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5.E: Gases- Homework

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    Turn in your answers for the following questions - show your work

    1. The volume of a bicycle tire is 1.35 liters and the manufacturer recommends a tire pressure of 125 PSI.
      1. If you want the bicycle tire to have the correct pressure at 20.0 °C, what volume of air is required at STP?
      2. If you fill the tire with nitrogen, what is the mass of the gas?
      3. You fill the bicycle tire to 125 PSI on a cold december day (-22 °F), and leave it until a hot day in July (101 °F). What is the pressure of the tire (assuming that it does not leak and it does not change volume or burst).
    2. A fire extinguisher with a volume of 3.0 liters is filled with 150.0 grams of CO2.
      1. Assuming that it is an ideal gas, what is the pressure at 20.0 °C?
      2. What is the volume of the CO2 at 1.0 atm and 25 °C after the CO2 is released from the fire extinguisher?
    3. A ballon used for sampling stratospheric ozone is filled with 150.0 kg of He. What is the volume of the balloon when,
      1. The balloon starts from a research station in Antartica at sea level where the barrometric pressure is 755 mmHg and the temperature is -25.0 °C.
      2. The balloon rises to 29,028 ft (8,848 m, the height of Mt Everest and about typical crusing altitude for a jet aircraft) the temperature is -70 °C and the pressure is 2.30x104 Pa.
      3. The balloon enters the stratosphere, at 65000 ft (20,000 m, crusing altutude for a U2 spy plane) the temperature is -70 °C and the pressure is 3.68x103 Pa.

    The Following Questions are for your practice - Do Not Turn In.  They include answers so you can check your work

    Gas Pressure

    1. A typical barometric pressure in Denver, Colorado, is 615 mm Hg. What is this pressure in atmospheres and kilopascals?
      answer
      0.809 atm; 82.0 kPa
    2.  
    3. Consider this scenario and answer the following questions: On a mid-August day in the northeastern United States, the following information appeared in the local newspaper: atmospheric pressure at sea level 29.97 in., 1013.9 mbar.
      1. What was the pressure in kPa?
      2. The pressure near the seacoast in the northeastern United States is usually reported near 30.0 in. Hg. During a hurricane, the pressure may fall to near 28.0 in. Hg. Calculate the drop in pressure in torr.
      answer
      (a) 101.5 kPa; (b) 51 torr drop
    4.  

    Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law

    1. How would the graph in Figure change if the number of moles of gas in the sample used to determine the curve were doubled?

      CNX_Chem_09_03_BoylesLaw1.jpg

      When a gas occupies a smaller volume, it exerts a higher pressure; when it occupies a larger volume, it exerts a lower pressure (assuming the amount of gas and the temperature do not change). Since P and V are inversely proportional, a graph of \(1/P\) vs. \(V\) is linear.
      answer
      The curve would be farther to the right and higher up, but the same basic shape.
    2. Determine the volume of 1 mol of CH4 gas at 150 K and 1 atm, using

      fig-ch01_patchfile_01.jpg
      Figure \(\PageIndex{1}\): The volume and temperature are linearly related for 1 mole of methane gas at a constant pressure of 1 atm. If the temperature is in kelvin, volume and temperature are directly proportional. The line stops at 111 K because methane liquefies at this temperature; when extrapolated, it intersects the graph’s origin, representing a temperature of absolute zero.

      answer

      16.3 to 16.5 L

    3. A spray can is used until it is empty except for the propellant gas, which has a pressure of 1344 torr at 23 °C. If the can is thrown into a fire (T = 475 °C), what will be the pressure in the hot can?
      answer

      3.40 × 103 torr

    4. A weather balloon contains 8.80 moles of helium at a pressure of 0.992 atm and a temperature of 25 °C at ground level. What is the volume of the balloon under these conditions?

      CNX_Chem_09_02_WeatherBall_img.jpg

      answer

      217 L

    5. The effect of chlorofluorocarbons (such as CCl2F2) on the depletion of the ozone layer is well known. The use of substitutes, such as CH3CH2F(g), for the chlorofluorocarbons, has largely corrected the problem. Calculate the volume occupied by 10.0 g of each of these compounds at STP:
      1. CCl2F2(g)
      answer

      (a) 1.85 L CCl2F2

    6. A balloon that is 100.21 L at 21 °C and 0.981 atm is released and just barely clears the top of Mount Crumpet in British Columbia. If the final volume of the balloon is 144.53 L at a temperature of 5.24 °C, what is the pressure experienced by the balloon as it clears Mount Crumpet?
      answer

      0.644 atm

    Stoichiometry of Gaseous Substances, Mixtures, and Reactions

    1. A cylinder of O2(g) used in breathing by emphysema patients has a volume of 3.00 L at a pressure of 10.0 atm. If the temperature of the cylinder is 28.0 °C, what mass of oxygen is in the cylinder?
      answer

      38.8 g

    2. What is the molar mass of a gas if 0.0494 g of the gas occupies a volume of 0.100 L at a temperature 26 °C and a pressure of 307 torr?
      answer

      1.) convert torr to atm and °C to °K

      \(307\:torr=0.404atm\)

      \(26°C= 300.°K\)

      2.) Use the equation \(PV=nRT\) and solve for \(n\)

      \(n=\dfrac{PV}{RT}\)

      \(n=\dfrac{(0.404\:\cancel{atm})(0.100\:\cancel{L})}{(0.08206\dfrac{\cancel{atm}\:\cancel{L}}{mol\:\cancel{°K}})(300.\cancel{°K})}=0.00165\:moles\)

      3.) Then divide grams by the number of moles to obtain the molar mass:

      \(\dfrac{0.0494g}{0.00165\:moles}=30.0\dfrac{g}{mole}\)

    3. Lime, CaO, is produced by heating calcium carbonate, CaCO3; carbon dioxide is the other product.
      1. Outline the steps necessary to answer the following question: What volume of carbon dioxide at 875° and 0.966 atm is produced by the decomposition of 1 ton (1.000 × 103 kg) of calcium carbonate?
      2. Answer the question.
      answer

      (a) Balance the equation. Determine the grams of CO2 produced and the number of moles. From the ideal gas law, determine the volume of gas. (b) 7.43 × 105 L

    4. A sample of a compound of xenon and fluorine was confined in a bulb with a pressure of 18 torr. Hydrogen was added to the bulb until the pressure was 72 torr. Passage of an electric spark through the mixture produced Xe and HF. After the HF was removed by reaction with solid KOH, the final pressure of xenon and unreacted hydrogen in the bulb was 36 torr. What is the empirical formula of the xenon fluoride in the original sample? (Note: Xenon fluorides contain only one xenon atom per molecule.)
      answer

      XeF2

    Non-Ideal Gas Behavior

    1. Graphs showing the behavior of several different gases follow. Which of these gases exhibit behavior significantly different from that expected for ideal gases?

      This figure includes 6 graphs. The first, which is labeled, “Gas A,” has a horizontal axis labeled, “Temperature,” and a vertical axis labeled, “Volume.” A straight blue line segment extends from the lower left to the upper right of this graph. The open area in the lower right portion of the graph contains the label, “n, P constant.” The second, which is labeled, “Gas B,” has a horizontal axis labeled, “P,” and a vertical axis labeled, “P V.” A straight blue line segment extends horizontally across the center of this graph. The open area in the lower right portion of the graph contains the label, “n, T constant.” The third, which is labeled, “Gas C,” has a horizontal axis labeled,“P V divided by R T,” and a vertical axis labeled, “Moles.” A blue curve begins about halfway up the vertical axis, dips slightly, then increases steadily to the upper right region of the graph. The fourth, which is labeled, “Gas D,” has a horizontal axis labeled, “P V divided by R T,” and a vertical axis labeled, “Moles.” A straight blue line segment extends horizontally across the center of this graph. The open area in the lower right portion of the graph contains the label “n, P constant.” The fifth, which is labeled, “Gas E,” has a horizontal axis labeled, “Temperature,” and a vertical axis labeled, “Volume.” A blue curve extends from the lower left to the upper right of this graph. The open area in the lower right portion of the graph contains the label “n, P constant.” The sixth graph, which is labeled, “Gas F,” has a horizontal axis labeled, “Temperature,” and a vertical axis labeled, “Pressure.” A blue curve begins toward the lower left region of the graph, increases at a rapid rate, then continues to increase at a relatively slow rate moving left to right across the graph. The open area in the lower right portion of the graph contains the label, “n, V constant.”

      answer

      Gases C, E, and F

    This page titled 5.E: Gases- Homework is shared under a CC BY license and was authored, remixed, and/or curated by Scott Van Bramer.