Basic Chemical Thermodynamics - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 39

(c) What will be the standard free energy change if the temperature is
decreased to 278 K? Is the reaction more or less favorable at this
temperature?
2.16 3 Capillary rise is an important phenomenon in enhanced oil recovery, the
recovery of nonaqueous-phase liquids from contaminated aquifers, the rise
of sap in trees, and also in the determination of surface tension of liquids.
This is based on the balance of forces between the surface tension and
hydrostatic forces due to gravity.
(a) Consider a small capillary partially immersed in water. The water
rises to an equilibrium height given by h . Equate the pressure given
by the Young-Laplace equation for the hemispherical interface with
that of the hydrostatic pressure and derive the equation σ = rgh/ 2 Δρ ,
where r is the radius of the capillary, g is a gravitational constant, and
Δρ is the difference in density between water and air.
(b) Soils are considered to have capillary size pores. Calculate the capil-
laryriseofwaterinsoilporesofdiameters100,1000,and10,000 μ m.
This gives the shape of the boundary between air and water in soil
pores. Repeat the calculation for a nonaqueous-phase contaminant
such as chloroform in contact with groundwater. σ = 20 mN/m 1 and
Δρ = 150 kg/m 3 . What conclusions can you draw about the shape of
the boundary in this case?
2.17 1 Calculate the minimum work necessary to increase the area of the surface
of water in a beaker from 0.001 to 0.005 m 2 at 298 K.
2.18 2 A parcel of water 1 kg in mass is located 1 km above a large body of
water. The temperature of the air, lake, and the water parcel is uniform
and remains at 22 ◦ C. What will be the change in entropy if the water
parcel descends and mixes with the lake water and reaches equilibrium
with it?
2.19 2 A gas container has compressed air at 5 × 10 5 Pa at 300 K. What is the
maximum useful work available from the system per kilogram of air? The
atmospheric pressure is 1 × 10 5 Pa at 300 K?
2.20 2 A hydroxyl radical (OH ! ) plays an important role in atmospheric
chemistry.
(a) It is produced mainly via the reaction of a photoexcited oxygen
atom (O ∗ ) with moisture: O ∗ + H 2 O → 2OH • . Using the table in
Appendix 2 and the fact that the heat of formation of O ∗ in the
gaseous state is 440 kJ/mol, obtain the enthalpy of the above reaction
at standard state.
(b) OH • is an effective scavenger of other molecules, for exam-
ple, OH • + NO 2 → HNO 3 . Obtain the standard enthalpy of the
reaction.
2.21 1 Oxides of sulfur are an important class of inorganic pollutants in the atmo-
sphere resulting mainly from coal burning. For the oxidation of SO 2 in air
by the reaction SO 2 ( g ) +

1
2 O 2 ( g ) → SO 3 (g), what is the free energy at
298 K? Use the table in Appendix 2.
2.22 2 The sun's heat on a lake surface leads to the evaporation of water. If the heat
flux from the sun is assumed to be 5 J/min/cm 2 , how much water will be
evaporated on a clear summer day from a square meter of the lake surface
in 5 h? What volume of the atmosphere is required to hold the evaporated