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Problem 27a
(a) Amonton's law expresses the relationship between pressure and temperature. Use Charles's law and Boyle's law to derive the proportionality relationship between P and T.
- In the contact process, sulfur dioxide and oxygen gas react to form sulfur trioxide as follows: 2 SO2(g) + O2(g) → 2 SO3(g). At a certain temperature and pressure, 50 L of SO2 reacts with 25 L of O2. If all the SO2 and O2 are consumed, what volume of SO3, at the same temperature and pressure, will be produced?
Problem 28
Problem 29b
(b) What is the molar volume of an ideal gas at STP?
Problem 31
Suppose you are given two 1-L flasks and told that one contains a gas of molar mass 30 and the other a gas of molar mass 60, both at the same temperature. The pressure in flask A is x atm, and the mass of gas in the flask is 1.2 g. The pressure in flask B is 0.5x atm, and the mass of gas in that flask is 1.2 g. Which flask contains the gas of molar mass 30, and which contains the gas of molar mass 60?
Problem 32
Suppose you are given two flasks at the same temperature, one of volume 2 L and the other of volume 3 L. The 2-L flask contains 4.8 g of gas, and the gas pressure is x atm. The 3-L flask contains 0.36 g of gas, and the gas pressure is 0.1x. Do the two gases have the same molar mass? If not, which contains the gas of higher molar mass?
Problem 33
Complete the following table for an ideal gas:
- Calculate each of the following quantities for an ideal gas: (a) the volume of the gas, in liters, if 1.50 mol has a pressure of 126.7 kPa at a temperature of -6 °C, (b) the absolute temperature of the gas at which 3.33 * 10^-3 mol occupies 478 mL at 99.99 kPa, (c) the pressure, in pascals, if 0.00245 mol occupies 413 mL at 138 °C.
Problem 34
- A neon sign is made of glass tubing whose inside diameter is 3.0 cm and length is 10.0 m. If the sign contains neon at a pressure of 265 Pa at 30 °C, how many grams of neon are in the sign? (The volume of a cylinder is πr²h.)
Problem 36
Problem 37b
The adult blue whale has a lung capacity of 5.0×103 L. Calculate the mass of air (assume an average molar mass of 28.98 g/mol) contained in an adult blue whale’s lungs at 0.0°C and 1.00 atm, assuming the air behaves ideally.
Problem 38a
If the pressure exerted by ozone, O3, in the stratosphere is 3.0×10−3atm and the temperature is 250 K, how many ozone molecules are in a liter?
Problem 38b
Carbon dioxide makes up approximately 0.04% of Earth’s atmosphere. If you collect a 2.0-L sample from the atmosphere at sea level (1.00 atm) on a warm day (27°C), how many CO2 molecules are in your sample?
Problem 39b
A scuba diver’s tank contains 0.29 kg of O2 compressed into a volume of 2.3 L. b. What volume would this oxygen occupy at 26°C and 0.95 atm?
Problem 40a
An aerosol spray can with a volume of 250 mL contains 2.30 g of propane gas (C3H8) as a propellant. a. If the can is at 23°C, what is the pressure in the can?
Problem 40c
An aerosol spray can with a volume of 250 mL contains 2.30 g of propane gas (C3H8) as a propellant. c. The can’s label says that exposure to temperatures above 130°F may cause the can to burst. What is the pressure in the can at this temperature?
Problem 41
A 35.1 g sample of solid CO2 (dry ice) is added to a container at a temperature of 100 K with a volume of 4.0 L. If the container is evacuated (all of the gas is removed), sealed, and then allowed to warm to room temperature (𝑇=298 K) so that all of the solid CO2 is converted to a gas, what is the pressure inside the container?
Problem 42
A 334-mL cylinder for use in chemistry lectures contains 5.225 g of helium at 23°C. How many grams of helium must be released to reduce the pressure to 75 atm assuming ideal-gas behavior?
Problem 43b
Chlorine is widely used to purify municipal water supplies and to treat swimming pool waters. Suppose that the volume of a particular sample of Cl2 gas is 8.70 L at 895 torr and 24°C. b. What volume will the Cl2 occupy at STP?
Problem 43c
Chlorine is widely used to purify municipal water supplies and to treat swimming pool waters. Suppose that the volume of a particular sample of Cl2 gas is 8.70 L at 895 torr and 24°C. c. At what temperature will the volume be 15.00 L if the pressure is 8.76×102 torr?
Problem 44b
Many gases are shipped in high-pressure containers. Consider a steel tank whose volume is 55.0 gallons that contains O2 gas at a pressure of 16,500 kPa at 23°C. b. What volume would the gas occupy at STP?
Problem 44c
Many gases are shipped in high-pressure containers. Consider a steel tank whose volume is 55.0 gallons that contains O2 gas at a pressure of 16,500 kPa at 23°C. c. At what temperature would the pressure in the tank equal 150.0 atm?
Problem 44d
Many gases are shipped in high-pressure containers. Consider a steel tank whose volume is 55.0 gallons that contains O2 gas at a pressure of 16,500 kPa at 23°C. d. What would be the pressure of the gas, in kPa, if it were transferred to a container at 24°C whose volume is 55.0 L?
Problem 46a
The physical fitness of athletes is measured by 'VO2 max,' which is the maximum volume of oxygen consumed by an individual during incremental exercise (for example, on a treadmill). An average male has a VO2 max of 45 mL O2/kg body mass/min, but a world-class male athlete can have a VO2 max reading of 88.0 mL O2/kg body mass/min. (a) Calculate the volume of oxygen, in mL, consumed in 1 hr by an average man who weighs 85 kg and has a VO2 max reading of 47.5 mL O2/kg body mass/min. (b) If this man lost 10 kg, exercised, and increased his VO2 max to 65.0 mL O2/kg body mass/min, how many mL of oxygen would he consume in 1 hr?
Problem 47
Rank the following gases from least dense to most dense at 1.00 atm and 298 K: CO, N2O, Cl2, HF.
Problem 48
Rank the following gases from least dense to most dense at 1.00 atm and 298 K: SO2,HBr,CO2.
Problem 49
Which of the following statements best explains why a closed balloon filled with helium gas rises in air? (a) Helium is a monatomic gas, whereas nearly all the molecules that make up air, such as nitrogen and oxygen, are diatomic. (b) The average speed of helium atoms is greater than the average speed of air molecules, and the greater speed of collisions with the balloon walls propels the balloon upward. (c) Because the helium atoms are of lower mass than the average air molecule, the helium gas is less dense than air. The mass of the balloon is thus less than the mass of the air displaced by its volume. (d) Because helium has a lower molar mass than the average air molecule, the helium atoms are in faster motion. This means that the temperature of the helium is greater than the air temperature. Hot gases tend to rise.
Problem 51a
(a) Calculate the density of NO2 gas at 0.970 atm and 35 °C.
Problem 52
Calculate the molar mass of a vapor that has a density of 7.135 g/L at 12°C and 743 torr.
Problem 53
In the Dumas-bulb technique for determining the molar mass of an unknown liquid, you vaporize the sample of a liquid that boils below 100°C in a boiling-water bath and determine the mass of vapor required to fill the bulb. From the following data, calculate the molar mass of the unknown liquid: mass of unknown vapor, 1.012 g; volume of bulb, 354 cm3; pressure, 742 torr; temperature, 99°C.
Problem 55
Magnesium can be used as a “getter” in evacuated enclosures to react with the last traces of oxygen. (The magnesium is usually heated by passing an electric current through a wire or ribbon of the metal.) If an enclosure of 0.452 L has a partial pressure of O2 of 3.5×10−6 torr at 27°C, what mass of magnesium will react according to the following equation?
Problem 56
Calcium hydride, CaH2, reacts with water to form hydrogen gas:
CaH2(𝑠)+2 H2O(𝑙)⟶Ca(OH)2(𝑎𝑞)+2 H2(𝑔)
This reaction is sometimes used to inflate life rafts, weather balloons, and the like, when a simple, compact means of generating H2 is desired. How many grams of CaH2 are needed to generate 145 L of H2 gas if the pressure of H2 is 825 torr at 21°C?