Environmental Studies Chapter 4 Homework Given the reaction is occurring by attack by

c. If there is an inversion at 50 m, assume the soot plume becomes

fully mixed vertically beneath it. Then use Eq. (4.20) to estimate the

30. Over the hour travel time, the solvent vapor concentration is being

reduced from a predicted 2 ng/m

3

to a measured 0.2 ng/m

3

:

Predicted concentration due only to dispersion:

31. a. Use the skew T-log Pdiagram in Fig. 4.7 to determine if the air

b. Again using Fig. 4.7, start at 1500 m and 15 C and follow a wet

c. As an example for these conditions, air at an ambient temperature

e129CHAPTER 4 SOLUTIONS

32. a. Assume an average [OH]of110

6

molecules/cm

3

, based on

the order of magnitude of the concentrations provided in

b. Methane oxidation in the troposphere and diffusion into the

33. The atmospheric half-life of acrolein will depend on the sum of the

pseudo-first-order rate constants for reactions with OHand O

3

.

e130 SOLUTIONS MANUAL ONLINE

Summing the two rate constants:

34. a. First estimate the source strength, treating the fuel as 2,3-

dimethylpentane and using Eq. (1.25):

A gas exchange coefficient for air-side control can be estimated

from Eq. (2.35):

From Table 4.5, the Pasquill stability category is F. From Table 4.6:

From Eq. (4.16), at 1.3 m height,

e131CHAPTER 4 SOLUTIONS

35. At the time of the temperature profile measurement, shortly after

sunrise, inversion conditions prevail. At 11 a.m., once the surface

air temperature has risen to 18 C, a mixing height can be estimated.

Assuming the air is dry, as defined in Section 4.2.1,the dry adiabatic lapse

rate of 5.4 F/1000 ft can be plotted, starting at the surface temperature of

64.4 F(18C). The intersection of the temperature profile and the

adiabatic lapse rate provides an estimate of the mixing height. The

mixing height under these conditions occurs at approximately 2230 ft.

a. To estimate the CO concentration in the air over the city, assume a

simple box model:

b. First estimate the pseudo-first-order rate constant corresponding

to reaction with OH:

36. a. At steady state, assuming a negligible radon-222 concentration in

outdoor air, Eq. (4.14) can be written as:

e132 SOLUTIONS MANUAL ONLINE

Eq. (4.14) can then be written as:

b. The steady-state ethylene concentration can be estimated using

Eq. (4.15):

c. The steady-state radon concentration in the closed cellar can be

estimated from Eq. (4.14):

37. First estimate the rate of PM emission from the battleship:

From Table 4.6, for Pasquill stability category C:

e133CHAPTER 4 SOLUTIONS

From Eq. (4.17a):

From Eq. (4.17b):

38. a. The low at point A probably originates from shear along the polar

front; at midlatitudes, air is moving west to east, while the polar air

b. At Kansas City, the windspeed is 15 knots (as indicated by one full

d. Near Springfield, Illinois, the cold front has passed, leaving clear

39. First, estimate the mixing height by drawing a line with a slope

equal to the dry adiabatic lapse rate, beginning at the surface

e134 SOLUTIONS MANUAL ONLINE

40. First estimate the rate at which HCl is produced:

Then convert the wind speed into units of (m/sec):

a. For nighttime conditions with a wind speed of 7.7 m/sec, the

Pasquill stability category from Table 4.5 is D. Using Fig. 4.28, s

y

e135CHAPTER 4 SOLUTIONS

b. i. 3 ppm HCl is 3 mg/liter HCl. Converting the mass to moles:

Now, check that the concentrations of HCO3and CO32

are negligible. Assuming the raindrops are in equilibrium

with atmospheric CO

2

, use Eqs. (2.42) and (2.43):

ii. Given a pH of 8 and a C

T

of 510

4

mol/liter, the Deffeyes

41. First calculate the dewpoint for air initially at 85 F and 95% RH. From

Table 4.3, at 85 F(29.4C), the vapor pressureof water is approximately

e136 SOLUTIONS MANUAL ONLINE

42. a. The half-life of TCE in the lake can be estimated by predicting a

first-order decay constant based on the gas exchange coefficient

and the lake depth, and then using Eq. (1.21):

b. The pseudo-first-order rate constant for TCE reacting with this

concentration of OHin the atmosphere can be estimated as:

43. Equation (4.15) can be used to estimate the formaldehyde

concentration at steady state, assuming a negligible formaldehyde

concentration in outdoor air and no formaldehyde sink:

e137CHAPTER 4 SOLUTIONS

When the carpet is taken outdoors, the source of formaldehyde is

removed. Assuming the carpet’s contribution to an ambient

formaldehyde concentration in the outside air is negligible,

Eq. (4.14) can be written as:

44. a. First estimate the rate of fly ash emission from the wood-fired

power plant:

From Eq. (4.16):

b. The plume of fly ash will touch the ground when 2s

z

30 m

45. Given the typical range of deposition velocities of 0.1-1 cm/sec,

assume a deposition velocity of 0.3 cm/sec. First calculate the annual

deposition of ash particles:

e138 SOLUTIONS MANUAL ONLINE

To estimate the annual amount of base deposited by dry processes,

calculate the molecular weight of Ca(OH)

2

and recognize that calcium

is a divalent ion:

To estimate the annual amount of acid deposited, recognize that

the concentration of mineral acid in the precipitation is 10

4

eq/liter,

given the pH of 4.

46. From Table 1.3, the vapor pressure of chloroform is 0.32 atm. Using

Eq. (1.25):

The rate of chloroform input to the wardroom is:

Using Eq. (1.25):

47. a. From Eq. (4.14), assuming steady state, no sink for isoflurane, and

negligible outside concentration:

e139CHAPTER 4 SOLUTIONS

b. Isoflurane :3xðÞþ2IðÞþ6IðÞþIIðÞ¼0

48. When the wood is burned, assume 1 mol of CH

2

O produces 1 mol of

CO

2

, as in respiration. The source strength of CO

2

can be estimated as:

From Eq. (4.16):

49. From Eq. (4.14), at steady state:

e140 SOLUTIONS MANUAL ONLINE

Given the mine volume of 10

7

liter:

of 1.210

liter/hr.

50. a. First calculate the source strength in units of molecules/sec:

Assuming negligible ventilation, the source strength must equal

the sink strength by reaction with OHfor the entire building:

Then:

51. a. From Fig. 4.25, the half-life of

222

Rn is 3.8 days. From Eq. (1.21),

k¼0:693=3:8 day



1 day=24 hr



¼7:6103=hr:

e141CHAPTER 4 SOLUTIONS

The rate at which radon is decaying is thus:

b. From Eq. (4.14), at steady state, on a per liter basis:

c. C12H26 !12CO2þtrace CO

From Eq. (4.14), at steady state:

e142 SOLUTIONS MANUAL ONLINE

52. a. First calculate the CH

4

source strength in mol/sec using Eq. (1.25):

From Eq. (4.16):

b. From Fig. 4.28, s

y

¼8 m and s

z

¼4.8 m. The maximum CH

4

c. First calculate the rate at which CH

4

is being vented through the

stack (the stack gas velocity):

e143CHAPTER 4 SOLUTIONS

53. The average oxidation state of carbon in C

3

H

8

is (8/3). In CO

2

,

the carbon has an oxidation state of (IV). The number of electrons

54. a. Estimate a diffusion-limited, pseudo-first-order rate constant

in water:

e144 SOLUTIONS MANUAL ONLINE

b. Estimate a diffusion-limited, pseudo-first-order rate constant in

air:

e145CHAPTER 4 SOLUTIONS