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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]of110
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 OHand 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(18C). 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 HCO3and 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 510
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(29.4C), 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 OHin 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 :3xðÞþ2IðÞþ6IðÞþIIðÞ¼0
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 1.210
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 OHfor 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
¼7:6103=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
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
