1,001 Chemistry Practice Problems For Dummies (2014)
Part I. The Questions
Chapter 12. Gases
Most of the gas laws depend upon various combinations of volume (V), temperature (T), pressure (P), and moles (n). In some cases, all four are important; in others, one or two are held constant. Although a number of pressure or volume units will work, all temperatures used in the calculations must be in kelvins. Graham’s law is the only law in this chapter that doesn’t depend upon V, T, P, or n.
The Problems You’ll Work On
In this chapter, you work with gases in the following ways:
Converting units of pressure
Using Boyle’s law, Charles’s law, and Gay-Lussac’s law
Finding pressure, volume, and temperature with the combined gas law
Relating volume to moles with Avogadro’s law
Working with the ideal gas law
Finding partial pressures with Dalton’s law
Exploring effusion rates with Graham’s law
Doing stoichiometry calculations
Note: The Appendix includes a periodic table for reference.
What to Watch Out For
Remember the following when working on gases:
Know the basic forms of the gas laws. Know which gas laws are direct relationships and which are inverse relationships.
All temperatures used in calculations must be in kelvins. A negative kelvin temperature is impossible.
The conversion 22.4 L/mol only works for gases at standard temperature and pressure (STP).
Converting Pressure Units
782–789 Convert between the pressure units.
782. How many torr are in 2.5 atm of pressure?
783. How many kilopascals are in 0.75 atm of pressure?
784. How many atmospheres are in 528 mm Hg?
785. The pressure in a car tire is 38.7 psi. What is the pressure in atmospheres?
786. A vessel is pressurized to 5.00 atm. What is the pressure in millimeters of mercury?
787. How many millimeters of mercury are in 1,050 torr?
788. How many torr are in 3.11 kPa?
789. The pressure exerted by a gas in a bicycle tire is 50.0 psi. How many kilopascals is that?
Boyle’s Law
790–799 Perform the calculations using Boyle’s law. This law may be implemented as P_{1}V_{1} = P_{2}V_{2} when the gas’s temperature is held constant.
790. The pressure of 5.0 L of a gas changes from 3.0 atm to 10.0 atm while the temperature remains constant. What is the gas’s new volume in liters?
791. The original pressure of a gas was 765 torr, and the volume changed from 17.5 L to 12.5 L while the temperature remained constant. What is the gas’s new pressure in torr?
792. The pressure of 44.8 L of a gas changes from 0.75 atm to 0.25 atm while the temperature remains constant. What is the gas’s new volume in liters?
793. As the volume of a gas changes from 547 mL to 861 mL, the temperature remains constant. If the original pressure was 1.75 atm, what is the gas’s new pressure in atmospheres?
794. The pressure of a gas changes from 95.0 kPa to 211 kPa, and the volume changes to 45.0 mL. What was the gas’s original volume in milliliters if the temperature remained constant during the process?
795. A gas’s volume changes from 2,645 mL to 379 mL while the temperature remains constant. If the final pressure is 5.10 atm, what was the gas’s original pressure in torr?
796. The pressure of a gas increased from 1,020 torr to 7,660 torr while the temperature was held constant. If the final volume of the gas is 0.210 L, what was the original volume in milliliters?
797. The volume of a gas decreased from 1.00 L to 600. mL while the temperature remained constant. If the final pressure is 720. torr, what was the gas’s initial pressure in atmospheres?
798. The pressure of a gas changes from 1.50 atm to 540 torr, and the volume changes to 730 mL. What was the gas’s initial volume in liters if the temperature remained constant?
799. The pressure of a gas changes from 920 mm Hg to 2.5 atm while the temperature remains constant. If the final volume is 0.34 L, what was the gas’s original volume in milliliters?
Charles’s Law
800–809 Complete the calculations using Charles’s law. You can implement this law as (where T is in kelvins and pressure is held constant).
800. If a 4.2-L sample of a gas is heated from 200. K to 400. K while the pressure remains constant, what is the new volume in liters?
801. A gas sample has a volume of 473 mL after being heated from 20. K to 40. K at constant pressure. What was the gas’s initial volume in milliliters?
802. A gas is cooled from 323 K to 223 K while the pressure is held constant. If the final volume is 2.50 L, what was the gas’s original volume in liters?
803. A 20.0-L gas sample is held at a constant pressure while the temperature drops from 300. K to 75.0 K. What is the gas’s new volume in liters?
804. While the pressure is held constant, a 50.0-mL sample of a gas is cooled from 100.0°C to 50.0°C. What is the gas’s new volume in milliliters?
805. While the pressure is held constant, the volume of a gas sample changes from 350. mL to 0.100 L. What is the final temperature in kelvins if the original temperature was 127°C?
806. If 981 mL of a gas is heated from 335 K at constant pressure and the volume increases to 1,520 mL, what will be the new temperature in kelvins?
807. The volume of a gas decreased from 2.63 L to 627 mL, and the final temperature is 275 K. If the pressure remained constant, what was the initial temperature of the gas in kelvins?
808. The volume of a gas changed from 90.0 mL to 10.0 mL while the pressure was held constant. If the final temperature of the gas is –35°C, what was the initial temperature in kelvins?
809. The volume of a gas increases from 750 mL to 3.0 L. If the pressure was held constant and the starting temperature was 95°C, what will be the new temperature in kelvins?
Gay-Lussac’s Law
810–819 Complete the calculations using Gay-Lussac’s law. You can implement this law as (where T is in kelvins and the volume is held constant).
810. The temperature of a gas rises from 300. K to 450. K while the volume remains constant. If the original pressure is 900. torr, what will the final pressure be in torr?
811. While the temperature of a gas changes from 500. K to 300. K, the volume doesn’t change. If the initial pressure was 2.5 atm, what is the gas’s final pressure in atmospheres?
812. The temperature of a gas sample decreases from 425 K to 225 K, and the final pressure is 675 torr. If the volume is held constant, what was the gas’s initial pressure in torr?
813. The temperature of a gas sample increases from 315 K to 505 K, and the final pressure is 8.10 atm. If the volume is held constant, what was the gas’s initial pressure in atmospheres?
814. A gas sample is cooled from 310 K to 280 K while the volume is held constant. What will be the final pressure in kilopascals if the original pressure is 470 kPa?
815. A gas starts at 801°C with a pressure of 780. mm Hg and reaches a pressure of 1,280 mm Hg. If the volume remains constant, what is the final temperature in kelvins?
816. A gas starts at 100.°C with a pressure of 1.00 atm and reaches a pressure of 2.50 atm. If the volume is held constant, what is the final temperature of the gas in degrees Celsius?
817. The final temperature of a gas sample is 521 K, and the pressure changes from 428 torr to 1.25 atm. If the volume remains constant, what was the original temperature in kelvins?
818. The final temperature of a gas sample is 175 K, and the pressure changes from 44.1 psi to 2,028 torr. If the volume is held constant, what was the original temperature in degrees Celsius?
819. The initial temperature of a gas sample was 75°C, and the pressure changes from 0.612 atm to 34.9 in. Hg. If the volume is held constant, what is the final temperature in degrees Celsius?
The Combined Gas Law
820–829 Complete the calculations using the combined gas law, which may be represented as (where T is in kelvins and the number of moles is constant).
820. Solve for the missing value:
P_{1} = 2.00 atm |
P_{2} = ? atm |
V_{1} = 75.0 mL |
V_{2} = 125 mL |
T_{1} = 223 K |
T_{2} = 273 K |
821. Solve for the missing value:
P_{1} = 970 torr |
P_{2} = 760 torr |
V_{1} = 4.1 L |
V_{2} = ? L |
T_{1} = 273 K |
T_{2} = 400. K |
822. Solve for the missing value:
P_{1} = ? atm |
P_{2} = 5.1 atm |
V_{1} = 327 mL |
V_{2} = 188 mL |
T_{1} = 323 K |
T_{2} = 544 K |
823. Solve for the missing value:
P_{1} = 280 mm Hg |
P_{2} = 760 mm Hg |
V_{1} = ? mL |
V_{2} = 50. mL |
T_{1} = 520 K |
T_{2} = 220 K |
824. A gas sample that has a pressure of 4.23 atm, a volume of 1,870 mL, and a temperature of 293 K is allowed to expand to a volume of 6.01 L with a final temperature of 373 K. What is the final pressure of the gas in atmospheres?
825. A sample of a gas has a volume of 10.0 L at a pressure of 450 torr and a temperature of 773 K. What will the final volume be in liters if the conditions are changed to standard temperature and pressure (STP)?
826. The original volume of a gas sample was 0.75 L at a temperature of 25°C. The final volume, temperature, and pressure are 2,647 mL, 100.°C, and 5.5 atm, respectively. What was the original pressure in atmospheres?
827. The original pressure of a gas sample was 3.00 atm at a temperature of 300.°C. The final volume, temperature, and pressure are 594 mL, 200.°C, and 3,862 mm Hg, respectively. What was the original volume in milliliters?
828. A gas sample had an initial pressure, volume, and temperature of 970 torr, 220. mL, and 50. K, respectively. Its final pressure is 0.78 atm, and its final volume is 2.4 L. What is the gas’s final temperature in kelvins?
829. A gas sample had an initial pressure of 35.3 psi and an initial volume of 10.0 L. Its final pressure is 6.18 atm, its final volume is 4,290 mL, and its final temperature is 572 K. What was the initial temperature in kelvins?
Avogadro’s Law
830–835 Complete the calculations using Avogadro’s law, which states that the volume of a gas is directly proportional to the number of moles: . Using Avogadro’s law, you can determine that at standard temperature and pressure (273 K and 1 atm), 1 mol of gas will occupy 22.4 L. Note: Assume that this volume is an exact value for the following problems.
830. In liters, what is the volume of a sample of helium gas that has a mass of 100. g at standard temperature and pressure?
831. In liters, what is the volume of a sample of CO_{2}(g) that has a mass of 25.0 g at standard temperature and pressure?
832. How many molecules of nitrogen gas are present in 9.14 L of N_{2}(g) at standard temperature and pressure?
833. How many grams are in a 37.89-L sample of methane, CH_{4}, at standard temperature and pressure?
834. A 55.0-L gas sample contains 2.10 mol of dinitrogen tetroxide (N_{2}O_{4}) at 1.0 atm of pressure and 298 K. If the sample completely decomposes according to the following reaction, how many liters of NO_{2} are produced?
835. At a certain temperature and pressure, a 12.4-L sample containing 0.296 mol of ozone (O_{3}) reacts completely according to the following reaction. How many liters of O_{2} are produced?
The Ideal Gas Law
836–845 Complete the calculations using the ideal gas law, which says PV = nRT (where P is pressure in atmospheres, V is volume in liters, n is the number of moles, R is a constant equal to 0.0821 L·atm/K·mol, and T is temperature in kelvins).
836. What is the pressure in atmospheres of a 5.00-mol gas sample that occupies 12.5 L at 400. K?
837. What is the volume, in liters, of 8.91 mol of a gas at a pressure of 0.747 atm at 200. K?
838. How many moles of helium are in a gas sample that has a volume of 500.0 mL at a pressure of 3.00 atm and a temperature of 298 K?
839. What is the temperature, in kelvins, of 0.60 mol of a gas that occupies 2.8 L at a pressure of 4.1 atm?
840. How much space, in liters, would 40.6 mol of carbon dioxide gas occupy at a temperature of 205°C and a pressure of 1.50 atm?
841. What is the temperature, in kelvins, of a 0.333-mol sample of a gas that has a pressure of 6.98 psi and a volume of 11.2 L?
842. How many moles of oxygen gas occupy 3,050 mL at a pressure of 672 torr and 75°C?
843. What is the pressure, in atmospheres, of 0.618 g of chlorine gas (Cl_{2}) if it occupies a volume of 75.0 mL at a temperature of 255 K?
844. What is the molar mass of a gas if 261 g of the gas occupies 555 L at a pressure of 0.90 atm and a temperature of 373 K?
845. What is the molar mass of a gas that has a mass of 12.15 g at a pressure of 1.05 atm, a volume of 11.3 L, and a temperature of 523 K?
Dalton’s Law of Partial Pressures
846–854 Complete the calculations using Dalton’s law of partial pressures, which says that the total pressure is the sum of the individual partial pressures of the components of a gas mixture.
846. What is the total pressure of a mixture of gases containing N_{2}, O_{2}, and He with the following partial pressures?
847. Samples of Ar, Cl_{2}, and F_{2} are mixed together. If their individual pressures are as follows, what is the total pressure, in atmospheres, exerted by the gases?
848. Gases P_{x}, P_{y}, and P_{z} exist in a ratio of 7:3:2 in a gas sample. If the total pressure is 5.12 atm, what is the partial pressure of P_{x} in atmospheres?
849. A mixture of SO_{3}, SO_{2}, and O_{2} has a total pressure of 4.42 atm. The partial pressure of SO_{3} is 1.77 atm, and the partial pressure of SO_{2} is 1.02 atm. What is the partial pressure of O_{2} in atmospheres?
850. A mixture of gases contains butane, ethane, and propane with a total pressure of 1,482 torr. The mixture contains 0.822 mol of butane, 0.282 mol of ethane, and 0.550 mol of propane at the same temperature. What is the partial pressure of the propane in torr?
851. When 15.0 g of N_{2} gas and 20.0 g of O_{2} gas are added to a 10.0-L container at 25°C, what is the partial pressure of the N_{2} gas in atmospheres?
852. When 15.0 g of N_{2} gas and 20.0 g of O_{2} gas are added to a 10.0-L container at 25°C, what is the total pressure, in atmospheres, that the gases exert on the container?
853. When a sample of ammonium nitrite is heated, it decomposes according to the following reaction to form 4.25 L of nitrogen gas (collected over water) at 26°C and 757.0 torr. What is the pressure due to the nitrogen gas, and how many grams of ammonium nitrite were used?
Note: The vapor pressure of water at 26°C is 25.21 torr.
854. Oxygen gas is collected over water during the thermal decomposition of potassium chlorate at a pressure of 762.0 torr and a temperature of 22°C. What is the pressure, in torr, due to the oxygen if 242 mL of oxygen gas is formed? And how many grams of potassium chloride remain after the reaction is complete? Note: At 22°C, the vapor pressure of water is 19.83 torr.
Graham’s Law
855–857 Answer the questions on Graham’s law.
855. At the same temperature and pressure, which gas, Ar or O_{2}, will diffuse faster and why?
856. At the same temperature and pressure, which gas, NH_{3} or CO_{2}, will diffuse more slowly and why?
857. Given equal amounts of SO_{2} and ClO_{2} at the same temperature and pressure, which gas effuses faster and by how much?
Gas Stoichiometry
858–861 Complete the calculations using gas stoichiometry.
858. Excess chlorine gas reacts with 60.9 L of hydrogen gas to form hydrogen chloride gas according to the following equation:
What is the maximum volume of hydrogen chloride gas that can be produced at standard temperature and pressure?
859. When mercury(II) oxide is heated, liquid mercury and oxygen gas are the products. What is the maximum mass of mercury that can be produced if 100. L of oxygen gas is collected at standard temperature and pressure?
860. Liquid hydrogen peroxide decomposes to form liquid water and oxygen gas. How many liters of oxygen gas can be produced if 862 g of hydrogen peroxide completely decomposes at standard temperature and pressure?
861. Nitrogen gas reacts with hydrogen gas to form ammonia. What is the maximum volume of ammonia gas at standard temperature and pressure that can be produced from 25.0 L of nitrogen gas and 75.0 L of hydrogen gas?