Experiment #16  The Ideal Gas Law: Analysis Of An Aluminum-Zinc Alloy

 

Objective

 

In this experiment the percentage zinc and aluminum in an alloy sample will be calculated by reacting  it with strong acid and using the ideal gas law to determine the amount of hydrogen gas  produced.  The hydrogen gas produced will be collected under water at known pressure and temperature conditions. Then, by substituting volume of the gas collected, temperature of reaction and, the partial pressure of hydrogen gas into the ideal gas equation, the number of moles of hydrogen produced can be calculated.  The number of hydrogen moles produced can then be related to the percentages of aluminum and zinc in the sample using the balanced equations. 

 

Discussion

 

Some of the more active metals will react readily with solutions of strong acids, producing hydrogen gas and a solution of a salt of the metal.  Small amounts of hydrogen are commonly prepared by the action of hydrochloric acid on metallic zinc:

 

Zn(s) + 2 H+ (aq) ® H2(g) + Zn2+ (aq)                        (1)

 

From this equation it is clear that one mole of zinc produces one mole of hydrogen gas in this reaction.  If the hydrogen were collected under known conditions, it would be possible to calculate the mass of zinc in a pure sample by measuring the amount of hydrogen it produced on reaction with acid. 

 

Since aluminum reacts spontaneously with strong acids in a manner similar to that shown by zinc,

2 Al(s) + 6 H+(aq) ® 2 Al3+(aq) + 3 H2(g)                        (2)

 

we could find the amount of aluminum in a pure sample by measuring the amount of hydrogen produced by its reaction with an acid solution.  In this case two moles of aluminum would produce three moles of hydrogen. 

 

Since the amount of hydrogen produced by a gram of zinc is not the same as the amount produced by a gram of aluminum,

 

1 mole Zn ® 1 mole H2      therefore,        65.4 g Zn     and,          1.00 g  Zn                   (3)

                                                                 1 mole H2                            0.0153 mole H2

 


 

 

2 moles Al ® 3 moles H2   therefore,        18.0 g Al    and,           1.00 g Al                      (4)

                                                                 1 mol                            0.0556 mole H2

 

it is possible to react an alloy of zinc and aluminum of known mass with acid, determine the amount of hydrogen gas evolved, and calculate the percentages of zinc and aluminum in the alloy, using Relations 3 and 4. The object of this experiment is to make such an analysis.

 

In this experiment you will react a weighed sample of an aluminum-zinc alloy with an excess of acid and collect the hydrogen gas evolved in a bottle over water (Figure 1).  If you measure the volume, temperature, and total pressure of the gas and use the Ideal Gas Law, taking proper account of the pressure of water vapor in the system, you can calculate the number of moles of hydrogen produced by the sample:

 

            PH2V  = nH2 RT, nH2 =    PH2V                                (5)

                RT

 

The volume V and the temperature T of the hydrogen are easily obtained from the data.  (Remember that the volume of a gas is equal to the volume of the container holding it.)  The pressure exerted by the dry hydrogen PH2 requires more attention.  The total pressure P of  the gas in the bottle is, by Dalton's Law of Partial Pressures, equal to the partial pressure of the  of the hydrogen PH2 , plus the partial pressure of the water vapor PH2O:

 

                                                  P = PH2  + PH2O                                              (6)

 

The water vapor in the bottle is present with liquid water, so the gas is saturated with water vapor; the pressure of water PH2O , under these conditions is equal to the vapor pressure VPH2O  at the temperature of the experiment.  This value is constant at a given temperature and can be found in the CRC Handbook.  The pressure inside the bottle will be nearly equal to the barometric pressure Pbar , which can be read off the barometer in the lab.  Substituting these values into (6) and solving for PH2, we obtain

 

                                                       PH2 = Pbar - VPH2O                                    (7)

 

Using (5), you can now calculate the number of moles of hydrogen, nH2 , produced by your weighed sample.  You can then calculate the percentages of Al and Zn in the sample by properly applying (3) and (4) to your results.  For a sample containing gAl  grams aluminum and gZn grams of zinc, it follows that,

 

                        nH2 = (gAl  x  0.0556 mol H2)  + ( gZn  x   0.0153 mol H2)                     (8)

                                                1 gram Al                             1 gram Zn                                         

For a one gram sample, gAl and gZn represent the mass fractions of Al and Zn, that is, %Al/100 and  % Zn/100.  Therefore,

 

                             NH2  =  ( %Al  x 0.0556 ) +    (  %Zn  x  0.0153 )             (9)

                                               100                              100

where NH2 is the number of moles of H2 per 1 gram of sample.

Since it is also true that,                              

                                                                  % Zn =100 - % Al                                               (10)

Equation (9) can be written in the form

 

NH2  =  ( %Al  x  0.0556) +    (  100 - %Al  x  0.0153)                  (11)          

    100                                  100

 

We can solve Equation 11 directly for % Al if we know the number of moles of H2 evolved per gram of sample (NH2).  To save time in the laboratory and to avoid arithmetic errors, it is highly desirable to prepare in advance a graph giving NH2 as a function of % Al.  Then when NH2, has been determined in the experiment, % Al in the sample can be read directly from the graph.  Directions for preparing such a graph are given in Problem 1 in the Pre lab Questions.

 

Experimental Procedure                                              

 

 

Your instructor will demonstrate the correct setup and operation of this apparatus.

 

 

1.      Obtain a suction flask, large test tube, stopper assemblies, and a sample of Al-Zn alloy from the supply cart.  Assemble the apparatus as demonstrated by your instructor.

2.      Take a gelatin capsule and weigh it on the analytical balance to + 0.0001 g.

3.      Pour your alloy sample out on a piece of paper and add about half of it to the capsule.  If necessary, break up the turnings into smaller pieces by simply tearing them. 

4.      Cover the capsule and weigh it again.  The mass of sample should be between 0.1500 and 0.2500 g. Use care in both weighings, since the sample is small and a small weighing error will produce a large experimental error. 

5.      Put the remaining alloy back in its container.

6.      Fill the suction flask and beaker about 2/3 full of water. 

7.      Moisten the stopper on the suction flask and insert it firmly into the flask. 

8.      Open the pinch clamp and apply suction to the tubing attached to the side arm of the suction flask. 

9.      Pull water into the flask from the beaker until the water level in the flask is 4 or 5 cm below the side arm.  To apply suction, use a suction bulb or a short piece of rubber tubing attached temporarily to the tube that goes through the test tube stopper. 

10.  Close the pinch clamp to prevent siphoning.  The tubing from the beaker to the flask should be full of water, with no air bubbles.

11.  Carefully remove the tubing from the beaker and put the end on the lab bench.  As you do this, no water should leak out of the end of the tubing. 

12.  Pour the water remaining in the beaker into another beaker, letting the 400-mL beaker drain for a second or two. 

13.  Without drying it, weigh the empty beaker on a top-loading balance to + 0.1 g. Put the tubing back in this beaker.

14.  Pour 10 ml of 6 M HCl, hydrochloric acid, as measured in your graduated cylinder, into the large test tube. 

15.  Drop the gelatin capsule into the HCl solution; if it sticks to the tube, poke it down into the acid with your stirring rod.

16.  Insert the stopper firmly into the test tube and open the pinch clamp.  If a little water goes into the beaker at that point, pour that water out, letting the beaker drain for a second or two.

17.  Within 3 or 4 minutes the acid will eat through the wall of the capsule and begin to react with the alloy.  The hydrogen gas that is formed will go into the suction flask and displace water from the flask into the beaker.  The volume of water that is displaced will equal the volume of gas that is produced.

18.  As the reaction proceeds you will probably observe a dark foam, which contains particles of unreacted alloy.  The foam may carry some of the alloy up the tube.  Wiggle the tube gently to make sure that all of the alloy gets into the acid solution.  The reaction should be over within 5 to 10 minutes.  At that time the liquid solution will again be clear, the foam will be essentially gone, the capsule will be all dissolved, and there should be no unreacted alloy. 

19.  When the reaction is over, close the pinch clamp and take the tubing out of the beaker. 

20.  Weigh the beaker and the displaced water to + 0.1g.

21.  Measure the temperature of the water and the barometric pressure.

22.  Pour the acid solution into the waste crock. 

23.  Reassemble the apparatus and repeat the experiment with the remaining sample of alloy.
 

Prelaboratory Questions                                                       Experiment 16:  Gas Laws

                                               

1.  On a separate graph paper, construct a graph of NH2, vs. % Al (NH2 in the y-axis and %Al in the x axis).  To do this, refer to Equation 11 and the discussion preceding it.  Note that a plot of NH2 vs. % Al should be a straight line (why?).  To fix the position of a straight line it is necessary to locate only two points.  The most obvious way to do this is to find NH2, when % Al = 0 and when % Al = 100.  If you wish you may calculate some intermediate points (for example, NH2, when % Al = 50, or 20, or 70); all these points should lie on the same straight line.

 

2. A student obtained the following data in this experiment.  Fill in the blanks in the data and make the indicated calculations:

 

1-  Mass of gelatin capsule     0.1 168 g                     9-  Temperature, t           21 °C

 

2-  Mass of capsule plus                                             10-  Temperature, T      ______K

      alloy sample                     0.2754 g

11- Barometric pressure     746 mm Hg

3-  Mass of alloy sample,       _______g                   

12- Vapor pressure of

4-  Mass of empty beaker      141.23 g                             H2O at t (CRC)     ________mm Hg

                                                                                                           

5-  Mass of beaker plus                                             13-  Pressure of dry H2,

      displaced water                307.75 g                      PH2 (Eq. 7)     ________mm Hg =________atm

 

6-  Mass of displaced water   ________ g                

                                                                                

7-  Volume of displaced water                                                                       

(density = 1.00 g/mL)             ________ml

 

8- Volume, V, of H2 = Volume of displaced water ___________ml; ____________liters

 

Find the number of moles of H2 evolved, nH2 (Eq. 5; V in liters, PH2 in atm, T in K,

R = 0.0821 L-atm/mole K).                                                                      ___________moles H2

 

Find NH2 , the number of moles of H2 per gram of sample (nH2,/m)             ___________moles H2/g     

                                                                                     

Find the % Al in the sample from the graph prepared for Problem 1.   _____________% Al

Find the % Al in the sample by using Equation 11.                         _____________% Al

(see why graphs are helpful! J)                       

                                                                                                           

Data Sheet                                          Experiment 16:  Gas Laws

                                               

Collect all necessary data to determine the percentage aluminum in your unknown sample.  Don’t forget to include your unknown number.  Show all your calculations to your instructor and obtain the actual %Al in your unknown sample before you leave the lab.  Calculate percent error and discuss results in your report.