Page 38 - Physical chemistry eng

NUMERICAL PROBLEMS 15

gravity, R is the gas constant, T is the absolute tempera- of each gas, the total pressure, and the composition of the mix-
ture, and M is the molecular mass of the gas. As a result of ture in mole percent:
i
turbulent mixing, the composition of Earth’s atmosphere is a. 3.06 g H 2 and 2.98 g O 2
constant below an altitude of 100 km, but the total pressure b. 2.30 g N and 1.61 g O
0 -M ave gz>RT
decreases with altitude as P = P e where M ave is 2 2
the mean molecular weight of air. At sea level, c. 2.02 g CH 4 and 1.70 g NH 3
x = 0.78084 and x He = 0.00000524 and T = 300. K . P1.27 A mixture of H 2 and NH 3 has a volume of 139.0 cm 3
N 2
a. Calculate the total pressure at 8.5 km, assuming a mean at 0.00°C and 1 atm. The mixture is cooled to the temperature
molecular mass of 28.9 g mol –1 and that T = 300. K of liquid nitrogen at which ammonia freezes out and the
throughout this altitude range. remaining gas is removed from the vessel. Upon warming the
3
vessel to 0.00°C and 1 atm, the volume is 77.4 cm . Calculate
b. Calculate the value that x >x He would have at 8.5 km in
N 2 the mole fraction of NH in the original mixture.
the absence of turbulent mixing. Compare your answer 3 3
with the correct value. P1.28 A sealed flask with a capacity of 1.22 dm contains
4.50 g of carbon dioxide. The flask is so weak that it will burst
P1.21 An initial step in the biosynthesis of glucose 5
if the pressure exceeds 9.500 * 10 Pa . At what temperature
C H O is the carboxylation of pyruvic acid CH COCOOH
6 12 6
3
to form oxaloacetic acid HOOCCOCH COOH will the pressure of the gas exceed the bursting pressure?
2
P1.29 A balloon filled with 11.50 L of Ar at 18.7°C and
CH COCOOH(s) + CO (g) : HOOCCOCH COOH(s) 1 atm rises to a height in the atmosphere where the pressure is
3
2
2
If you knew nothing else about the intervening reactions 207 Torr and the temperature is –32.4°C. What is the final
involved in glucose biosynthesis other than no further car- volume of the balloon? Assume that the pressure inside and
boxylations occur, what volume of CO 2 is required to produce outside the balloon have the same value.
1.10 g of glucose? Assume P = 1 atm and T = 298 K . P1.30 Carbon monoxide competes with oxygen for bind-
ing sites on the transport protein hemoglobin. CO can be
P1.22 Consider the oxidation of the amino acid glycine poisonous if inhaled in large quantities. A safe level of CO
NH CH COOH to produce water, carbon dioxide, and urea in air is 50. parts per million (ppm). When the CO level
2
2
NH CONH 2 : increases to 800. ppm, dizziness, nausea, and unconscious-
2
NH CH COOH(s) + 3O (g) : ness occur, followed by death. Assuming the partial pressure
2
2
2
of oxygen in air at sea level is 0.20 atm, what proportion of
NH CONH (s) + 3CO (g) + 3H O(l) CO to O 2 is fatal?
2
2
2
2
Calculate the volume of carbon dioxide evolved at P1.31 The total pressure of a mixture of oxygen and hydro-
P = 1.00 atm and T = 305 K from the oxidation of 0.022 g gen is 1.65 atm. The mixture is ignited and the water is
of glycine. removed. The remaining gas is pure hydrogen and exerts a
P1.23 Assume that air has a mean molar mass of 28.9 g mol –1 pressure of 0.190 atm when measured at the same values of T
and that the atmosphere has a uniform temperature of 25.0°C. and V as the original mixture. What was the composition of
Calculate the barometric pressure in Pa in Santa Fe, for the original mixture in mole percent?
which z = 7000. ft . Use the information contained in P1.32 Suppose that you measured the product PV of 1 mol of
Problem P1.20. a dilute gas and found that PV = 24.35 L atm at 0.00°C and
P1.24 When Julius Caesar expired, his last exhalation had a 33.54 L atm at 100.°C. Assume that the ideal gas law is valid,
3
volume of 450. cm and contained 1.00 mole percent argon. with T = t(°C) + a , and that the values of R and a are not
Assume that T = 300. K and P = 1.00 atm at the location of known. Determine R and a from the measurements provided.
his demise. Assume further that T has the same value through- P1.33 Liquid N 2 has a density of 875.4 kg m –3 at its normal
out Earth’s atmosphere. If all of his exhaled Ar atoms are now boiling point. What volume does a balloon occupy at 298 K
-3
uniformly distributed throughout the atmosphere, how many and a pressure of 1.00 atm if 3.10 * 10 L of liquid N 2 is
3
inhalations of 450. cm must we make to inhale one of the Ar injected into it? Assume that there is no pressure difference
atoms exhaled in Caesar’s last breath? Assume the radius of between the inside and outside of the balloon.
6
Earth to be 6.37 * 10 m . [Hint: Calculate the number of Ar P1.34 Calculate the volume of all gases evolved by the
atoms in the atmosphere in the simplified geometry of a plane complete oxidation of 0.375 g of the amino acid alanine
of area equal to that of Earth’s surface. See Problem P1.20 for CH3CH(NH )COOH if the products are liquid water, nitro-
2
the dependence of the barometric pressure and the composi- gen gas, and carbon dioxide gas; the total pressure is
tion of air on the height above Earth’s surface. 1.00 atm; and T = 298 K .
3
P1.25 Calculate the number of molecules per m in an ideal P1.35 As a result of photosynthesis, an acre of forest
gas at the standard temperature and pressure conditions of (1 acre = 4047 square meters) can take up 1000. kg of CO 2 .
0.00°C and 1.00 atm. Assuming air is 0.0314% CO 2 by volume, what volume of
3
P1.26 Consider a gas mixture in a 1.50 dm flask at 22.0°C. air is required to provide 350. kg of CO 2 ? Assume T = 310 K
For each of the following mixtures, calculate the partial pressure and P = 1.00 atm .