Environmental Studies Chapter 1 Homework To express concentration in terms of moles of air

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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):

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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:

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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 1.210

13

can probably be

ignored:

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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

½¼

105106:3

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:

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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

which can be rewritten as:

Therefore, the molar ratio is:

e9CHAPTER 1 SOLUTIONS

13. t

1/2

¼1.110

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

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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

:

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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:

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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:

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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

½HCOO

½

HCOOH½

¼1:8104mol=liter

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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:

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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 HCO3is 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 H2CO3in the water. At a

e17CHAPTER 1 SOLUTIONS

From mass action:

25. a. From Table 1.3, the Henry’s law constant with units is 1.1510

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:

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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:

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