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Combined Gas Law Worksheet Solutions

Gas Laws: Combined Gas Law

The following problems may be solved using the relationships described by either Charlesí or Boylesí laws, together in the combined gas law. Show all the steps to the solution of the problem.

V1P1T2 = V2P2T1

1. Carbon dioxide occupies a 2.54 dm3 container at STP. What will be the volume when
     the  pressure is 150 KPa and 26oC?

     V2[2.54 dm3][101.3 KPa][26oC + 273K]  =  1.88 dm3
[150 KPa   ][273            K]

2. Oxygen occupies a fixed container of 5.5L at STP. What will happen to the pressure if
     the temperature rises to 300K?

      P2 = [5.5 L] [ 101.3 KPa][300 K]   =  111.3 KPa
              [5.5 L]                     [273 K]

3. Methane is compressed in a closed 15.8 dm3 container at 101.3 KPa. If the volume
    drops to 8.7 dm3 and the temperature begins at 25oC and then drops to 18oC , what will
    the pressure of the gas be?

    P2 = [ 101.3 KPa][15.8 dm3][300 K]   =  179.6 KPa
                                 [8.7 dm3 ][273 K]

4. A helium balloon is fully inflated at 1.2 L. When the clerk is filling the balloon, she stops
    to make sure it is not going to explode and checks the pressure. The pressure is 5.7 KPa
    and the temperature at the store is 24oC. The balloon is 0.75L full. She stops when the
    balloon is fully inflated and the pressure is 7.2 KPa. When the customer takes the balloon
    outside, it explodes. What was the temperature outdoors?

    T = [24oC + 273K][  1.2 L][7.2 KPa]  =  600 K
                                   [0.75 L][5.7 KPa]    

5. Oxygen gas is added to a rebreather at the same rate as it would be in the open air. 
     The volume is 4.8 dm3 and the temperature is 25 oC. The pressure is1 atm. Once the
     tank is lowered under the water the pressure increases to 2 atm and the temperature
     drops to 12oC.  Is the tank in danger of exploding if itís maximum volume is 5.0 dm3?

      V2[4.8 dm3][1 atm][12oC + 273K]  =  2.1 dm3  
[2 atm][25oC + 273K]       not in danger of exploding   

6. Ozone is formed due to electricity passing through the air and splitting some O2 atoms
    which then join briefly to form O3, ozone. Your olfactory sense can detect 1.00 mL
    ozone in 10 L of air at STP. You are surprised that the noreaster is accompanied by
    thunderstorms. You detect the scent of ozone in the air and the pressure is 94.5 Kpa and
    the temperature is 4 oC.  What is the new volume of ozone?

    V2[1.00 mL][101.3 KPa][           273K]  =  1.09 mL
[94.5  KPa][4 oC + 273K]

7. You are researching the gases that keep lily pads afloat. The cell vacuoles that contain the
     oxygen that keeps the plant afloat are approximately 17.7 mL. They can expand and
     contract with changes in temperature and pressure, but that is the optimal volume at
     25 oC and standard pressure. If the volume drops below 14.2 mL the leaves are
     submerged. You observe the lily pads in the pond are below water level, so the volume
     is down. If the pressure is 98.2 KPa, what is the temperature?

     T = [25oC + 273K][17.7 mL ][101.3 KPa]  =  246.6 K  
                                   [14.2 mL ][98.2    KPa]      

8. You like to skin dive. The best corals are at a depth of approximately 10m. You take a
     deep breath and dive. Your lung capacity is 2.4L total. The air temperature is 32 oC and
     the pressure is 101.3 Kpa. At 10 m the temperature is 21 oC and 141.2 Kpa. What is
     the volume of your lungs?

     V2[2.4 L][101.3 KPa][32 oC + 273K]  =  1.66 L
[141.2KPa][21 oC + 273K]

9. If you breathe 3.0 L of helium at 25 oC and 101.3 Kpa, you will talk funny. You think
    that would be fun. You breathe all the helium in a container at 15 oC and 110.6 Kpa and
    you arenít talking funny. Why not?

    V2[3.0 L][101.3 KPa][15oC + 273K ]  =  2.66 L
[110.6KPa][25 oC + 273K]     not enough volume to talk funny

10. A researcher is studying the relationship between volume of burps and stress. Burps due
      to stress are just swallowed air. Your diaphragm detects pressure as discomfort at
      210.0 Kpa. (body temperature is 37 oC). If you feel discomfort and you burp, into the
      researcherís balloon, the balloon slightly inflates to 6.45 mL at 101.3 Kpa and 27 oC.
     What volume did the burp occupy in your body?

      V2[6.45 mL][101.3 KPa][37 oC + 273K]  =  3.22 mL
      [210.0 KPa][27 oC + 273K]


Gas Law Problems