Page 83 - Air pollution and greenhouse gases from basic concepts to engineering applications for air emission control

2.4 Practice Problems 57

10. Which molecule has the highest root-mean-square speed (a) nitrogen molecule
(N 2 )at 100 °C, (b) Oxygen molecule (O 2 ) at 200 °C, (c) Chlorine molecule
under STP conditions?
11. Assuming spherical oxygen molecules with a radius of 1.65 10 10 m, find the
mean free path of oxygen molecules at sea level at 293 K.
12. If a gas after fuel combustion at 1000 K contains, by volume, 79 % N 2 ,6%O 2 ,
7% CO 2 , and 8 % H 2 O, what is its molar weight? Can you approximate the
molar weight of this flue gas with that of standard dry air?
13. What should be the pressure of N 2 (g) above the solution to increase the
solubility of the N 2 (g) to a value of 100.0 mL N 2 per L?
14. What is the mole concentration of O 2 in a saturated solution when the O 2
pressure is 0.21 atm at 25 °C?
15. 15 mL of CO 2 (g) dissolves in 1.0L of water at 25 °C temperature and 1.0 atm
pressure. What will be the mole concentration of CO 2 (g) in the saturated
solution at 25 °C When the CO 2 pressure is 0.25 atm?
16. A truck tire at the gage pressure of 220 kPa and the temperature of 27 °C
contains 12 L of air. Assume that the temperature drops to -40 °C. Determine
the gage pressure in the tire.
17. At 27 °C and 1 atm the viscosity and density of air are 1.81 × 10 −5 Pa.s and
3
1.2 kg/m , respectively. Determine the diameter and mean free path of an air
molecule.
−5
18. At 27 °C and 1 atm the viscosity and density of helium (He) are 1.9 × 10 Pa
3
and 0.18 kg/m , respectively. Determine the diameter of helium molecule and
diffusion coefficient of this gas.
19. At 20 °C and 1 atm the viscosity and density of methane are 2.01 × 10 −5 Pa.s
3
and 0.717 kg/m , respectively. Determine the diameter of methane molecule,
mean free path, and diffusion coefficient.
20. Estimate the following maximum solubility of the air compounds CO 2 ,O 2 and
CH 4 in water under standard conditions. Assume the gas phase is pure dry air.
21. The Henry’s law constant of SO 2 at 20 °CinaSO 2 -water system is 0.014 10 5
atm/mol fraction in water.
What is the Henry’s law constant with a unit of (Pa/mol fraction in water)? At
5
30 °C, H = 0:016 10 atm/mol fraction in water, does it imply a higher or
lower SO 2 solubility in water?
3
22. Under certain condition, air density is 1.1 kg/m . Under the same condition,
estimate the density of a gas mixture containing, by volume, 95 % CH 4 and 5 %
3
CO? How many moles of CH 4 in a volume of 0.2 m of this mixture gas?
23. Determine the volume occupied by 1 mol of ideal gas at 15 °C and 1 atm.
24. Find density of dry air at STP conditions (T = 25 °C and P = 1 atm). Assume
that dry air has 79 % N 2 , and 21.0 % O 2 . Given molar weights of N 2 and O 2 are
28 and 32 g/mole, respectively.