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Solutions Manual Online
CHAPTER 1 SOLUTIONS
1. From Table A.10 in the Appendix, first obtain the atomic weights of
the elements composing SO42:
2. From Table A.10 in the Appendix, the atomic weights of the elements
composing SO
2
are:
S:32 g/mol
O:16 g/mol
Thus the molecular weight of SO
2
is 64 g/mol (needed in part (b)).
a. 25 mgSO
2
3air
b. To express concentration in terms of moles of air, the average
molecular weight of air must be determined. This can be done in
one of two ways:
i. At standard conditions of temperature and pressure (STP, 0 C
ii. Alternatively, one can use a simple averaging approach to
3. The maximum depth of fuel oil in the tank will occur at steady state.
At steady state, the rate of inflow will equal the rate of outflow.
Equations for inflow and outflow can be written as:
4. Refer to Eq. (1.lb):
e2 SOLUTIONS MANUAL ONLINE
5. a. First estimate the concentration of H
2
S, given that the maximum
partial pressure of H
2
S(g) is 1 atm. Using the Henry’s law constant:
Then using the dissociation constants and the known [H
þ
]:
and
b. The reaction of CH
2
Br
2
with HS
is a second-order reaction (note
the units of the rate constant, k):
e3CHAPTER 1 SOLUTIONS
To calculate the pseudo-first-order rate constant, [HS
]is
needed:
Use Eq. (1.20) to solve for the time it takes for 90% of the CH
2
Br
2
to react:
6. a. The flux of org-N in a wastewater infiltration basin occurs by
advection. Therefore, use Eq. (1.2a) to calculate the flux density:
b. The flux of salt in a tube, assuming no advection, occurs by
molecular diffusion. Fick’s first law, Eq. (1.3), can be used to
describe molecular diffusion:
e4 SOLUTIONS MANUAL ONLINE
c. In an automobile exhaust pipe, the flux of CO
2
occurs almost
entirely by advection:
7. a. A kinetic model would be more useful. There cannot be an
b. Assuming that the concern is to deice the sidewalk before start of
c. An equilibrium model would best describe the concentration of
8. The first solution provided here is nearly an exact solution. Define
citric acid as HX. Given that the acid is added to water, the species in
e5CHAPTER 1 SOLUTIONS
This equation can be rewritten as:
Eq. (4) can now be written as:
To solve this equation, the constant 1.210
13
can probably be
ignored:
e6 SOLUTIONS MANUAL ONLINE
Combining the above equation with Eqs. (1) and (3) yields:
Thus:
9. To check whether this analysis is complete and accurate, see if the
charges balance, according to the principle of electroneutrality. To do
so, all concentrations must be converted to equivalents per volume.
Cations:
Anions:
e7CHAPTER 1 SOLUTIONS
Does the sum of cation equivalents equal the sum of anion
equivalents?
10. [H2CO3]¼10
5
M
From Table 1.1,
a. At pH 4, HCO3
½¼
105106:3
b. In seawater having an ionic strength of 0.5 M, the activity
11. The reaction of methyl dichloroacetate with water can be written as:
e8 SOLUTIONS MANUAL ONLINE
12.
3
H (tritium) has a half-life of approximately 12 years.
a. Its decay constant is related to its half-life as shown by Eq. (1.21).
3
3
which can be rewritten as:
Therefore, the molar ratio is:
e9CHAPTER 1 SOLUTIONS
13. t
1/2
¼1.110
4
days for
137
Cs.
Use Eq. (1.21) to estimate the decay constant:
14. From Table 1.3, log (K
ow
) for m-cresol is 1.96. Assume that the density
of fatty tissue in the fish is approximately that of water, 1 mg/liter, so
that 0.1 ppm m-cresol in fatty tissue can be rewritten as 0.1 mg/liter
fatty tissue.
15. After equilibrium has been established in the stoppered flask, the
partitioning of o-xylene among phases can be described by two
e10 SOLUTIONS MANUAL ONLINE
16. a. Fick’s first law (Eq. 1.3) can be used to estimate the flux of dye at
points 1.5 and 2 cm along the tube at times t
1
and t
2
:
e11CHAPTER 1 SOLUTIONS
b. At time t
1
, the slope of the curve is maximum at x¼2 cm, and
2
17. The mass balance equation can be used to solve this problem. Given
Given the average lake depth of 10 ft, the surface area of the lake is
approximately:
e12 SOLUTIONS MANUAL ONLINE
Solving the mass balance equation for the influent concentration of
TCA:
18. Before the nitrous acid is added to the water, the pH of the water
is controlled by the ionization of H2CO3, assuming no other
acids or bases are present (Table 1.1):
e13CHAPTER 1 SOLUTIONS
a. Once the HNO
2
is added to the water, the expected species in the
water are:
By electroneutrality, [H
þ
] is approximately equal to [NO2]in
this acidic solution. Therefore:
b. There are four mass action equations that constrain the
composition of the system at equilibrium:
There is one electroneutrality equation:
e14 SOLUTIONS MANUAL ONLINE
There is one mass conservation equation:
19. Equation (1.3) can be used to estimate the flux of CCl
4
out of the plastic
tube:
a. Then use the wall area of the plastic tube to estimate the rate of
b. To ensure that the CCl
4
concentration in the gas stream is constant:
i. the rate of gas flow past the plastic tube must be sufficient to
20. First use Eq. (1.21) to estimate the rate at which the radioactivity
declines:
21.
Hþ
½HCOO
½
HCOOH½
¼1:8104mol=liter
e15CHAPTER 1 SOLUTIONS
22. Flux densities can be estimated using Eqs. (1.2a) and (1.3).
a. Using Eq. (1.2a):
c. Assume air at the tank bottom is in equilibrium with the liquid;
23. a. The following chemical species will be present in the flask,
assuming the flask is not open to the atmosphere:
e16 SOLUTIONS MANUAL ONLINE
b. The equations that constrain the system include:
i. two mass action equations:
ii. one electroneutrality equation:
iii. three mass conservation equations:
24. a. At pH 8.3, the concentration of HCO3is much greater than the
From mass action:
b. The mass of CO
2
in the very small gas volume can be assumed to
be negligible compared to the mass of H2CO3in the water. At a
e17CHAPTER 1 SOLUTIONS
From mass action:
25. a. From Table 1.3, the Henry’s law constant with units is 1.1510
3
atm m
3
/mol. To convert it to a dimensionless form:
b. The percent of the 10 mg of naphthalene that is in the headspace of
the sealed bottle can be estimated as:
26. The approximate flux density can be estimated using Fick’s first law
(Eq. 1.3) and assuming a molecular diffusion coefficient in water of
10
5
cm
2
/sec:
27. a. The chemical species that can occur at equilibrium are:
e18 SOLUTIONS MANUAL ONLINE
b. From Table 1.1, the mass action constraints are:
c. The mass conservation constraints are:
d. Electroneutrality is the other constraint on the composition of the
system:
e19
