Gas Laws
Matthew Grandbois, Sarah Madden, Eric Nelson
Chem 120H
9/19/00

Purpose:

 The purpose of this lab was to justify the gas laws through experimentation.  The second purpose of this lab was to determine an unknown metal through experimentation.

Methodology:

 To justify the gas laws, we tested a gas law tube under various conditions.  To justify Charles’ Law we placed the tube in various temperature water baths and observed the pressure of the gas inside.  We then extrapolated the temperature of absolute zero by plotting all of the points on a graph.  To justify Boyle’s Law we observed the tube while horizontal and vertical.  We recorded the length of the air tube, and then calculated the pressure using Boyle’s Law.
 To determine the unknown metal we reacted it with hydrochloric acid.  We placed a measured amount of the metal into a test tube with hydrochloric acid.  During the reaction the test tube was isolated, and the gas produced during the reaction was captured and put through a glass tube that was connected to a isolated beaker full of water.  When the gas reached the beaker, it displaced the water into another tube that emptied into an open beaker.  The volume of the water displaced was recorded as the volume of the hydrogen gas produced.  From these observations the gram formula weight of the metal was calculated through stoichiometry.  Once the gram formula weight was known, the element could then be determined.

Data:

Calculations:

To calculate the final pressure of the increasing pressure system we found the sum of the barometric pressure and the original length of mercury in the tube.

 Final Pressure = Barometric Pressure + Length of Hg
                         = 726 mm Hg + 27 mm Hg
                         = 753 mm Hg

Once we knew the final pressure of the system, we could determine the final length of the air column within the tube.   The final length was the product of the original length and the ratio of the original pressure with respect to the final pressure.

 Final length  = Original length    x      Original pressure
                                                               Final pressure
 
                      = 118 mm     x      726 mm Hg
                                                   753 mm Hg
                      = 114 mm

To determine the final pressure of the decreasing pressure system, we did the calculations the same way that we did the calculations of the increasing pressure system except that we found the difference of the two.  The final pressure was determined.

 Final Pressure = Barometric Pressure - Length of Hg
                         = 726 mm Hg - 27 mm Hg
                         = 699 mm Hg
 
We determined the final length of the air column using the same calculations as the increasing pressure system.

 Final length  = Original length   x   Original pressure
                                                           Final pressure

                      = 123 mm   x     699 mm
                                                699 mm
                      = 123 mm

The percentage of error from each of the systems was calculated by finding the difference of the recorded final length and calculated final length and then dividing by the recorded length.  That is then multiplied by 100%.

 Percentage error = (Recorded Length - Calculated Length)     X    100%
                                             Calculated Length

                             = (117 - 114)    X   100%
                                      117

                             =   2.56 %

The percentage error for the decreasing pressure system was found to be 0 % because the recorded length and the calculated length were found to be the same.

We converted the barometric pressure from millimeters of mercury to atmospheres.

   P = 726 mm Hg     x       1 atm
                                     760 mm Hg
      = 0.955 atm
To determine the unknown metal is, we must determine its gram formula weight.  To find that we must use stoichiometry.  The known element in the equation is the hydrogen gas. We chose this as the known variable because we used an excess of hydrochloric acid during our experiment. We recorded that 0.082 L of hydrogen gas was produced during the experiment.  Using the ideal gas law, we calculate the number of moles of hydrogen in the sample.
 
 

    N =             Pressure x Volume
               Gas Constant x Temperature
 
       =                  (0.955 atm) x (0.082 L)
                (0.0820578 L atm/(mol K)) x 276.15 K

       =       0.00346 mol H2

Now we can use mole to mole stoichiometry to determine how many moles of the unknown metal we used.  We assume that the coefficients are equal and the amount of the metal is 0.00346 mol.  We recorded the mass of the metal to be 0.0855 g.  We can now determine the gram formula weight of the metal by finding the ratio of the mass with respect to the molar amount.

   GFW  = Mass / moles

             = 0.0855 g / 0.00346 mol

              = 24.7 g/mol

We then compared the calculated molecular weight to the periodic table and found the unknown metal to be magnesium.

Conclusion:

 During this experiment we have justified the combined gas law by observing its product in action.  When we increased the temperature, the volume also increased.  This justifies Charles’ Law.  Also Boyle’s law was justified.  We observed that when the volume decreased the pressure increased.  We finally learned how to use stoichiometry to determine the unknown metal in a reaction.  We determined that metal to be magnesium.

Lab Index