Gas Stoichiometry Solutions

1) A quantity of gas at a temperature of 18^oC has a volume of 124.5 cm³ at a pressure of
     97.8 KPa.  How many moles of gas are there?   PV=nRT

    n= [         mol K     ][97.8 KPa         ][0.1245dm³] = 0.005 mol gas
           [8.31 dm³ KPA][18^oC + 273=K]        

2) At a pressure of 105.2 KPa,  1.42  moles of a gas occupy 1.74 dm³.  What is the
     temperature in Kelvin?   PV=nRT

     T = [         mol K     ][105.2 KPa][1.74dm³] = 15.51K
           [8.31 dm³ KPA ][1.42 mol   ]        

3) Hydrogen sulfide occupies 278.2 cm³ at 26^oC and standard pressure.  What is the mass
    of the hydrogen sulfide? PV=nRT

    mass=   [8.31 dm³ KPA][   33.0g H₂S][26^oC + 273=K                      ] = 2.9Kg
                [         mol K     ][1 mole H₂S ][101.3 KPa       ][0.2782dm³]     

4) Three and twenty-seven hundredths moles of carbon dioxide are in a vessel of
     undetermined size at 106.3 KPa and 21.8^oC.  What is the volume of the vessel?
     PV=nRT

     V= [3.27 mol][8.31 dm³ KPA][21.8^oC + 273=K] = 75.4 dm³
                         [         mol K     ][106.3 KPa  ]     

5) A gas at 1.24^oC occupies a 3.51 dm³ container.  If there are 3.34 moles of the gas,
     at what pressure is the gas? PV=nRT

     P= [3.34 mol][8.31 dm³ KPA][1.24^oC + 273=K] = 2170 KPa
                         [         mol K     ][3.51 dm³]     

6) If 1.39 g of carbon monoxide is reacted with oxygen, what volume of carbon dioxide
    is produced at  12.3^oC at 107.4KPa?

                     2CO +  O₂ --> 2CO₂

     mol CO₂ = [1.39g CO][1mol CO][2 mol CO₂ ] =  0.05 mol CO₂
                                         [28 g CO ][2 mol CO  ]

    V= [0.05 mol][8.31 dm³ KPA][12.3^oC + 273=K] = 1.09 dm³
                         [         mol K     ][107.4 KPa  ]     

7) If 14.4 dm³ of ethane is combusted at 102.7^oC and 99.3KPa, how many grams of
    water will be produced?

                       2C₂H₆ +  7O₂ -->  4CO₂ +  6H₂O

       n= [         mol K     ][99.3 KPa              ][14.4 dm³] = 0.46 mol C₂H₆
             [8.31 dm³ KPa ][102.7^oC + 273=K]        

       mass H₂O = [0.46 mol C₂H₆][6 mol H₂O ][18 g   H₂O]  =  24.8 g H₂O
                                                    [2 mol C₂H₆][1 mol H₂O]

8) What volume of C₈H₁₈ is required to fill a 1.4 dm³ airbag with CO₂ if the wrecker truck
     burns octane at STP? (Exhaust fumes are used to fill airbags to upright flipped tractor
     trailers.)

                         2C₈H₁₈ +  25O₂ --> 16CO₂ + 18H₂O

       n= [         mol K     ][101.3 KPa              ][1.4 dm³] = 0.63 mol CO₂
             [8.31 dm³ KPa ][273K]        

       v C₈H₁₈ = [0.63 mol CO₂][ 2 mol C₈H₁₈ ][22.4 dm³ C₈H₁₈] =  1.76 dm³ C₈H₁₈
                                                [16 mol CO₂    ][1 mol       C₈H₁₈]

9) A scuba diver dives with a tank containing 5L of air.  Twenty-two percent of the air
     is oxygen.  If the diver produces 1.62 mol carbon dioxide for every 2.05 mol of oxygen
     he/she inhales, what is the volume (at STP) of carbon dioxide produced if 4.2 L of air
     are consumed at 202.6 KPa and 14.7^oC?

     air w 2.05 mol O₂ --consumed yields-->1.62 mol CO₂

     4.2 L air = 4.2 dm³  air    4.2 dm³ air x 0.22 = 0.924 dm³ O₂

       n= [         mol K     ][202.6 KPa          ][0.924 dm³] = 0.078 mol O₂
             [8.31 dm³ KPa ][14.7^oC + 273=K]        

      v CO₂ = [0.078 mol O₂][1.62 mol CO₂][22.4 dm³ CO₂]  = 1.38  dm³ CO₂
                                           [2.05 mol O₂    ][1 mol CO₂      ]

10) If 34.6g of Zn are reacted with an excess of hydrochloric acid at standard pressure,
       what is the temperature of the hydrogen gas produced if it occupies a 2.00 dm³
        container?

                         2Zn  +  2HCl  -->  ZnCl₂  +  H₂ 

       n H₂ =  [34.6 Zn][1 mol Zn  ][1 mol H₂] =  0.265 mol H₂
                                  [65.4 g Zn][2 mol Zn ]

       T  = [101.3 KPa    ][2.00dm³ ][mol K            ] =   92 K
               [0.265 mol H₂]                [8.31 KPa dm³]