the separate half-reactions

electrically neutral • anode is where oxidation takes place (electrons are released, so it is the negative electrode) • electrons move from the anode to the cathode (where reduction takes place – electrons are attracted to the

“positive” electrode) Figure 20.5 Voltaic Cell

• e.g. CuNO3(aq) with a Cu electrode (cathode) and ZnNO3(aq) with a Zn electrode (anode) • This voltaic cells consists of: An oxidation half-reaction: Zn(s) Zn2+(aq) + 2e– (at the anode). • A reduction half-reaction: Cu2+(aq) + 2e– Cu(s) (at the cathode). • The two solid metals are the electrodes (cathode and anode).


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Sample Exercise 20.4 (p. 867)

The following oxidation-reduction reaction is spontaneous: Cr2O7

2-(aq) + 14 H+

(aq) + 6 I-(aq) 2 Cr3+

(aq) + 3 I2(s) + 7 H2O(l) A solution containing K2Cr2O7 and H2SO4 is poured into one beaker, and a solution of KI is poured into another. A salt bridge is used to join the beakers. A metallic conductor that will not react with either solution (such as platinum foil) is suspended in each solution, and the two conductors are connected with wires through a voltmeter or some other device to detect an electric current. The resultant voltaic cell generates an electric current. Indicate the reaction occurring at the anode, the reaction at the cathode, the direction of electron and ion migrations, and the signs of the electrodes. (Draw a diagram.)

Practice Exercise 1 (20.4) The following two half-reactions occur in a voltaic cell: Ni(s) Ni2+

(aq) + 2 e- (electrode = Ni) Cu2+

(aq) + 2 e- Cu(s) (electrode = Cu) Which one of the following descriptions most accurately describes what is occurring in the half-cell containing the Cu electrode and Cu2+

(aq) solution?

a) The electrode is losing mass and cations from the salt bridge are flowing into the half-cell. b) The electrode is is gaining mass and cations from the salt bridge are flowing into the half-cell. c) The electrode is losing mass and anions from the salt bridge are flowing into the half-cell. d) The electrode is is gaining mass and anions from the salt bridge are flowing into the half-cell.


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The two half-reactions in a voltaic cell are Zn(s) Zn2+

(aq) + 2 e- ClO3

-(aq) + 6 H+

(aq) + 6 e- Cl-(aq) + 3 H2O(l)

a) Indicate which reaction occurs at the anode and which at the cathode. b) Which electrode is consumed in the cell reaction? c) Which electrode is positive?

A Molecular View of the Electrode Process

• “Rules” of voltaic cells: • At the anode electrons are products. • Oxidation occurs at the anode. • Any ions that are getting oxidized (usually, but not always, anions) flow towards the anode. • Any ions that are products of oxidation flow away from the anode. • At the cathode electrons are reactants. • Reduction occurs at the cathode. • Any ions that are getting reduced (usually, but not always, cations) flow towards the anode. • Any ions that are products of reduction flow away from the cathode. • The flow of electrons from anode to cathode requires an external wire. • The transfer of ions through a salt bridge maintains overall charge balance for the two

compartments.


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20.4 Cell EMF • Electrons flow from anode to cathode because the cathode has a lower electrical potential energy than the

anode. • Potential difference = difference in electrical potential, measured in volts. • One volt (V) = the potential difference required to impart one joule (J) of energy to a charge of one

coulomb (C):

• Electromotive force (emf) = the force required to push electrons through the external circuit. • Cell potential: Ecell = emf of a cell = the cell voltage. Ecell is > 0 for a spontaneous reaction. • For 1M solutions or 1 atm pressure for gases at 25oC (standard conditions), the standard emf (standard

cell potential) is called Eocell.

• e.g. for the reaction: Zn(s) + Cu2+(aq) Zn2+(aq) + Cu(s) Eo

cell = +1.10 V

Standard Reduction (Half-Cell) Potentials

• Standard reduction potentials, Eo

red are measured relative to a standard. • The emf of a cell can be calculated from standard reduction potentials: E o

cell= Eored(cathode) – Eo

red (anode) • We use the following half-reaction as our standard: 2H+ (aq, 1M) + 2e– H2(g, 1 atm) Eo

cell = 0V. • This electrode is called a standard hydrogen electrode (SHE) or the normal hydrogen electrode (NHE). • The SHE is assigned a standard reduction potential of zero.

CJ1V1 =


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Figure 20.9


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For the Zn-Cu2+ voltaic cell shown in Figure 20.5, we have Zn(s) + Cu2+

(aq, 1M) Zn2+(aq, 1M) + Cu(s) Eo

cell = 1.10 V Given that the standard reduction potential of Zn2+ to Zn is -0.76 V, calculate the Eo

red for the reduction of Cu2+ to Cu. Cu2+

(aq, 1M) + 2 e- Cu(s) (0.34 V)

Practice Exercise 1 (20.5) A voltaic cell based on the reaction 2 Eu2+

(aq) + Ni2+(aq) 2 Eu3+

(aq) + Ni(s) generates Eo = 0.07 V. Given the standard reduction potential of Ni2+ given in Table 20.1 (-0.28 V) what is he standard reduction potential for the reaction Eu3+

(aq) + e- Eu2+(aq)?

a) -0.35 V b) 0.35 V c) -0.21 V d) 0.21 V e) 0.07 V


A voltaic cell is based on the following half-reactions: In+

(aq) In3+(aq) + 2 e-

Br2(l) + 2 e- 2 Br-(aq)

The standard emf for this cell is 1.46 V. Using the data in Table 20.1 or your AP Chem packet, calculate Eo

red for the reduction of In3+ to In+. (-0.40 V)


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Using the standard reduction potentials listed in Table 20.1, calculate the standard emf for the voltaic cell described in Sample Exercise 20.4, which is based on the following reaction: Cr2O7

2-(aq) + 14 H+

(aq) + 6 I-(aq) 2 Cr3+

(aq) + 3 I2(s) + 7 H2O(l) (0.79 V)

Practice Exercise 1 (20.6) Using the data in Table 20.1 what value would you calculate for the standard emf (Eo

cell) for a voltaic cell that employs the overall cell reaction 2 Ag+

(aq) + Ni(s) 2 Ag(s) + Ni2+(aq)?

a) +0.52 V b) -0.52 V c) +1.08 V d) -1.08 V e) +0.80 V

Practice Exercise 2 (20.6) Using the data in Table 20.1, calculate the standard emf for a cell that employs the following overall cell reaction:

2 Al(s) + 3 I2(s) 2 Al3+(aq) + 6 I-

(aq) (+2.20 V)


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A voltaic cell is based on the following two standard half-reactions:

Cd2+(aq) + 2 e- Cd(s)

Sn2+(aq) + 2 e- Sn(s)

By using the data in Appendix E, determine

a) the half-reactions that occur at the cathode and the anode, and b) the standard cell potential (0.267 V)

Practice Exercise 1 (20.7) Consider three voltaic cells, each similar to the one shown in Figure 20.5. In each voltaic cell, one half-cell contains a 1.0 M Fe(NO3)2(aq) solution with an Fe electrode. The contents of the other half-cells are as follows: Cell 1: a 1.0 M CuCl2(aq) solution with a Cu electrode Cell 2: a 1.0 M NiCl2(aq) solution with a Ni electrode Cell 3: a 1.0 M ZnCl2(aq) solution with a Zn electrode In which voltaic cell(s) does iron act as the anode?

a) Cell 1 b) Cell 2 c) Cell 3 d) Cells 1 and 2 e) All three cells.


A voltaic cell is based on a Co2+/Co half-cell and an AgCl/Ag half-cell. a) Which half-reaction occurs at the anode? b) What is the standard cell potential? (0.499 V)


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Strengths of Oxidizing and Reducing Agents

• We can use the table standard reduction potentials to determine the relative strengths of reducing (and oxidizing) agents. • The more positive the Eo

red the stronger the oxidizing agent (written in the table as a reactant) • The more negative the Eo

red the stronger the reducing agent (written as a product in the table). • We can use this to predict if one reactant can spontaneously oxidize another. • e.g. F2 can oxidize H2 or Li. Ni2+ can oxidize Al(s). • We can use this table to predict if one reactant can spontaneously reduce another. • e.g. Li can reduce F2.

Sample Exercise 20.8 (p. 875) Using Table 20.1, rank the following ions in order of increasing strength as oxidizing agents: NO3

-(aq), Ag+

(aq), Cr2O7

2-(aq).

Practice Exercise 1 (20.8) Based on the data in Table 20.1, which of the following species would you expect to be the strongest oxidizing agent (i.e. most likely to be reduced)?

a) Cl-(aq) b) Cl2(g) c) O2(g) d) H+

(aq) e) Na+(aq)

Practice Exercise 2 (20.8) Using Table 20.1, rank the following species from the strongest to the weakest reducing agent (i.e. most likely to be reduced to the least likely to be reduced): I-

(aq), Fe(s), Al(s).


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20.5 Free Energy and Redox Reactions

• For any electrochemical process Eo = Eo

red(reduction process) – Eored(oxidation process).

• A positive Eo indicates a spontaneous process (galvanic cell). • A negative Eo indicates a nonspontaneous process.

Sample Exercise 20.9 (p. 876) Using standard reduction potentials (Table 20.1), determine whether the following reactions are spontaneous under standard conditions:

a) Cu(s) + 2 H+(aq) Cu2+

(aq) + H2(g) b) Cl2(g) + 2 I-

(aq) 2 Cl-(aq) + I2(s)

Practice Exercise 1 (20.9) Which of the following elements is capable of oxidizing Fe2+

(aq) ions to Fe3+(aq) ions: chlorine, bromine, iodine?

a) I2 b) Cl2 c) Cl2 and I2 d) Cl2 and Br2 e) all three elements

Practice Exercise 2 (20.9) Using standard reduction potentials (Appendix E), determine whether the following reactions are spontaneous under standard conditions:

a) I2(s) + 5 Cu2+(aq) + 6 H2O(l) 2 IO3

-(aq) + 5 Cu(s) + H+

(aq) b) Hg2+

(aq) + 2 I-(aq) Hg(l) + I2(s)

c) H2SO3(aq) + 2 Mn(s) + 4 H+(aq) S(s) + 2 Mn2


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( )( ) e molV500,96

e mol500,961 --

JCF ==

EMF and ∆G • We can show that: ∆G = - nFE • Where ∆G is the change in free energy, n is the number of moles of electrons transferred, F is Faraday's

constant and E is the emf of the cell. • We define a faraday (F) as: • Since n and F are positive, if ∆G < 0 then E > 0, and the reaction will be spontaneous. • When the reactants and products are in their standard states: ∆Go = –nFEo


a) Use the standard reduction potentials listed in Table 20.1 to calculate the standard free-energy change, ∆Go, and the equilibrium constant, K, at 298 K for the following reaction:

4 Ag(s) + O2(g) + 4 H+(aq) 4 Ag+

(aq) + 2 H2O(l) (∆Go = -170 kJ/mol, K = 9 x 1029)

b) Suppose the reaction in part (a) were written as 2 Ag(s) + ½ O2(g) + 2 H+

(aq) 2 Ag+(aq) + H2O(l)

What are the values of Eo, ∆Go and K when the reaction is written in this way? (Eo = +0.43 V, ∆Go = - 83 kJ/mol, K = 4 x 1014)


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For the reaction 3 Ni2+

(aq) + 2 Cr(OH)3(s) + 10 OH-(aq) 3 Ni(s) + 2 CrO4

2-(aq) + 8 H2O(l)

∆Go = +87 kJ/mol. Given the standard reduction potential of Ni2+(aq) in Table 20.1, what value do you calculate

for the standard reduction potential of the half-reaction CrO4

2-(aq) + 4 H2O(l) + 3 e- Cr(OH)3(s) + 5 OH-

(aq)?

a) -0.43 V b) -0.28 V c) 0.02 V d) -0.13 V e) -0.15 V

Practice Exercise 2 (20.10) Consider the reaction 2 Ag+

(aq) + H2(g) 2 Ag(s) + 2 H+(aq)

Calculate ∆Gof for the Ag+

(aq) ion from the standard reduction potentials in Table 20.1 and the fact that ∆Gof for

H2(g), Ag(s) and H+(aq) are all zero. Compare your answer with the value given in Appendix C.

20.6 Cell EMF Under Nonstandard Conditions • A voltaic cell is functional until E = 0 at which point equilibrium has been reached. • The cell is then “dead.” • The point at which E = 0 is determined by the concentrations of the species involved in the redox reaction.


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The Nernst Equation • We can calculate the cell potential under nonstandard conditions. • Recall that:

∆G = ∆Go + RTlnQ • We can substitute in our expression for the free energy change:

−nFE = −nFEo + RTlnQ • Rearranging, we get the Nernst equation:

or

• Note the change from natural logarithm to log base 10. • The Nernst equation can be simplified by collecting all the constants together and using a temperature of

298 K:


Calculate the emf at 298 K generated by a voltaic cell in which the reaction is Cr2O7

2-(aq) + 14 H+

(aq) + 6 I-(aq) 2 Cr3+

(aq) + 3 I2(s) + 7 H2O(l)

when [Cr2O7

2-] = 2.0 M, [H+] = 1.0 M, [I-] = 1.0 M, and [Cr3+] = 1.0 x 10-5 M. (E = +0.89 V)

Practice Exercise 1 (20.11) Consider a voltaic cell whose overall reaction is Pb2+

(aq) + Zn(s) Pb(s) + Zn2+(aq). What is the emf generated by

this voltaic cell when the ion concentrations are [Pb2+] = 1.5 x 10-3 M and [Zn2+] = 0.55 M?

a) 0.71 V b) 0.56 V c) 0.49 V d) 0.79 V e) 0.64 V

QnFRTEE ln−°=

QnF

RTEE log303.2−°=

Qn

EE log0592.0−°=


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For the Zn-Cu voltaic cell depicted in Figure 20.5 would the emf increase, decrease, or stay the same, if you increased the Cu2+

(aq) concentration by adding CuSO4.5H2O to the cathode compartment?


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If the voltage of a Zn-H+ cell (like that in Figure 20.9) is 0.45 V at 25oC when [Zn2+] = 1.0 M and PH2 = 1.0 atm, what is the pH of the cathode solution? (5.2)

Practice Exercise 1 (20.12) Consider a voltaic cell where the anode half-reaction is Zn(s) Zn2+

(aq) + 2 e- and the cathode half-reaction is Sn2+

(aq) + 2 e- Sn(s). What is the concentration of Sn2+ if Zn2+ is 2.5 x 10-3 M and the cell emf is 0.660 V? Use the reduction potentials in Appendix E that are reported to three significant figures.

a) 3.3. x 10-2 M b) 1.9 x 10-4 M c) 9.0 x 10-3 M d) 6.9 x 10-4 M e) 7.6 x 10-3 M

Practice Exercise 2 (20.12) What is the pH of the solution in the cathode compartment of the cell pictured in Figure 20.9 when PH2 = 1.0 atm, [Zn2+] in the anode compartment is 0.10 M, and cell emf is 0.542 V? (pH = 4.23)


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Concentration Cells • A concentration cell is one whose emf is generated solely because of a concentration difference.

Sample Exercise 20.13 (p. 885) A voltaic cell is constructed with two hydrogen electrodes. Electrode 1 has PH2 = 1.00 atm and an unknown concentration of H+

(aq). Electrode 2 is a standard hydrogen electrode ([H+] = 1.00 M, PH2 = 1.00 atm). At 298 K the measured cell voltage is 0.211 V, and the electrical current is observed to flow from electrode 1 through the external circuit to electrode 2. Calculate [H+] for the solution at electrode 1. What is its pH? (pH = 3.57)

Practice Exercise 1 (20.13) A concentration cell constructed from two hydrogen electrodes, both with PH2 = 1.00 M. One electrode is immersed in pure H2O and the other in 6.0 M hydrochloric acid. What is the emf generated by the cell and what is the identity of the electrode that is immersed in hydrochloric acid?

a) -0.23 V, cathode b) 0.46 V, anode c) 0.023 V, anode d) 0.23 V, cathode e) 0.23 V, anode

Practice Exercise 2 (20.13) A concentration cell is constructed with two Zn(s)-Zn2+

(aq) half-cells. The first half-cell has [Zn2+] = 1.35 M, and the second half-cell has [Zn2+] = 3.75 x 10-4 M. a) Which half-cell is the anode of the cell? b) What is the emf of the cell? (0.105 V)


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Cell EMF and Chemical Equilibrium • A system is at equilibrium when ∆G = 0. • From the Nernst equation, at equilibrium and 298 K (E = 0 V and Q = Keq) • Thus, if we know the cell emf, we can calculate the equilibrium constant.

20.9 Electrolysis

• Electrolysis reactions are nonspontaneous reactions that require an external current in order to force the

reaction to proceed. • They take place in electrolytic cells. • In voltaic and electrolytic cells, reduction occurs at the cathode, and oxidation occurs at the anode. • However, in electrolytic cells, electrons are forced to flow from the anode to the cathode. • In electrolytic cells the anode is positive and the cathode is negative. • In voltaic cells the anode is negative and the cathode is positive.

Electrolysis with Active Electrodes

• Active electrodes: electrodes that take part in electrolysis. Example: electroplating.

0592.0log

log0592.00

°=

−°=

nEK

Kn

E

eq

eq


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Quantitative Aspects of Electrolysis

• We want to know how much material we obtain with electrolysis. • The charge of one mol of electrons is 96,500 C (1 F). • A coulomb is the amount of charge passing a point in one second when the current is one ampere. • The amount of Cu can be calculated from the current (I) and time (t) required to plate. Q = I t

Sample Exercise 20.14 (p. 895) Calculate the number of grams of aluminum produced in 1.00 hr by the electrolysis of molten AlCl3 if the electrical current is 10.0 A. (3.3.6 g Al)

Practice Exercise 1 (20.14) How much time is needed to deposit 1.0 g of chromium metal from an aqueous solution of CrCl3 using a current of 1.5 A? a) 3.8 x 10-2 s b) 21 min. c) 62 min. d) 139 min. e) 3.2 x 103 min.


a) The half-reaction for formation of magnesium metal upon electrolysis of molten MgCl2 is Mg2+ + 2e- Mg. Calculate the mass of magnesium formed upon passage of a current of 60.0 A for a period of 4.00 x 103 s.

(30.2 g Mg)

b) How many seconds would be required to produce 50.0 g of Mg from MgCl2 if the current is 100.0 A?

(3.97 x 103 s)


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Electrochemistry Terminology Current = a flow of electrical charge through a conductor. The current at a particular cross-section is the rate of flow of the charge. The charge may be carried by electrons (in metals), ions (electrolyte solutions) or positive holes (semi-conductors). Measured in amperes. Coulomb is the central unit for electrochemistry, enables us to maneuver amongst charge, voltage, current, watts, electrons and mass. The Faraday relates the charge to the number of electrons. 1 V = 1 J/C 1 A = 1 C/s 1 W = 1 J/s 1 F = 96,500 C/mol e- Electrical work: energy units x time 1 watt = 1 J/s 1 watt = 1 V x 1 A # Watts = volts x amps or J x C C s

Sample Integrative Exercise 20 (p. 897) The Ksp at 298 K for iron (II) fluoride is 2.4 x 10-6.

a) Write a half-reaction that gives the likely products of the two-electron reduction of FeF2(s) in water. b) Use the Ksp value and the standard reduction potential of Fe2+

(aq) to calculate the standard reduction potential for the half-reaction in part (a). (-0.606 V)

c) Rationalize the difference in the reduction potential for the half-reaction in part (a) with that for

Fe2+(aq).

chapter 20. · pdf fileap chemistry chapter 20 electrochemistry - 5 - practice exercise 2...

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