Electrochemistry
The potential in volts has been measured for many different reduction half-reactions. The potential value is measured against the standard hydrogen elec-trode, which is assigned a value of zero. For consistency, these half-reactions are always written in the direction of the reduction. A half-reaction that has a posi-tive reduction potential proceeds in the direction of the reduction when it is cou-pled with a hydrogen electrode. A reaction that has a negative reduction potential proceeds in the oxidation direction when it is coupled with a hydrogen electrode. Table 1gives some common standard reduction potentials.
Problem Solving
Standard Standard
electrode electrode
Reduction potential, E0 Reduction potential, E0 half-reaction (in volts) half-reaction (in volts)
MnO4⫺⫹8H⫹⫹5e⫺^
Mn2⫹⫹4H2O ⫹1.50 Fe
3⫹
⫹3e⫺^Fe ⫺0.04 Au3⫹⫹3e⫺^Au ⫹1.50 Pb2⫹⫹2e⫺^Pb ⫺0.13 Cl2⫹2e⫺^2Cl⫺ ⫹1.36 Sn
2⫹
⫹2e⫺^Sn ⫺0.14 Cr2O7
2⫺⫹
14H⫹⫹6e⫺^
2Cr3⫹⫹7H2O ⫹1.23 Ni 2⫹
⫹2e⫺^Ni ⫺0.26 MnO2⫹4H⫹⫹2e⫺^
Mn2⫹⫹2H2O ⫹1.22 Cd
2⫹
⫹2e⫺^Cd ⫺0.40 Br2⫹2e⫺^2Br⫺ ⫹1.07 Fe
2⫹⫹
2e⫺^Fe ⫺0.45 Hg2⫹⫹2e⫺^Hg ⫹0.85 S ⫹2e⫺^S2⫺ ⫺0.48 Ag⫹⫹e⫺^Ag ⫹0.80 Zn2⫹⫹2e⫺^Zn ⫺0.76
Hg2 2⫹⫹
2e⫺^2Hg ⫹0.80 Al3⫹⫹3e⫺^Al ⫺1.66 Fe3⫹⫹e⫺^Fe2⫹ ⫹0.77 Mg2⫹⫹2e⫺^Mg ⫺2.37 MnO4⫺⫹e⫺^MnO4
2⫺
⫹0.56 Na⫹⫹e⫺^Na ⫺2.71 I2⫹2e⫺^2I⫺ ⫹0.54 Ca
2⫹⫹
2e⫺^Ca ⫺2.87 Cu2⫹⫹2e⫺^Cu ⫹0.34 Ba2⫹⫹2e⫺^Ba ⫺2.91 S ⫹2H⫹(aq) ⫹2e⫺^
H2S(aq) ⫹0.14 K⫹⫹e⫺^K ⫺2.93
Copyright © by Holt, Rinehart and Winston. All rights reserved.
You can use reduction potentials to predict the direction in which any redox reaction will be spontaneous. A spontaneous reaction occurs by itself, without outside influence. The redox reaction will proceed in the direction for which the difference between the two half-reaction potentials is positive. This direction is the same as the direction of the more positive half-reaction.
General Plan for Solving Electrochemical Problems
Write the individual half-reactions for both
oxidation and reduction.
Substitute and solve. Balanced ionic equation for the redox
reaction
Reduction occurs at the cathode.
Oxidation occurs at the anode.
Look up the reduction potential for the half-reaction in Table 1.
Look up the reduction potential for the half-reaction in Table 1.
1
E0
cell⫽ E0cathode⫺ E0anode
5
Balanced equation for
reduction
2a
Balanced equation for
oxidation
2b
Cathode
3a
Anode
3b
E0 cathode
4a
E0 anode
Sample Problem 1
Calculate the cell potential to determine whether the following reaction is spontaneous in the direction indicated.
Cd2ⴙ(aq) ⴙ2Iⴚ(aq)→Cd(s) ⴙI2(s)
Solution
ANALYZEWhat is given in the problem? reactants and products
What are you asked to find? whether the reaction is spontaneous
PLAN
What steps are needed to determine whether the reaction is spontaneous?
Separate into oxidation and reduction half-reactions. Find reduction potentials for each. Solve the equation for the cell potential to determine if the reaction is spontaneous.
reduction occurs at the cathode
oxidation occurs at the anode write the individual
half-reactions
Cd2⫹(aq) ⫹ 2I⫺(aq) 3 Cd(s) ⫹ I 2(s)
1
Cd2⫹(aq) ⫹ 2e⫺3 Cd(s)
2a
2I⫺(aq) 3 I
2(s) ⫹ 2e⫺
2b
look up the reduction potential for the half-reaction in Table 1
look up the reduction potential for the half-reaction in Table 1 Cathode
3a
Anode
3b
Items Data
Reactants Cd2⫹(aq) ⫹2I⫺(aq)
Products Cd(s) ⫹I2(s)
E0cathode ? V
E0anode ? V
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Write the given equation.
Cd2⫹(aq) ⫹2I⫺(aq) →Cd(s) ⫹I2(s)
The oxidation number of cadmium decreases; it is reduced.
Cd2⫹(aq) ⫹2e⫺→Cd(s)
The oxidation number of iodine increases; it is oxidized.
2I⫺(aq) →I2(s) ⫹2e⫺
Cadmium is the cathode, and iodine is the anode.
Determine spontaneity. If the cell potential is positive, the reaction is sponta-neous as written. If the cell potential is negative, the reaction is not spontasponta-neous as written, but the reverse reaction is spontaneous.
COMPUTE
E0cell⫽ ⫺0.40 V ⫺0.54 V ⫽ ⫺0.94 V
The reaction potential is negative. Therefore, the reaction is not spontaneous. The reverse reaction would have a positive potential and would, therefore, be spontaneous.
Cd2⫹(aq) ⫹2I⫺(aq) →Cd(s) ⫹I2(s) not spontaneous
Cd(s) ⫹I2(s) →Cd 2⫹
(aq) ⫹2I⫺(aq) spontaneous
EVALUATE
Are the units correct?
Yes; cell potentials are in volts.
Is the number of significant figures correct?
Yes; the number of significant figures is correct because the half-cell potentials have two significant figures.
Is the answer reasonable?
Yes; the reduction potential for the half-reaction involving iodine was more positive than the potential for the reaction involving cadmium, which means that I2has a greater attraction for electrons than Cd
2ⴙ
. Therefore, I2is more likely
to be reduced than Cd2ⴙ. The reverse reaction is favored. E0
cathode⫽
from Table 1 ⫺0.40 V
E0
anode⫽ ⫹0.54 V from Table 1
E0 cathode
⫽ ⫺ E0
anode
E0 cell
Practice
Use the reduction potentials in Table 1 to determine whether the following reac-tions are spontaneous as written. Report the E0cellfor the reactions.
1.Cu2⫹⫹Fe → Fe2⫹⫹Cu ans: ⴙ0.79 V; spontaneous
2.Pb2⫹⫹Fe2⫹→Fe3⫹⫹Pb ans: ⴚ0.90 V; nonspontaneous
3.Mn2⫹⫹4H2O ⫹Sn 2⫹→
MnO4⫺⫹8H⫹⫹Sn ans: ⴚ1.64 V; nonspontaneous
4.MnO4 2⫺
Copyright © by Holt, Rinehart and Winston. All rights reserved.
5.Hg22⫹⫹2MnO42⫺→2Hg ⫹2MnO4⫺ans: ⴙ0.24 V; spontaneous
6.2Li⫹⫹Pb →2Li ⫹Pb2⫹ans: ⴚ2.91 V; nonspontaneous
7.Br2⫹2Cl⫺→2Br⫺⫹Cl2ans: ⴚ0.29 V; nonspontaneous
Sample Problem 2
A cell is constructed in which the following two half-reactions can occur in either direction.
Zn2ⴙⴙ2eⴚ^Zn Br2ⴙ2eⴚ^2Brⴚ
Write the full ionic equation for the cell in the spontaneous direction, identify the reactions occurring at the anode and cathode, and determine the cell’s voltage.
Solution
ANALYZEWhat is given in the problem? the reversible half-reactions of the cell
What are you asked to find? the equation in the spontaneous direction; the voltage of the cell
PLAN
What steps are needed to determine the spontaneous reaction of the cell and the cell voltage?
Determine which half-reaction has the more positive reduction potential. This will be the reduction half-reaction; it occurs at the cathode. Reverse the other half-reaction so that it becomes an oxidation half-reaction; it occurs at the anode. Adjust the half-reactions so that the same number of electrons are lost as are gained. Add the reactions together. Compute the cell voltage by the formula E0cellⴝE
0
cathodeⴚ E 0
anode, using the reduction potentials for the
reaction at each electrode.
Items Data
Half-reaction 1 Zn2⫹⫹2e⫺^Zn
Half-reaction 2 Br2⫹2e⫺^2Br
Reduction potential of 1 ⫺0.76 V
Reduction potential of 2 ⫹1.07 V
Full ionic reaction ?
Copyright © by Holt, Rinehart and Winston. All rights reserved.
First, look up the reduction potentials for the two half-reactions in Table 1.
Br2has the larger reduction potential; therefore, it is the cathode. Zn has the smaller reduction potential; therefore, it is the anode.
The cathode half-reaction is
Br2⫹2e⫺→2Br
The anode half-reaction is
Zn →Zn2⫹⫹2e⫺
The full-cell equation is
Br2⫹2e⫺→2Br⫺
⫹Zn →Zn2⫹⫹2e⫺
Br2⫹Zn →2Br⫺⫹Zn2⫹
Substitute the reduction potentials for the anode and cathode into the cell poten-tial equation, and solve the equation.
E0
cell⫽E ⫺ 0 cathode E 0 anode Zn E0 Br2 E0 Zn⫽
E0 ⫺0.76 V from Table 1 Br2⫽
E0 ⫹1.07 V from Table 1 look up the
reduction potential for the half-reaction in Table 1
look up the reduction potential for the half-reaction in Table 1
Br2⫹ 2e⫺^ 2Br⫺
reduction occurs at the cathode
substitute and solve
oxidation occurs at the anode
combine to write the full ionic equation
Zn2⫹⫹ 2e⫺^ Zn
Br2⫹ 2e⫺3 2Br⫺ Zn 3 Zn2⫹⫹ 2e⫺
Br2⫹ Zn 3 2Br⫺⫹ Zn2⫹
E0 cell⫽ E
0
cathode⫺ E 0
anode the half-cell with
the larger reduction potential is the cathode
the half-cell with the smaller reduction potential is the anode
E0
half-reaction E0half-reaction
COMPUTE
Br2⫹Zn →2Br⫺⫹Zn 2⫹
E0cell⫽1.07 V ⫺(⫺0.76 V) ⫽1.83 V
EVALUATE
Are the units correct?
Yes; the cell potential is in volts.
Is the number of significant figures correct?
Yes; the half-cell potentials were given to two decimal places.
Is the answer reasonable?
Yes; you would expect the reaction to have a positive cell potential because it should be spontaneous.
Practice
If a cell is constructed in which the following pairs of reactions are possible, what would be the cathode reaction, the anode reaction, and the overall cell voltage?
1.Ca2⫹⫹2e⫺^Ca Fe3⫹⫹3e⫺^Fe
ans: cathode: Fe3ⴙⴙ3eⴚ3Fe, anode: Ca3Ca2ⴙⴙ2eⴚ, E0cellⴝ ⴙ2.83 V
2.Ag⫹⫹e⫺^Ag
S ⫹2H⫹⫹2e⫺^H2S
ans: cathode: Agⴙⴙeⴚ3Ag, anode: H2S3S ⴙ2Hⴙⴙ2eⴚ, E 0
cellⴝ ⴙ0.66 V
3.Fe3⫹⫹e⫺^Fe2⫹ Sn2⫹⫹2e⫺^ Sn
ans: cathode: Fe3ⴙⴙeⴚ3Fe2ⴙ, anode: Sn 3Sn2ⴙⴙ2eⴚ, E0cell ⴝ ⴙ0.91 V
4.Cu2⫹⫹2e⫺^Cu Au3⫹⫹3e⫺^Au
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Additional Problems
Use reduction potentials to determine whether the reactions in the following 10 problems are spontaneous.
1.Ba ⫹Sn2⫹→Ba2⫹⫹Sn
2.Ni ⫹Hg2⫹→Ni2⫹⫹Hg
3.2Cr3⫹⫹7H2O ⫹6Fe 3⫹
→Cr2O7 2⫺
⫹14H⫹⫹6Fe2⫹
4.Cl2⫹Sn →2Cl⫺⫹Sn 2⫹
5.Al ⫹3Ag⫹→Al3⫹⫹3Ag
6.Hg2 2⫹
⫹S2⫺→2Hg ⫹S
7.Ba ⫹2Ag⫹→Ba2⫹⫹2Ag
8.2I⫺⫹Ca2⫹→I2⫹Ca
9.Zn ⫹2MnO4⫺→Zn 2⫹
⫹2MnO4 2⫺
10.2Cr3⫹⫹3Mg2⫹⫹7H2O →Cr2O7 2⫺⫹
14H⫹⫹3Mg
In the following problems, you are given a pair of reduction half-reactions. If a cell were constructed in which the pairs of half-reactions were possible, what would be the balanced equation for the overall cell reaction that would occur? Write the half-reactions that occur at the cathode and anode, and calculate the cell voltage.
11.Cl2⫹2e⫺^2Cl⫺ Ni2⫹⫹2e⫺^ Ni
12.Fe3⫹⫹3e⫺^Fe Hg2⫹⫹2e⫺^Hg
13.MnO4⫺⫹e⫺^MnO42⫺ Al3⫹⫹3e⫺^ Al
14.MnO4⫺⫹8H⫹⫹5e⫺^Mn 2⫹⫹
4H2O S ⫹2H⫹⫹2e⫺^H2S
15.Ca2⫹⫹2e⫺^Ca Li⫹⫹e⫺^Li
16.Br2⫹2e⫺^2Br⫺
MnO4⫺⫹8H⫹⫹5e⫺^Mn 2⫹
⫹4H2O
17.Sn2⫹⫹2e⫺^ Sn Fe3⫹⫹e⫺^Fe2⫹
18.Zn2⫹⫹2e⫺^ Zn
Cr2O72⫺⫹14H⫹⫹6e⫺^2Cr3⫹⫹7H2O
19.Ba2⫹⫹2e⫺^Ba Ca2⫹⫹2e⫺^Ca
20.Hg2 2⫹
