Page 37 - Physical chemistry eng

14 CHAPTER 1 Fundamental Concepts of Thermodynamics

H O at constant temperature. Calculate the mole fraction of vessels is opened and both are cooled to a temperature of
2
each component in the resulting mixture after oxidation, 12.2°C. What is the final pressure in the vessels?
assuming that the H O is present as a gas. P1.13 A mixture of oxygen and hydrogen is analyzed by
2
P1.5 A gas sample is known to be a mixture of ethane and passing it over hot copper oxide and through a drying tube.
3
butane. A bulb having a 230.0 cm capacity is filled with the Hydrogen reduces the CuO according to the reaction
3
gas to a pressure of 97.5 * 10 Pa at 23.1°C. If the mass of CuO(s) + H (g) : Cu(s) + H O(l) , and oxygen reoxidizes
2
2
the gas in the bulb is 0.3554 g, what is the mole percent of the copper formed according to Cu(s) + 1>2 O (g) : CuO(s) .
2
3
butane in the mixture? At 25°C and 750. Torr, 172.0 cm of the mixture yields
3
P1.6 One liter of fully oxygenated blood can carry 77.5 cm of dry oxygen measured at 25°C and 750. Torr after
0.18 liters of O 2 measured at T = 298 K and P = 1.00 atm . passage over CuO and the drying agent. What is the original
Calculate the number of moles of O 2 carried per liter of composition of the mixture?
'
blood. Hemoglobin, the oxygen transport protein in blood P1.14 An athlete at high performance inhales 3.75 L of air
has four oxygen binding sites. How many hemoglobin mole- at 1.00 atm and 298 K. The inhaled and exhaled air contain
cules are required to transport the O 2 in 1.0 L of fully oxy- 0.50 and 6.2% by volume of water, respectively. For a respira-
genated blood? tion rate of 32 breaths per minute, how many moles of water
P1.7 Yeast and other organisms can convert glucose per minute are expelled from the body through the lungs?
(C H O ) to ethanol (CH CH OH) by a process called P1.15 Devise a temperature scale, abbreviated G, for which
3
6 12 6
2
–1
alchoholic fermentation. The net reaction is the magnitude of the ideal gas constant is 5.52 J G –1 mol .
C H O (s) : 2C H OH(l) + 2CO (g) P1.16 Aerobic cells metabolize glucose in the respiratory
2 5
6 12 6
2
system. This reaction proceeds according to the overall reaction
Calculate the mass of glucose required to produce 2.25 L of
CO 2 measured at P = 1.00 atm and T = 295 K . 6O (g) + C H O (s) : 6CO (g) + 6H O(l)
6 12 6
2
2
2
P1.8 A vessel contains 1.15 g liq H O in equilibrium with Calculate the volume of oxygen required at STP to metabo-
2
water vapor at 30.°C. At this temperature, the vapor pressure lize 0.025 kg of glucose (C H O ) . STP refers to standard
6 12 6
of H O is 31.82 torr. What volume increase is necessary for temperature and pressure, that is, T = 273 K and
2
all the water to evaporate? P = 1.00 atm . Assume oxygen behaves ideally at STP.
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P1.9 Consider a 31.0 L sample of moist air at 60.°C and one P1.17 An athlete at high performance inhales 3.75 L of air
atm in which the partial pressure of water vapor is 0.131 atm. at 1.0 atm and 298 K at a respiration rate of 32 breaths per
Assume that dry air has the composition 78.0 mole percent minute. If the exhaled and inhaled air contain 15.3 and 20.9%
N 2 , 21.0 mole percent O 2 , and 1.00 mole percent Ar. by volume of oxygen respectively, how many moles of oxy-
a. What are the mole percentages of each of the gases in gen per minute are absorbed by the athlete’s body?
-3
-3
the sample? P1.18 A mixture of 2.10 * 10 g of O 2 , 3.88 * 10 mol
b. The percent relative humidity is defined as %RH = of N 2 , and 5.25 * 10 20 molecules of CO are placed into a
P H 2 O >P * H 2 O where P H 2 O is the partial pressure of water in vessel of volume 5.25 L at 12.5°C.
the sample and P * H 2 O = 0.197 atm is the equilibrium vapor a. Calculate the total pressure in the vessel.
pressure of water at 60.°C. The gas is compressed at 60.°C b. Calculate the mole fractions and partial pressures of
until the relative humidity is 100.%. What volume does the each gas.
mixture contain now?
P1.19 Calculate the pressure exerted by benzene for a molar
c. What fraction of the water will be condensed if the total
volume of 2.00 L at 595 K using the Redlich-Kwong equation
pressure of the mixture is isothermally increased to
of state:
81.0 atm?
RT a 1
P1.10 A typical diver inhales 0.450 liters of air per breath P = -
and carries a 25 L breathing tank containing air at a pressure V m - b 2T V (V m + b)
m
of 300. bar. As she dives deeper, the pressure increases by nRT n a 1
2
1 bar for every 10.08 m. How many breaths can the diver take = -
V - nb 2T V(V + nb)
from this tank at a depth of 35 m? Assume that the tempera-
ture remains constant.
The Redlich-Kwong parameters a and b for benzene are
6
–1
3
P1.11 Use the ideal gas and van der Waals equations to cal- 452.0 bar dm mol –2 K 1/2 and 0.08271 dm mol , respec-
culate the pressure when 2.25 mol H 2 are confined to a vol- tively. Is the attractive or repulsive portion of the potential
ume of 1.65 L at 298 K. Is the gas in the repulsive or dominant under these conditions?
attractive region of the molecule–molecule potential?
P1.20 In the absence of turbulent mixing, the partial pres-
3
P1.12 A rigid vessel of volume 0.400 m containing H 2 at sure of each constituent of air would fall off with height
0 -M i gz>RT
21.25°C and a pressure of 715 * 10 3 Pa is connected to a sec- above sea level in Earth’s atmosphere as P = P e
i
i
3
ond rigid vessel of volume 0.750 m containing Ar at 30.15°C where P i is the partial pressure at the height z, P 0 i is the partial
3
at a pressure of 203 * 10 Pa . A valve separating the two pressure of component i at sea level, g is the acceleration of