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Ideal Gas Law

Video Summary

Combined Gas Law

Instructions: Solve each of the following. If a varible is not give assume it is held constant. You can enter a 1 for any variable that is held constant, or is
not included. For example, if temperature is held constant simply substitute a 1 for T1 and T2 so that is cancels.
Pressure conversions: 1 ATM = 760 mmHg = 760 torr = 101.325 kPa = 101,325 Pa
P1V1 P2V2
=
T1 T2

1. 1.00 L of a gas at standard temperature and pressure is compressed to 473 mL. What is the new pressure of the gas? 2.11 ATM

2. On hot days, you may have noticed that potato chip bags seem to look more inflated, even though they have not been opened. If I have a 250 mL
bag at a temperature of 19℃, and I leave it in my car which has a temperature of 60.0℃, what will the new volume of the bag be? 285 mL pressure
remains constant

3. A gas that has a volume of 28 liters, a temperature of 45 ℃ , and an unknown pressure has its volume increased to 34 liters and its temperature
decreased to 35℃. If I measure the pressure after the change to be 2.0 ATM, what was the original pressure of the gas? 2.51 ATM

4. If I initially have a gas at a pressure of 12 ATM, a volume of 23 liters, and a temperature of 200 K, and then I raise the pressure to 10,640 mmHg and
increase the temperature to 300 K, what is the new volume of the gas? 29.6 L

5. A soda bottle is flexible enough that the volume of the bottle can change even without opening it. If you have an empty soda bottle (volume of 2 L) at
room temperature (25℃), what will the new volume be if you put it in your freezer (-4℃)? 1.81 L

6. I have an unknown volume of gas at a pressure of 0.5 ATM and a temperature of 325 K. If I raise the pressure to 135 kPa, decrease the temperature
to 320 K, and measure the final volume to be 48 liters, what was the initial volume of the gas? 129.9 L

7. A man heats a balloon in the oven. If the balloon initially has a volume of 0.4 liters and a temperature of 20℃, what will the volume of the balloon be
after he heats it to a temperature of 250℃? 0.71 L

8. In a thermonuclear device, the pressure of 0.050 liters of gas within the bomb casing reaches 4.0 x106 ATM. When the bomb casing is destroyed by
the explosion, the gas is released into the atmosphere where it reaches a pressure of 760 torr. What is the volume of the gas after the explosion? 2.0
x105 L

9. If I have 17 liters of gas at a temperature of 67℃ and a pressure of 88.89 ATM, what will be the pressure of the gas if I raise the temperature to 94℃
and decrease the volume to 12 liters? 135.92 ATM

10. 10.0 L of a gas is found to exert 97.0 kPa at 25.0 ℃ . What would be the required temperature (in Celsius) to change the pressure to standard
pressure (volume is held constant)? 38.3℃

11. I have an unknown volume of gas held at a temperature of 115 K in a container with a pressure of 60 ATM. If by increasing the temperature to 225 K
and decreasing the pressure to 30 ATM causes the volume of the gas to be 29 liters, how many liters of gas did I start with? 7.4 L
12. Synthetic diamonds can be manufactured at pressures of 6.00 x104 ATM. If we took 2.00 liters of gas at 1.00 ATM and compressed it to a pressure
of 6.00 x104 ATM, what would the volume of that gas be? 3.33 x10-5 L

13. The highest pressure ever produced in a laboratory setting was done by compressing 67.56 liters of a gas that was initially at a pressure of 0.30
ATM, to a volume of 1.0 X10-5 liters. What is the world record for highest pressure ever? 2.0 X106 ATM

14. What is the temperature inside my refrigerator if a balloon placed inside that initially has a temperature of 8.8℃ and a volume of 0.5 liters is reduce
in volume to 0.25 L? -132.3℃

15. 5.00 L of a gas is collected at 22.0℃ and 745.0 mmHg. When the temperature is changed to standard conditions, what is the new pressure? 689.47
mmHg

16. A gas takes up a volume of 17 liters and is under STP conditions. If I raise the temperature to 350 K and lower the pressure to 1.5 ATM, what is the
new volume of the gas? 14.5 L

17. What is the temperature of 4.5 liters of gas if raising the temperature to 29℃ decreases the volume to 4.74 L while the pressure is not changed?
14℃

18. If I have 21 liters of gas held at a pressure of 78 ATM and a temperature of 900 K, what will be the volume of the gas if I decrease the pressure to
45 ATM and decrease the temperature to 750 K? 30.3 L

19. If I have 2.9 L of gas at a pressure of 5 ATM and a temperature of 50℃, what will be the temperature of the gas if I decrease the volume of the gas
to 2.4 L and decrease the pressure to 315 kPa? 165.81 K

20. Two flasks are connected by a stopcock as shown below. The 5.0 L flask contains CH4 at a pressure of 3.0 ATM, and the 1.0 L flask contains C2H6
at a pressure of 0.55 ATM.
Calculate the total pressure of the system after the stopcock is opened. Assume that the temperature remains constant. answer. 2.6 ATM

Solutions

"This paper will no doubt be found interesting by those who take an interest in it" - John Dalton

Ideal Gas Law

Video Summary

Ideal Gas Law

Instructions: Solve the following problems by appling the ideal gas law and mole concept. Remeber that you must convert all units to match those in
the ideal gas law constant (R = 0.08206 ATM*L/K*mol.)
MM m mRT dRT
d= , MM = , P= , P= , PV = nRT
V n VMM MM
(MM = molar mass, m = mass, n = moles, d = density)
(P = pressure, V = volume, T = temperature, R = ideal gas constant)
Ideal Gas Law Constant at STP (0.08206 ATM*L/K*mol)
Molar Volume of a gas at STP is 22.4 L/1 mol

Section 1: Molar mass, density and STP problems

1. What is the mass, in grams, of 125 mL of CO2 at STP? 0.246 grams of CO2

2. What is the density at STP of methane gas (CH4), in grams per liter? .714 grams per liter

3. A chemical reaction produced 2.50 moles of nitrogen gas. What volume, in liters, does this gas sample occupy at STP? 56 liters

4. What is the molar mass of a gas that has a density of 0.840 g/L at STP? 18.8 g/mol

5. What is the molar mass of a 0.625 g gas sample that has a volume of 165 mL at STP? 84.8 g/mol

6. What volume, in liters, is occupied by 0.750 mol of hydrogen gas at STP? 16.8 L

7. What is the mass, in grams, of 72.5 L of NH3 at STP? 55.0 g

8. What is the density at STP of hydrogen sulfide gas (H2S), in grams per liter? 1.52 g/L

9. Find the molar mass of a gas that has a density of 1.15 g/L at STP. 25.8 g/mol

Section 2: Ideal gas law (PV = nRT) problems

10. A 0.215 g gas sample occupies a volume of 225 mL at 27°C and 740. mm Hg. What is the molar mass of this gas? 24.3 grams per mole

11. A 0.625 g gas sample occupies a volume of 320. mL at -23°C and 700. mm Hg. What is the molar mass of this gas? 43.5 g/mol

12. What pressure in atmospheres is exerted by 1.50 mol NH3 in a 3.75 L container at 27°C? 9.85 atm

13. What mass of nitrogen (N2), in grams, is contained in a 7.25 L tank at 37° C and 2.50 ATM pressure? 19.9 g

14. What is the volume of 8.15 moles of SO2 gas at 28.5°C and 0.985 ATM? 205 L

15. What is the temperature of 1.50 mol argon gas that is contained in a 500.0 mL flask at 15.8 ATM? 64.1 K

16. How many moles of nitrogen gas are present in a one-liter flask if the pressure is 1520 mm Hg and the temperature is 26.7°C? 0.0813 moles

17. What is the molar mass of an unknown gas if a 1.25 g sample occupies 1.00 L at 26.3° C and 0.990 ATM? 31.0 g/mole

18. If 958 mL of an unknown gas has a mass of 2.58 g at 22°C and 750. mm Hg, what is its molar mass? 66.1 g/mol

19. A compound, which has the empirical formula CH2Br, has a vapor density of 6.00 g L−1 at 375 K and 0.983 ATM. Using these data, determine the
molar mass and the molecular formula of the compound. 188 g/mol

Solutions

“The gas-law of learning: . . . any amount of information no matter how small will fill any intellectual void no matter how large.” ― Hugh Nibley,

Ideal Gas Law

Dalton's Law of Partial Pressure Practice
1. Three of the primary components of air are carbon dioxide, nitrogen, and oxygen. In a sample containing only a mixture of these gases at exactly
1.00 ATM, the partial pressure of the carbon dioxide and nitrogen are given as PCO2 = 0.285 ATM, PN2= 0.581 ATM. What is the partial pressure of
oxygen gas? 0.134 ATM O2

2. The volume of hydrogen collected over water is 453 mL at 291 K. What is the partial pressure of the H2(g) if the total pressure is 780 mm Hg? 764.5
mm Hg

3. The partial pressure of carbon dioxide collected over water at 30.° C is 749 mm Hg. If the total pressure is780.8 mm Hg, calculate the partial
pressure of water at 30.° C.
Temperature °C - Vapor Pressure (mm Hg)
18 15.505
20 17.52
22 19.835
30 _______
4. Determine the partial pressure in atmospheres for oxygen gas collected by water displacement if the water temperature is 22.0°C and the total
pressure of the gases in the collection bottle is 777.5 mm Hg. 1.0 ATM

5. When 4.0 L He(g), 6.0 L of N2(g), and 10. L of Ar(g), all at 0 °C and 1.0 ATM, are pumped into an evacuated 10.0 L rigid container, the final pressure
in the container at 0 °C is what? 2.0 ATM

6. Three sealed 1.0 L vessels each contain a different inert gas at 298 K. The pressure of Ar in the first vessel is 3.0 ATM. The ratio of the numbers of
Ar, Ne, and He atoms in the vessels is 3:1:8, respectively.
a. Draw a particulate diagram of the situation described above. Your diagram should include three containers with the correct ratio of gas particles and
an evacuate container of twice the size (2 liters).
b. What is the total pressure of the gases if the three gases are combined in the above-evacuated 1.0 L vessel at 298 K? 12.0 ATM
c. What would be the total pressure of the gases if the three gases were combined in the above-evacuated 2.0 L vessel at 298 K?6.0 ATM
7. Equal masses of oxygen gas (O2) and methane gas (CH4) are transferred to a previously evacuated rigid 1.0 L container at 298 K. If partial pressure
of oxygen gas is 0.33 ATM when the system is at a constant temperature and pressure, what is the total pressure of the container? 1.0 ATM
8. A flask contains 0.25 mole of SO2(g), 0.50 mole of CH4(g), and 0.50 mole of O2(g). The total pressure of the gases in the flask is 800 mm Hg. What
is the partial pressure of the SO2(g) in the flask? 160 mm Hg

Solutions

"You cannot teach a man anything; you can only help him/her discover it in him/herself" - Galileo

Ideal Gas Law

Video Summary

Ideal Gas Law Deviation

1. Real gases behave like ideal gases at higher temperature and lower pressures because:

2. The ideal gas law best describes the properties of which of the following gases at 0 °C and 1 ATM? A) NH3 B) SO C) H2 D) HCl
Why?

3. A vessel contains Ne(g) at a high pressure. Explain why the measured pressure is significantly greater than the pressure calculated using the ideal
gas law?

4. Ar(g) deviates more from ideal behavior at extremely high pressures than Ne(g) does. What is one reason for this difference?

5. At constant temperature, the behavior of a sample of a real gas more closely approximates that of an ideal gas as its volume is increased because
the average distance between molecules becomes _______________.

6. The diagrams above represent two samples of Xe gas in containers of equal volume at 280K. Sample 2 is found to have a higher pressure than
predicted. What is one explanation for this result.

The table below contains information about samples of four different gases at 273 K. The samples are in four identical rigid containers numbered 1
through 4.
7. The best explanation for the lower pressure in container 4 is that SO2 molecules is what?

Solutions

“Gases are distinguished from other forms of matter, not only by their power of indefinite expansion so as to fill any vessel, however large, and by the great effect heat has in dilating them, but by the
uniformity and simplicity of the laws which regulate these changes. — James Clerk Maxwell