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CHAPTER 5 HW

Name: Lab: MW 11-2 MW 2-5

GAS VARIABLES1

1.) The atmospheric pressure at the summit of Mt. Everest (29,029 ft) is roughly 250 mmHg. Convert this pressure into torr, atmospheres, and pounds per square inch.

2.) Use the Kinetic Molecular Theory of gases (i.e. a discussion of the gas particle’s interaction with the container walls) to explain the following observations:

a. When the plunger on a sealed syringe is extended, the pressure decreases inside the syringe. (Note: if the syringe were not sealed, the low pressure would withdraw material into the syringe; this is the normal mechanism of a syringe. This is also the mechanism of a bicycle pump.)

b. If a ping pong ball becomes dented, it can be restored to its original shape by placing it into boiling water. After a short amount of time in the hot water, the dent will be removed. Note: this only works if the ping pong ball has not become cracked (why?).

1 Q1) 250 torr, 0.33 atm, 4.8 psi; Q2a) Low V particles have further to travel, so fewer collisions with container walls and lower P, b) High T = faster molecules, so they contact container walls more often (higher P). See complete solutions for more detail.

10 15 20 5 10 15 20air

plug

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3.) A bag of potato chips is packed and sealed in Los Angeles (at sea level), then shipped to Lake Tahoe (in the mountains). The volume of the bag increases upon arrival at Lake Tahoe. What gas conditions most likely caused the volume increase? Use the Kinetic Molecular Theory of gases to explain.

4.) If you fill up your car’s tires at a gas station, you increase both the pressure and volume of the tires. Why does this not contradict Boyle’s law, which says that pressure and volume are inversely proportional?

5.) The following graph was generated by measuring the volume and Celsius temperature of a sample of gas (with constant moles and pressure).

a. What are the units of the slope and y-intercept?

Slope = y-intercept =

b. Use the provided slope and y-intercept to write the equation of the linear graph, using variables (not x,y).

__________________________________________

c. Use the graph to calculate the experimental temperature of absolute zero in Celsius.

6.) Use the Kinetic Molecular Theory of gases (i.e. a discussion of the gas particle’s interaction with the container walls) to explain why a latex balloon gets bigger when air is blow into it.2

2 Q3) Low P in Tahoe, so volume increases, see complete solutions for more detail; Q4) Boyle’s law only works when T and n are constant, here moles of gas increases; Q5a) L/˚C, b) Volume = 0.003700T + 0.9989, c) –270.0 ˚C; Q6) Moles increases.

m = 0.003700 b = 0.9989

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7.) Which graph (A-D) correctly shows the relationship between each set of variables? (Assume in each that other variables are kept constant.) Briefly explain your logic.3

a. Pressure vs. Volume

b. Pressure vs. Inverse Volume

c. Pressure vs. Temperature

d. Volume vs. Temperature

3 Q7) See complete solutions for all, a) D, b) A, c) A, d) A.

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8.) A glass vessel contains 28 g of nitrogen gas. Which of the processes listed below would double the pressure in the container? Explain your answers.

a. Adding 28 g of oxygen gas.

b. Adding 32 g of oxygen gas.

c. Raising the temperature from –73 ˚C to 127 ˚C.

d. Raising the temperature from 35 ˚C to 70 ˚C.

e. Adding enough liquid mercury to fill one-half the container.

GAS CALCULATIONS4

9.) A steel gas cylinder containing argon gas has a volume of 43 L. At 22.0 ˚C the pressure of argon gas is 135 atm. What would be the gas pressure if the temperature is increased to 44.0 ˚C?

4 Q8a) Not double, 28 g O2 is not an additional mole; b) Does double as 32 g O2 is an additional mole of gas and P ∝n, c) Does double as the T doubles in Kelvin, d) Not double, as T doesn’t double in Kelvin, e) Does double as V is cut in half, which increases P by 2 in order to keep PV constant; Q9) 145 atm.

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10.) A bicycle tire has an internal volume of 1.52 L and contains 0.406 mol of air. The tire will burst if its internal pressure reaches 7.25 atm. What temperature (in ˚C) does the air in the tire need to be to cause a blow-out?5

11.) Helium-filled weather balloons are used to carry instruments high into the atmosphere. Suppose a 4190 L balloon is launched at 22.5 ̊ C and 754 mmHg. If no helium escapes, what would be the volume of the balloon at a height of 20 miles, where the pressure is 76.0 mmHg and the temperature is –33.0 ˚C?

12.) A standard commercial “Balloon Time” helium tank is labeled to contain “8.9 cubic feet of helium,” which represents the volume of helium it can produce under typical conditions (1.00 atm and 25 ˚C). The tanks are pressurized to 260 psi.

a. What is the volume of helium (in L) in the pressurized tank? Assume the tank is at 25 ˚C.

b. It takes approximately 0.27 cubic feet (cf) of helium to fill one 9” latex balloon at 1.00 atm. How many 9” balloons could be filled with the Balloon Time helium tank?

5 Q10) 58 ˚C; Q11) 33,800 L; Q12a) 14 L, b) 33 balloons.

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13.) Jacques Charles launched the first manned hydrogen (H2) balloon in 1783. The balloon stayed aloft for almost 45 minutes and traveled 15 miles away. When it landed in a village, the people were so terrified they tore it to shreds with pitchforks. What was the volume of the balloon used by Charles if it contained about 1300 moles of H2 at 23 ˚C and 750 mmHg?6

14.) A person accidentally swallows one drop of liquid oxygen (O2), which has a density of 1.149 g/mL. Assuming the drop has a volume of 0.050 mL, what volume of O2 gas (in mL) will be produced in the person’s stomach at body temperature (37 ˚C) and a pressure of 1.0 atm?

15.) Dry ice (solid CO2) has occasionally been used as an explosive in mining. A hole is drilled, dry ice and a small amount of gunpowder are placed in a hole, a fuse is added, and the hole plugged. When lit, exploding gunpowder rapidly vaporizes the dry ice building up an immense pressure. Assume 500.0 g of dry ice is placed in a cavity with a volume of 0.800 L and the ignited gunpowder heats the CO2 to 430 ˚C. What is the final pressure inside the hole?

6 Q13) 32,000 L; Q14) 46 mL; Q15) 820 atm.

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MOLAR VOLUME7

16.) How many moles of hydrogen (H2) are present in 0.075 L of hydrogen gas at STP?

17.) The electrolysis of water produces both H2 and O2 gases, which can be collected separately, as shown in the picture below. Are there a greater number of moles of H2 or O2? Briefly explain how you know.

18.) Many bad odors are due to sulfur compounds, for example the scent of sweaty socks, bad breath, and flatulence. These odors are commonly caused by hydrogen sulfide (H2S), dimethylsulfide (CH3SCH3), and/or methyl mercaptan (CH3SH).

How many molecules of CH3SH are present in a 1.00 mL vessel that contains CH3SH gas at STP?

7 Q16) 0.0033 mol; Q17) H2 has more moles as it has a greater volume; Q18) 2.69 × 1019 molecules.

O2 H2

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GAS DENSITY8

19.) Carbon dioxide is used in some fire extinguishers as its high density allows for it to smother a fire. (Note: CO2 is an invisible gas, but comes out of the extinguisher as a white cloud. The CO2 from the tank expands and cools significantly, enough to condense moisture from the air, which is then visible).

Calculate the density of CO2 (g) at room temperature (24.2 ˚C) and 1.00 atm.

20.) Air, with an average molar mass of 28.96 g/mol, has a density of 1.18 g/mL at 25 ˚C and sea level. Forty miles above Earth’s surface, in the mesosphere where most meteors burn up, the temperature is –23 ˚C and the pressure is only 0.20 mmHg. What is the density of air at this altitude?

21.) An unknown diatomic gas has a density of 3.164 g/L at STP. What is the identity of the gas?

22.) In each pair, which has a higher density at room temperature?

a. N2 (g) vs. C8H18 (g) (C8H18 is similar to gasoline) c. Ar (g) vs. Ne (g)

b. NO2 (g) vs. CO (g) d. CO2 (s) vs. SF6 (g)

8 Q19) 1.8 g/L; Q20) 0.00037 g/L; Q21) MM=70.92 g/mol, it’s Cl2; Q22a) C8H18, b) NO2, c) Ar, d) CO2.

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GAS STOICHIOMETRY9

23.) A self-contained breathing apparatus uses canisters of potassium superoxide (KO2). It consumes CO2 exhaled by a person and replaces it with oxygen through the following reaction. These apparatuses are primarily used by firefighters, but also the US Navy.

4 KO2 (s) + 2 CO2 (g) → 2 K2CO3 (s) + 3 O2 (g)

What mass of KO2 is required to react with 8.90 L of CO2 at 22.0 ˚C and 767 torr?

24.) Explosive compounds are generally ones that react quickly to produce large amounts of energy and gases. The newly generated gases then undergo a rapid expansion, destroying objects in their path. Ammonium nitrate is predominantly used in agriculture as a fertilizer, but can decompose explosively when heated via the following equation.

2 NH4NO3 (s) → 2 N2 (g) + 4 H2O (g) + O2 (g)

The most recent explosion involving ammonium nitrate occurred in China in the summer of 2015, where 800 metric tons (800,000 kg) of NH4NO3 (MM = 80.04) detonated, killing 173 people. How many liters of gas were formed during the explosion, assuming the gases were at 1.00 atm and 450. ˚C (the temperature of an explosion)?

9 Q23) 52.8 g; Q24) 2 × 109 L.

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PARTIAL PRESSURES10

25.) For scuba dives below 150 feet, helium is often used to replace nitrogen in the scuba tank. If 15.2 g of He and 30.6 g of O2 are added to a previously evacuated 5.00 L tank at 22 ˚C, calculate the partial pressure of each gas as well as the total pressure in the tank.

26.) Hydrazine can be used as rocket fuel, and was repurposed in the movie The Martian (with Matt Damon, 2015) to produce hydrogen gas (via the equation below). The hydrogen gas was subsequently used by Matt Damon’s character to make water (via 2 H2 + O2 → 2 H2O) for his potato farm on the planet Mars.

N2H4 (g) → N2 (g) + 2 H2 (g)

If 12.00 g of hydrazine (MM = 32.06) is decomposed, and the N2 and H2 gases collected in a 15.0 L tank at 23˚C, what is the partial pressure of each gas and total pressure in the tank?

10 Q25) PHe= 18.4 atm, PO2= 4.63 atm, Ptotal= 23.0 atm; Q26) PN2= 0.606 atm, PH2= 1.21 atm, Ptotal= 1.82 atm;

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27.) A sample of O2 is collected over water at 21 ˚C and a total pressure of 742.2 mmHg. The vapor pressure of water at 21 ˚C is 18.663 mmHg. What is the partial pressure of O2 in the sample?

28.) Reaction of 0.2273 g of iron with excess acid produces H2 through the following unbalanced equation. The H2 is collected over water at 24.2 ˚C and a total pressure of 754.7 torr. What volume (in mL) of H2 is collected? The vapor pressure of water at 24.2 ˚C is 22.648 torr.

Fe (s) + HCl (aq) → FeCl2 (aq) + H2 (g)

KINETIC ENERGY, GAS VELOCITIES11

29.) Do all molecules in a 1 mol sample of CH4 have the same kinetic energy at 273 K?

30.) Consider two gas samples at 20 ˚C, one with CO at 760 torr, and another with H2 at 100 torr.

a. In which sample will the gas molecules have the greatest average velocity? Explain.

b. Why would it be difficult to quickly know which sample had the highest average velocity if the samples were not at the same temperature? Explain.

11 Q27) 723.5 mmHg; Q28) 103.1 mL; Q29) No, distribution of energies; Q30a) H2, has lowest MM, b) Both T and MM affect it.

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31.) Consider separate 1.0 L gaseous samples of He, Xe, Cl2, and O2, all at STP.12

a. Rank the gases in order of increasing average kinetic energy. Explain your answer.

b. Rank the gases in order of increasing root-mean-square velocity. Explain your answer.

c. How can separate samples of O2 and He each have the same average velocity?

32.) Calculate the root mean square velocity of CH4 (g) and N2 (g) at 273 K.

12 Q31a) Same T so same avg KE, b) Xe < Cl2 < O2 < He, follows MM, c) Different temps; Q32) 652 m/s (CH4), 493 m/s (N2).

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33.) At what temperature (in ˚C) does the average speed of an oxygen molecule (O2) equal that of an airplane moving at 580 miles per hour?

GAS DIFFUSION / EFFUSION13

34.) One of the main components of skunk spray is 3-methyl-1-butanethiol (C5H11SH) while one of the main components of lavender is linalool (C10H17OH). If separate containers containing gaseous samples of C5H11SH and C10H17OH are opened 10 feet away from you, which compound will you smell first? Explain your answer.

35.) In each pair, which effuses more quickly at room temperature?

a. N2 (g) vs. CO2 (g) b. CF4 (g) vs. F2 (g) c. 20Ne (g) vs. 22Ne (g)

36.) You have gaseous samples of ozone (O3) and ethylene (C2H4).

a. Which effuses more quickly at room temperature, O3 or C2H4?

b. How much faster does one sample effuse compared to the other?

13 Q33) –187 ˚C; Q34) C5H11SH, as it has lower MM; Q35a) N2, b) F2, c) 20Ne; Q36a) C2H4, b) C2H4 is 1.308 times faster.

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37.) What is the relative rate of effusion for F2O (g) compared to H2 (g)?

38.) The effusion rate of an unknown gas is found to be 31.50 mL/min. Under identical conditions, the effusion rate of O2 (g) is found to be 30.50 mL/min. Which unknown gas was used: CH4, CO, NO, CO2, or NO2?

39.) It takes 4.5 minutes for 1.0 L helium gas to effuse through a porous barrier. How long would it take 1.0 L of chlorine gas to effuse under identical conditions?14

14 Q37) H2 is 5.17 times faster, or F2O is 0.193 times as fast as H2; Q38) Unknown MM=30.00 g/mol, NO; Q39) 19 min.