Page 33 - Materials Chemistry, Second Edition

16 Practical Design Calculations for Groundwater and Soil Remediation

24.0 in.-Hg; and the ambient temperature is 68°F. Determine the 1-hr average
NAAQS value for NO at that location (in μg/m ).
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2
Solution:
(a) At T = 68°F and P = 24.0 in.-Hg, molar volume of an ideal gas
= (22.4 L/gmole)(29.92/24.0)[(460 + 68)/(460 + 32)]
= (22.4)(1.25)(1.07) L/gmole = 29.97 L/gmole
(b) Molecular weight of NO = (14)(1) + (16)(2) = 46 g/mole
2
Under this ambient condition, 0.100 ppmV of NO = (0.100)(MW
2
of NO /29.97) mg/m 3
2
= (0.100)(46/29.97)
= 0.153 mg/m = 153 μg/m (< 180 μg/m )
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3
3
∴ The maximum ambient receptor concentration exceeds the 1-hr
average NAAQS for NO .
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Discussion:
1. One may encounter questions of this nature in professional
engineers exams. In this example, both values of pressure and
temperature are included in the conversion between ppmV and
mass concentration, while P = 1 atm was assumed in the previ-
ous examples.
2. To calculate the molar volume of an ideal gas, we can always
use the Ideal Gas Law (PV = nRT) with a proper value of the
ideal, or universal, gas constant (R), see Table 2.1 for values of
the universal gas constant in different units. The approach here
started with 22.4 L/gmole, which is the molar volume of an ideal
gas at T = 0°C and P = 1 atm. (This value is a good one for us to
memorize.) Since the volume is proportional to temperature and
inversely proportional to pressure, the relationship, V /V = (T /
1
2
2
T )(P /P ), is valid.
2
1
1
3. Temperature used, in Ideal Gas Law–related calculations, should
be the absolute temperature in degrees Kelvin (K) or degrees
Rankine (°R). Note: T (in K) = T (in °C) + 273.15, and T (in °R) = T
(in °F) + 459.67. Also, T (in °R) = 1.8 × T (in K).
TABLE 2.1
Values of the Universal Gas Constant (R)
R = 82.05 (cm ∙atm)/(g mol)(K) = 83.14 (cm ∙bar)/(g mol)(K)
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3
R = 8.314 (J)/(g mol)(K) = 1.987 (cal)/(g mol)(K)
R = 0.7302 (ft ∙atm)/(lb mol)(R) = 10.73 (ft ∙psia)/(lb mol)(R)
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3
R = 1,545 (ft∙lb f )/(lb mol)(R) = 1.986 (Btu)/(lb mol)(R)