Page 896 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

Appendix H: Dissolved Gases

The issue of dissolved gases comes up in a variety of Referring to Figure H.1a, and applying Equation H.1,
situations both in unit processes and in the natural environ- the algebraic relation is, with subsequent substitution of
ment. The issues include (1) air stripping of dissolved gases numerical data,
as a unit process, (2) transfer of gas into solution as a unit
process, (3) gas precipitation as a spontaneous occurrence. p(A) abs ¼ p atm þ p(A) gage (H:1)
Gas transfer also occurs in the environment, e.g., oxygen
¼ 101:3 kPa þ 50 kPa
uptake, carbon dioxide uptake, precipitation of various gases
in a saturated local environment, e.g., oxygen, methane, ¼ 151 kPa
carbon dioxide, nitrogen, etc. The equilibrium between the
gas phase and the dissolved state for a given gas is expressed
by Henry’s law. Its application requires understanding the
H.1.2 IDEAL GAS LAW
ideal gas law and Dalton’s law of partial pressures. Other
kinds of fundamental notions help to establish the back- The ideal gas law is,
ground for understanding Henry’s law, an ostensibly simple
equation, e.g., the effect of elevation on atmospheric pres- p A V A ¼ n A RT (H:2)
sure, partial pressure of water vapor, molar composition of
air, etc. where
2
p A is the absolute pressure of gas ‘‘A’’ (Pa or N=m )
3
V A is the volume occupied by gas ‘‘A’’ (m )
H.1 FUNDAMENTALS OF GAS BEHAVIOR n A is the moles of gas of species A (mol)
Dealing with gases requires a few notions of gas behavior and R is the universal gas constant (8.314 510 N m=g-mol K)
also include conventions in stating the pressure, the ideal gas T is the temperature of gas ‘‘A’’ (K)
law, Dalton’s law, the effect of elevation on atmospheric
pressure, composition of ambient air, and the partial pressure The ideal gas equation is satisfactory for most engineering
of water vapor. These fundamentals are reviewed here. situations but is not accurate at very high pressures, which
includes any gas near the condensation point. Van der Waal’s
equation or the virial equation (Alberty and Silbey, 1992) will
H.1.1 CONVENTIONS FOR STATING PRESSURE
more closely approximate high pressure conditions.
Both the gage and absolute pressure are used in mathematical
expressions, depending on the circumstances. Gage pressure Example H.2 Application of Ideal Gas Law
is used commonly in practice while absolute pressure is to Determine Density at NTP
necessary in calculations based on scientific principles (such
as those involving the ideal gas law and Henry’s law). The
Statement
relation between the two is understood most easily by a
Very often, gas densities must be determined. The basis for
graphical depiction, Figure H.1. Gage pressure is always the calculation of gas densities is the ideal gas law. In such
relative to the atmosphere and is the difference between calculations, the SI system should be used. Conversion
pressures, such as the pressure between the inside and outside can be done to any other form desired after the basic
of a pressure gage. Referring to Figure H.1, the relationship calculation.
between absolute pressure and gage pressure is,
(a) Calculate the density of pure oxygen at NTP (normal
temperature and pressure).
p abs ¼ p atm þ p gauge (H:1)
1. Apply the ideal gas law,

Example H.1 Conversions between Gage Pressure pV ¼ nRT (ExH:2:1)
and Absolute Pressure
2. Rearrange Equation ExH.2.1,
Calculate the absolute pressure at point A if the gage
pressure is 50 kPa and the atmospheric pressure is n p
101.3 kPa. V ¼ RT

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