Gas Law Question & Answers

1.Which statement is false?

(a) The density of a gas is constant as long as its temperature remains constant.

(b) Gases can be expanded without limit.

(c) Gases diffuse into each other and mix almost immediately when put into the same container.

(d) The molecular weight of a gaseous compound is a non-variable quantity.

(e) Pressure must be exerted on a sample of a gas in order to confine it.

2.A sample of oxygen occupies 47.2 liters under a pressure of 1240 torr at 25^oC. What volume would it occupy at 25^oC if the pressure were decreased to 730 torr?

(a) 27.8 L

(b) 29.3 L

(c) 32.3 L

(d) 47.8 L

(e) 80.2 L

3.A sample of nitrogen occupies 5.50 liters under a pressure of 900 torr at 25^oC. At what temperature will it occupy 10.0 liters at the same pressure?

(a) 32^oC

(b) -109^oC

(c) 154^oC

(d) 269^oC

(e) 370^oC

4.Under conditions of fixed temperature and amount of gas, Boyle's law requires that

I. P₁V₁ = P₂V₂

II. PV = constant

III. P₁/P₂ = V₂/V₁

(a) I only

(b) II only

(c) III only

(d) I, II, and III

(e) another combination

5.The volume of a sample of nitrogen is 6.00 liters at 35^oC and 740 torr. What volume will it occupy at STP?

(a) 6.59 L

(b) 5.46 L

(c) 6.95 L

(d) 5.67 L

(e) 5.18 L

6.The density of chlorine gas at STP, in grams per liter, is approximately:

(a) 6.2

(b) 3.2

(c) 3.9

(d) 4.5

(e) 1.3

7.What pressure (in atm) would be exerted by 76 g of fluorine gas in a 1.50 liter vessel at -37^oC?

(a) 26 atm

(b) 4.1 atm

(c) 19,600 atm

(d) 84

(e) 8.2 atm

8.What is the density of ammonia gas at 2.00 atm pressure and a temperature of 25.0^oC?

(a) 0.720 g/L

(b) 0.980 g/L

(c) 1.39 g/L

(d) 16.6 g/L

(e) 0.695 g/L

9.A container with volume 71.9 mL contains water vapor at a pressure of 10.4 atm and a temperature of 465^oC. How many grams of the gas are in the container?

(a) 0.421 g

(b) 0.183 g

(c) 0.129 g

(d) 0.363 g

(e) 0.222 g

10.What is the molecular weight of a pure gaseous compound having a density of 4.95 g/L at -35 ^oC and 1020 torr?

(a) 24

(b) 11

(c) 72

(d) 120

(e) 44

11.A 0.580 g sample of a compound containing only carbon and hydrogen contains 0.480 g of carbon and 0.100 g of hydrogen. At STP, 33.6 mL of the gas has a mass of 0.087 g. What is the molecular (true) formula for the compound?

(a) CH₃

(b) C₂H₆

(c) C₂H₅

(d) C₄H₁₀

(e) C₄H₁₂

12.A mixture of 90.0 grams of CH₄ and 10.0 grams of argon has a pressure of 250 torr under conditions of constant temperature and volume. The partial pressure of CH₄ in torr is:

(a) 143

(b) 100

(c) 10.7

(d) 239

(e) 26.6

13.What pressure (in atm) would be exerted by a mixture of 1.4 g of nitrogen gas and 4.8 g of oxygen gas in a 200 mL container at 57^oC?

(a) 4.7

(b) 34

(c) 47

(d) 27

(e) 0.030

14.A sample of hydrogen gas collected by displacement of water occupied 30.0 mL at 24^oC on a day when the barometric pressure was 736 torr. What volume would the hydrogen occupy if it were dry and at STP? The vapor pressure of water at 24.0^oC is 22.4 torr.

(a) 32.4 mL

(b) 21.6 mL

(c) 36.8 mL

(d) 25.9 mL

(e) 27.6 mL

15.Which one of the following statements is not consistent with the kinetic-molecular theory of gases?

(a) Individual gas molecules are relatively far apart.

(b) The actual volume of the gas molecules themselves is very small compared to the volume occupied by the gas at ordinary temperatures and pressures.

(c) The average kinetic energies of different gases are different at the same temperature.

(d) There is no net gain or loss of the total kinetic (translational) energy in collisions between gas molecules.

(e) The theory explains most of the observed behavior of gases at ordinary temperatures and pressures.

16.A mixture of 0.50 mol H₂(g) and 0.50 mol N₂(g) is introduced into a 15.0 liter container having a pinhole leak at 30^oC. After a period of time, which of the following is true?

(a) The partial pressure of H₂ exceeds that of N₂ in the container.

(b) The partial pressure of N₂ exceeds that of H₂ in the container.

(c) The partial pressures of the two gases remain equal.

(d) The partial pressures of both gases increase above their initial values.

(e) The partial pressure of H₂ in the container increases above the initial value.

17.If helium effuses through a porous barrier at a rate of 4.0 moles per minute, at what rate (in moles per minute) would oxygen gas diffuse?

(a) 0.20

(b) 0.50

(c) 2.0

(d) 8.0

(e) 1.41

18.A real gas most closely approaches the behavior of an ideal gas under conditions of:

(a) high P and low T

(b) low P and high T

(c) low P and T

(d) high P and T

(e) STP

19.Which one of the following statements about the following reaction is false?

CH₄(g) + 2O₂(g) CO₂(g) + 2H₂O(g)

(a) Every methane molecule that reacts produces two water molecules.

(b) If 32.0 g of oxygen reacts with excess methane, the maximum amount of carbon dioxide produced will be 22.0 g.

(c) If 11.2 liters of methane react with an excess of oxygen, the volume of carbon dioxide produced at STP is (44/16)(11.2) liters.

(d) If 16.0 g of methane react with 64.0 g of oxygen, the combined masses of the products will be 80.0 g.

(e) If 22.4 liters of methane at STP react with 64.0 g of oxygen, 22.4 liters of carbon dioxide at STP can be produced.

20.What total gas volume (in liters) at 520^oC and 880 torr would result from the decomposition of 33 g of potassium bicarbonate according to the equation:

2KHCO₃(s) K₂CO₃(s) + CO₂(g) + H₂O(g)

(a) 56 L

(b) 37 L

(c) 10 L

(d) 19 L

(e) 12 L

21.Calculate the weight of KClO₃ that would be required to produce 29.5 L of oxygen measured at 127^oC and 760 torr.

2KClO₃(s) 2KCl(s) + 3O₂(g)

(a) 7.82 g

(b) 12.2 g

(c) 14.6 g

(d) 24.4 g

(e) 73.5 g

22.Which of the following statements is false?

(a) The properties of N₂(g) will deviate more from ideality at -100^oC than at 100^oC.

(b) Van der Waal's equation corrects for the non-ideality of real gases.

(c) Molecules of CH₄(g) at high pressures and low temperatures have no attractive forces between each other.

(d) Molecules of an ideal gas are assumed to have no significant volume.

(e) Real gases do not always obey the ideal gas laws.

23.The ideal gas law predicts that the molar volume (volume of one mole) of gas equals:

(a) gRT/PV

(b) (MW)P/RT

(c) 1/2ms^-2

(d) RT/P

(e) 22.4 L at any temperature and pressure

24.Three 1.0 liter flasks are filled with H₂, O₂ and Ne, respectively, at STP.

Which of the following statements is true?

(a) Each flask has the same number of gas molecules.

(b) The velocity of the gas molecules is the same in each flask.

(c) The density of each gas is the same.

(d) There are twice as many O₂ and H₂ molecules as Ne atoms.

(e) None of the above is true.

25.For a gas, which pair of variables are inversely proportional to each other (if all other conditions remain constant)?

(a) P, T

(b) P, V

(c) V, T

(d) n, V

(e) n, P

Answers:

1. (a) 2. (e) 3. (d) 4. (d) 5. (e) 6. (b) 7. (a) 8. (c) 9. (e) 10. (c) 11. (d) 12. (d) 13. (d) 14. (d) 15. (c) 16. (b) 17. (e) 18. (b) 19. (c) 20. (d) 21. (e) 22. (c) 23. (d) 24. (a) 25. (b)

Problem #1: A gas occupies 12.3 liters at a pressure of 40.0 mmHg. What is the volume when the pressure is increased to 60.0 mmHg?

(40.0 mmHg) (12.3 liters) = (60.0 mmHg) (x)

x = 8.20 L

Note three significant figures.

Problem #2: If a gas at 25.0 °C occupies 3.60 liters at a pressure of 1.00 atm, what will be its volume at a pressure of 2.50 atm?

(1.00 atm) ( 3.60 liters) = (2.50 atm) (x)

x = 1.44 L

Problem #3: To what pressure must a gas be compressed in order to get into a 3.00 cubic foot tank the entire weight of a gas that occupies 400.0 cu. ft. at standard pressure?

(400.0 cu. ft) (1.00 atm) = (x) (3.00 cubic foot)

x = 133 atm

It doesn't matter what the volume units are. It just matters that they be the same on each side.

Problem #4: A gas occupies 1.56 L at 1.00 atm. What will be the volume of this gas if the pressure becomes 3.00 atm?

(1.56 L) (1.00 atm) = (3.00 atm) (x)

0.520 L

Problem #5: A gas occupies 11.2 liters at 0.860 atm. What is the pressure if the volume becomes 15.0 L?

(11.2 liters) (0.860 atm) = (x) (15.0 L)

x = 0.642 atm

Problem #6: 500.0 mL of a gas is collected at 745.0 mmHg. What will the volume be at standard pressure?

(745.0 mmHg) (500.0 mL) = (760.0 mmHg) (x)

x = 490.1 mL

Problem #7: Convert 350.0 mL at 740.0 mmHg to its new volume at standard pressure.

(740.0 mmHg) (350.0 mL) = (760.0 mmHg) (x)

Problem #8: Convert 338 L at 63.0 atm to its new volume at standard pressure.

(63.0 atm) (338 L) = (1.00 atm) (x)

Problem #9: Convert 273.15 mL at 166.0 kPa to its new volume at standard pressure.

(166.0 kPa) (273.15 mL) = (101.325 kPa) (x)

Problem #10: Convert 77.0 L at 18.0 mmHg to its new volume at standard pressure.

(18.0 mmHg) (77.0 L) = (760.0 mmHg) (x)

Problem #11: When the pressure on a gas increases, will the volume increase or decrease?

Volume will decrease.

Problem #12: If the pressure on a gas is decreased by one-half, how large will the volume change be?

It will double in size.

Problem #13: A gas occupies 4.31 liters at a pressure of 0.755 atm. Determine the volume if the pressure is increased to 1.25 atm.

(0.755 atm) (4.31 liters) = (1.25 atm) (x)

Problem #14: 600.0 mL of a gas is at a pressure of 8.00 atm. What is the volume of the gas at 2.00 atm?

(8.00 atm) (600.0 mL) = (2.00 atm) (x)

Problem #15: 400.0 mL of a gas are under a pressure of 800.0 torr. What would the volume of the gas be at a pressure of 1000.0 torr?

(800.0 torr) (400.0 mL) = (1000.0 torr) (x)

Bonus Example #1: A particular balloon is designed by its manufacturer to be inflated to a volume of no more than 2.5 liters. If the balloon is filled with 2.0 liters of helium at sea level (101.3 kPa), and rises to an altitude at which the boiling temperature of water is only 88 degrees Celsius, will the balloon burst?

Solution:

Comment: These is no way of determining the starting temperature of the gas. However, we know something not in the problem: at sea level, the boiling point of water is 100 °C. So:

1) Let us use a ratio and proportion to estimate the pressure required for water to boil at 88 °C:

100 °C is to 101.3 kPa as 88 °C is to x

x = 89.144 kPa

2) Now, we can solve the problem using Boyle's Law:

P₁V₁ = P₂V₂

(101.3) (2.0) = (88.144) (x)

x = 2.27 L

The balloon will not burst.

Comment: Boyle's Law assumes that the temperature and amount of gas are constant. Since we never knew the starting temperature, we will assume it never changed as the balloon rose. If the temperature actually did change, but by some unknown value, then we cannot solve the problem.

Bonus Example #2: Two bulbs of different volumes are separated by a valve. The valve between the 2.00 L bulb, in which the gas pressure is 1.00 atm, and the 3.00 L bulb, in which the gas pressure is 1.50 atm, is opened. What is the final pressure in the two bulbs, the temperature being constant and the same in both bulbs?

Solution using Boyle's Law:

1) P₁V₁ = P₂V₂ twice

(1.00 atm) (2.00 L) = (x) (5.00 L)

x = 0.400 atm

(1.50 atm) (3.00 L) = (y) (5.00 L)

y = 0.900 atm

2) Add 'em up!

0.400 atm + 0.900 atm = 1.30 atm

Solution using the Ideal Gas Law:

1) PV = nRT twice:

(1.00) (2.00) = n₁RT

in the first bulb moles gas = n₁ = 2.00/RT

(1.50) (3.00) = n₂RT

in the second bulb moles gas = n₂ = 4.50/RT

2) PV = nRT for a third time

total volume = 2.00 + 3.00 = 5.00

(P₃) (5.00) = (n₁ + n₂)RT

(P₃) (5.00) = (2.00/RT + 4.50/RT)RT

(P₃) (5.00) = 6.50

P₃ = 6.50 / 5.00 = 1.30 atm