The Molar Volume of a Gas

 

Purpose:  To determine experimentally the molar volume of hydrogen gas  by measuring the volume of hydrogen gas produced by a given mass of magnesium metal.

 

Theory:  According to Advogadro's Law equal volumes of gases measured under the same temperature and pressure contain equal numbers of molecules.  As a result the masses of gas volumes are in the same ratio as the masses of their constituent particles.

 

The volume of gas chosen for comparison is the volume occupied by one mole of a gas.  This is commonly known as the molar volume. The volume of a gas depends on the pressure and temperature of the gas.  To keep the comparison on the same basis a standard temperature of 0C or 273 Kelvin and a standard pressure of 101.3 kPa (760 mm of mercury)  have been chosen.  Under these conditions the volume of one mole of gas is 22.4 dm3.

 

In this experiment you will determine the standard molar volume of a gas.  You will react a known mass of magnesium metal with excess hydrochloric acid and collect the hydrogen gas generated over water in a gas collection tube.   The chemical reaction for this process is:

 

Mg (s)   +  2 HCl (aq)     MgCl2 (aq)  +   H2  (g)

 

The gas collected will be saturated with water vapor and it will be at conditions other than STP.  If the level of gas in the collection tube is not equal to the level of water in the reaction beaker, the gas in the gas collection tube is not at atmospheric pressure.  It is necessary to make the appropriate correction.

 

Figure 1

Gas Collection Apparatus

 

If the  level of the water in the gas collection tube is not equal to atmospheric pressure the difference in pressure can be determined by dividing the difference in  levels by the specific gravity of mercury, 13.6.

 

                        P tube =  Patmospheric -   difference in levels in mm

                                                                                    13.6

 

Since the hydrogen is collected over water it is necessary to correct for the vapor pressure of water.  Using Dalton's Law, one can assume that the total pressure in the tube is the sum of the partial pressures of hydrogen and water vapor.  Hence the pressure of hydrogen in the tube is can be determined by subtracting the vapor pressure of water at the temperature  of the gas in the tube. 

                                                                                               

PH2    =   P tube - P H2O

The volume of gas collected at STP can be calculated from the adjusted pressure, the observed volume, and the ambient temperature  using the universal gas equation.  The number of moles of hydrogen can be calculated from the number of moles of magnesium used to generate it.  The standard molar volume can then be calculated  by proportion using the  number of moles of hydrogen gas and the volume occupied at STP by the hydrogen.

 

 

Apparatus

 

         barometer                                         Beaker                                          Magnesium ribbon

         thermometer                                     10 cm3 graduated cylinder        copper wire

         ring stand                                          1 hole rubber stopper                6.0 M HCl solution

         utility clamp                                       ruler

         gas collection tube                          safety glasses

 

Procedure

 

1.       Record the barometric pressure.  Obtain and record  the mass of 1.00 meter of magnesium ribbon.

2.       Obtain a piece of magnesium approximately 25 mm  long.  Measure the length of ribbon to the nearest 0.5 mm  and record the value.

3.       Obtain a piece of fine copper wire approximately 10 cm long.  Roll the magnesium in a small ball and encase it in a cage of copper wire.  Be sure to leave several centimeters of copper wire extended from the cage.  This handle will allow the ball of magnesium to be attached and anchored at the mouth of the gas collection cylinder.

4.       Assemble the ring stand and utility clamp to hold the gas collection apparatus. 

5.       Add approximately 300 cm3 of tap water  at room temperature to the 600 cm3 beaker.

7.       Carefully add 10 cm3 of 6 M hydrochloric acid to the gas collection tube.  Incline the tube slightly and continue filling the tube with tap water from the 600 cm3 beaker.  While pouring the tap water in the tube try to rinse down any acid that might have remained on the sides of the tube.  Avoid agitating the bottom acid or the interface between the water and the acid if possible.  Attach the magnesium package encased in copper wire  at mouth of the gas collection tube.  Insert a one hole rubber stopper to hold the magnesium ball in place.  Be sure that the tube is filled to capacity so that the rubber stopper must displace water as it is inserted.  Be careful not to trap any air bubbles in the tube.

8.       Cover the stopper hole with your finger and immediately invert it into the beaker containing the water.  Your apparatus should look like figure 1.   Secure the gas collection tube with the utility clamp so that the rubber stopper is slightly above the bottom of the beaker.  Allow the chemical reaction to continue until no more gas is generated.  When the reaction has stopped, allow the apparatus to cool 3-5 minutes so that it is at room temperature.

9.       Measure the volume of gas generated using  the scale on the gas collection tube and record this.

10.   Record the temperature of the water in the beaker.  This should closely approximate the temperature of the gas

11.   Measure the difference in the levels of the water in the beaker and the gas collection tube using a meter stick or ruler.   Record this value as h in millimeters

12.   Discard the solution in the tube and the beaker and rinse all of your apparatus with tap water.  Wash your hands before leaving the lab.

 

Sample DATA Table

 

Barometric Pressure

 

Torr

Length of Magnesium ribbon used

 

 

Millimeters

Mass of 1.00 meter  (1000 mm)  of Mg Ribbon

 

 

grams

Volume of the gas in the collection tube

 

 

cm3

Temperature of gas collected  Water Temperature)

 

 

oC

Difference in levels (h)

 

 

Millimeters

Vapor Pressure of water at Temperature recorded

 

Torr

 

 

 

 

        

 

Show the calculations clearly in your lab report.  You may follow the process below

 

  1. Calculate the Adjusted Pressure of the gas:

 

            PH2  =   P Barometric  -          h         -   Vapor Pressure of Water

                                              13.6            (for the temperature at which the gas was collected)

 

  1. To convert the measured volume of H2 to STP using the combined gas laws.

 

            VSTP   =  Vmeas    x      Adjusted Pressure      x                273 K

                                                760 torr                                 Room temp in Kelvin

 

  1. To calculate the mass of magnesium used

 

            Mass Mg    =  length (mm)  x     mass of 1.00    x     1 meter

                                                          meter Mg            1000 mm

 

  1. To calculate moles of Mg used 

 

                        Moles Mg   =     Mass Mg (grams)

                                                24.31 g/mol

 

  1. To convert the volume of gas collected to dm3,   divide by 1000 cm3/ dm3

 

  1. To calculate the molar volume of the gas, divide the volume of hydrogen at STP by the moles of hydrogen

 

  1. The true value of  the molar volume of any gas at STP is 22.4 dm3 mol-1.  Compare your calculated value and find the percent error