8.2 Charges
8.1.What is the charge on a small sphere that is attracted
to another sphere having charge 1.00 C if the spheres are
100.0 m apart and the force of attraction is 0.0225 N?
8.2.The force of attraction due to gravity follows an equation
similar to Coulomb’s law:
FGm^1 r 2 m^2
where m 1 and m 2 are the masses of the objects, ris the dis-
tance between the objects, and Gis the gravitational constant,
which equals 6.672 10
11 Nm^2 /kg^2.
(a)Calculate the force of gravitational attraction between
Earth and the sun if the mass of Earth equals 5.97 1024 kg,
the mass of the sun is 1.984 1030 kg, and the average dis-
tance between them is 1.494 108 km.
(b)Assuming that the sun and Earth would have the same
magnitude but opposite charges, what charge is necessary to
provide a coulombic force that equals the gravitational force
between the sun and Earth? How many moles of electrons is
that? To put your answer in perspective, consider that if Earth
were composed of pure iron, it would contain about 10^26
moles of Fe atoms.
8.3.Two small metallic bodies are given opposite charges,
with the negatively charged body having twice the charge of
the positively charged body. They are immersed in water (di-
electric constant 78) at a distance of 6.075 cm, and it is
found that the force of attraction between the two metal
pieces is 1.55 10
6 N. (a)What are the charges on the
pieces of metal? (b)What are the electric fields of the two
bodies?
8.4.In the centimeter-gram-second (cgs) system of units, a
statcoulomb is a unit of charge such that (1 statcoulomb)^2 /
(1 cm)^2 1 dyne, the cgs unit of force. How many stat-
coulombs are there in a coulomb?
8.5.What is the force of attraction between a negatively
charged electron and a positively charged proton at a distance
of 0.529 Å? You will need to look up the charge on the elec-
tron and proton (which have the same magnitude but oppo-
site sign charges), and use the fact that 1 Å 10
10 m.
8.3 & 8.4 Energy, Work, and
Standard Potentials
8.6.How much work is required to move a single electron
through a constant electric field of 1.00 V? (This amount of
work, or energy, is defined as an electron volt.)
8.7.Explain why an electromotive force is not,in fact, a force.
8.8.Explain why E°1/2values are not necessarily strictly addi-
tive. (Hint:consider the properties of intensive and extensive
variables.)
8.9.For each of the following reactions, determine the over-
all balanced electrochemical reaction, its standard electric po-
tential, and the standard Gibbs free energy of the reaction.
You may have to add solvent molecules (that is, H 2 O) to bal-
ance the reactions. Consult Table 8.2 for the half-reactions.
(a)MnO 2 O 2 →OH^ MnO 4
(b)Cu^ →Cu Cu^2
(c)Br 2 F^ →Br^ F 2
(d)H 2 O 2 H^ Cl^ →H 2 O Cl 2
8.10.On the left side of equation 8.21, G° is extensive (that
is, dependent on amount) whereas on the right side of equa-
tion 8.21, E° is intensive (that is, independent of amount).
Explain how the intensive variable can be related to the ex-
tensive variable.
8.11.Is the disproportionation reaction Fe^2 →Fe Fe^3
spontaneous? What is G° for the reaction?
8.12.A process requires 5.00 102 kJ of work to be per-
formed. Which of the following reactions might be used to
provide that work?
(a)Zn (s) Cu^2 →Zn^2 Cu (s)
(b)Ca (s) H^ →Ca^2 H 2
(c)Li (s) H 2 O →Li^ H 2 OH^
(d)H 2 OH^ Hg 2 Cl 2 →H 2 O Hg Cl^
8.13.If a calomel electrode is used instead of a standard hy-
drogen electrode, are the E° values shifted upor downby
0.2682 V? Justify your answer by determining the voltages of
the spontaneous electrochemical reactions of each standard
electrode with the half-reactions Li^ e^ →Li (s) and with
Ag^ e^ →Ag.
8.14.Determine E° and Gfor each of the following reactions.
(a)Au^3 2e^ →Au^
(b)Sn^4 4e^ →Sn
8.15.Conventional chemical wisdom states that metallic ele-
ments are more reactive on the lower left side of the periodic
table, and nonmetallic elements are more reactive on the up-
per right side of the periodic table. Electrochemically, this sug-
gests that fluorine and cesium would have the extreme values
of E°. Fluorine does have a very positive E° with respect to the
SHE, at 2.87 V. However, lithium has one of the highest E° val-
ues for a metal, at 3.045 V. (Cesium’s is only 2.92 V.) Can
you explain this?
8.16.Under biochemical standard states, the potential for the
reaction
NAD^ H^ 2e^ →NADH
is 0.320 V. If the concentrations of NAD^ and NADH are
1.0 M, what is the concentration of H^ under these condi-
tions? See the end of section 8.4 for E° for this reaction.238 Exercises for Chapter 8
EXERCISES FOR CHAPTER 1