Introduction:

The Kinetic Molecular Model provides a simple, qualitative method for estimating what will happen to a gas when it is heated, cooled, compressed or allowed to expand.  However, if we want to calculate the exact results of these changes, we must combine Boyle's, Charles', and Avogadro's individual gas laws together into one unified law of ideal gas behavior:

In this equation, P is the pressure in atmospheres, V is the volume in liters, n is the number of mols of gas, T is the absolute temperature in Kelvins, and R is the ideal gas constant (0.082 L•atm/mol•K).

The ideal gas law is based on the assumption that the molecules experience no intermolecular forces and that the molecules themselves occupy no volume. These assumptions are valid at low pressure and high temperature. Under these conditions, the molecules are too far apart to "feel" attractive forces exerted by other molecules. Furthermore, since the molecules are far apart, the volume occupied by the molecules themselves is negligible compared to the total volume occupied by the gas.

In reality, intermolecular forces do exist and molecules do occupy space. The extent to which these factors cause a gas to deviate from the ideal gas law at a particular temperature and pressure will depend upon its molecular structure.  These deviations become severe when a gas is subjected to high pressure and/or low temperatures.  Under these conditions, a gas begins to take on the characteristics of a liquid and the ideal gas law no longer applies.

Purpose:

The purpose of this experiment is two-fold:  first, to test your understanding of the Ideal Gas Law and second, to ascertain the level of laboratory skills you have developed over the semester.   To accomplish this, you will be generating carbon dioxide gas under controlled conditions.  With the proper technique, and a little algebra, you should be able to parley your observations and data into four very important results: 

  1. The molecular weight of carbon dioxide (CO2).
  2. The Ideal Gas Law constant 'R'. 
  3. The molar volume of carbon dioxide (CO2) at STP.
  4. The amount of sodium bicarbonate (NaHCO3) in an Alka-Seltzer tablet. 

At first glance it would appear that these are four very different experiments.  However, all four values can easily be determined from the reaction of an Alka-Seltzer tablet with hydrochloric acid.  One of the active ingredients is sodium bicarbonate which readily reacts with hydrochloric acid to produce carbon dioxide:

NaHCO3  +  HCl    NaCl  +  CO2  +  H2O

(of course, you remember this reaction from the Mole Concept lab earlier in the semester...Don't you?!?).

So by simply  measuring the amount of carbon dioxide generated from a given tablet and knowing the temperature and atmospheric pressure in the room, all of these results can be determined.  Now that is what I call...Fun with the Ideal Gas Law!!

Method:  Although you are trying to achieve four goals, the experiment itself is elegant in its simplicity.  It is loosely based on the Dumas method for determining the molecular weight of low boiling liquids (Section 12.10 of your Saunder's textbook).  However, instead of a liquid, you will be determining the molecular weight (molar mass) of a gas. 

Careful inspection of an Alka-Seltzer package reveals that each tablet contains three active ingredients:  acetylsalicyclic acid (aspirin - remember synthesizing that earlier this semester?), citric acid (a weak, triprotic acid), and sodium bicarbonate.  When the tablet is dissolved in water, some of the sodium bicarbonate reacts with the acetylsalicyclic acid to produce sodium acetylsalicylate (which is more water soluble than aspirin and so is absorbed by the blood stream more quickly).  The sodium bicarbonate also reacts with the citric acid to produce sodium citrate and the trade mark bubbles of carbon dioxide.  Even after both of these reactions are complete, there is still excess sodium bicarbonate remaining which as a weak base can react with excess stomach acid (hydrochloric acid) to relieve heart burn, etc.

To achieve all the goals of this experiment, you will first grind an Alka-Seltzer tablet to fine powder.  A portion of this power will then be placed into an empty gelatin capsule:


The capsule is then placed in a test tube containing hydrochloric acid.  The test tube/HCl/capsule is then placed in a sealed plastic wash bottle containing distilled water.  It will take a couple of minutes for the HCl to dissolve the capsule.  Once it does the hydrochloric acid will react with the sodium bicarbonate.  The carbon dioxide produced will build up pressure in the bottle which will force water out of the bottle.  The amount of carbon dioxide produced can then be calculated from the volume of water displaced:
  
It is important to use hydrochloric acid because it is a strong acid and will completely react with all of the sodium bicarbonate before it can react with the aspirin or the citric acid (a weak acid).

OK, the first task is to determine the molecular weight of carbon dioxide (yeah, yeah, I know its 44g/mol, but what does YOUR data say?).  Lets start with the Ideal Gas Law equation and solve for mols:



Remember that the number of mols of any substance can also be calculated by dividing the weight (in grams) of a compound by its molecular weight (MW):


Since both expressions are equal to n, they must be equal to each other:


This can be rearranged to give us the molecular weight of the carbon dioxide as:


So to calculate the molecular weight of carbon dioxide, we need to know the weight of carbon dioxide present, its absolute temperature, its partial pressure, and its volume.  You will be measuring all of these variables during the lab.  For the calculation of carbon dioxide's MW, we will assume that R is a constant (0.082 L•atm/mol•K).

All right, one down, three to go.  To calculate the MW of carbon dioxide above, we assumed that the Ideal Gas Law constant, R, had a value of 0.082 L•atm/mol•K.  Now we will assume that the MW of carbon dioxide is 44g/mol, and use this to calculate R.   Again, starting with the Ideal Gas Law equation, we can simply isolate R:


So calculate the value of R, we need to know the partial pressure of carbon dioxide, its absolute temperature, and its volume.  Again, you know all of these.  For this calculation, we will assume that the molecular weight of carbon dioxide is 44g/mol, which will allow us to calculate the mols needed for this calculation.  The only major hurtle is that 'partial pressure' thing.  The carbon dioxide gas produced in the reaction displaces water into the beaker. After the gas generation is complete, the pressure inside the bottle is equal to the atmospheric pressure.   At this point, the total pressure inside the bottle, according to Dalton's Law of Partial Pressures, is equal to the sum of the partial pressures of carbon dioxide (PCO2) and water vapor (PH2O):


You can easily read the atmospheric, Patm, from the barometer in the lab (How to read an Eco-Celli barometer), but we need to know PCO2 to calculate R.  It turns out that there are tables that document the vapor pressure of water at various temperatures (Vapor Pressure Table for Water).  So, simply subtract the partial pressure of water vapor from the atmospheric pressure measured by the barometer and you have the partial pressure of carbon dioxide.  Use that as the pressure, and you can calculate RQ.E.D.

Two down, two to go.  Now we would like to know the molar volume, V*, of carbon dioxide at STP (Standard Temperature and Pressure):



Of course you remember that the conditions at STP are zero degree Celsius and one atmosphere of pressure.  Since you did not run this experiment at those conditions, you will have to use the combined gas law to figure out what the volume would have been:



If carbon dioxide is indeed an ideal gas (and you did the lab correctly), the molar volume at STP should be 22.414 l/mol. 

Three down, one to go!  Now we want to know what percent of that Alka-Seltzer tablet was sodium bicarbonate.  Since we know how much carbon dioxide was produced, we can convert that to grams of sodium bicarbonate using the balanced chemical equation for this reaction (Grams to Mols to Mols to Grams....sound familiar).  Now simply divide the grams of sodium bicarbonate, by the total mass of the Alka-Seltzer used in each reaction and you will have the percent composition.

What did I say....Kinder spiel!

Procedure:

Please read the following procedure carefully before coming to lab.  This experiment is technique intensive.  None of the individual steps are difficult, however, if they are not performed in the proper order, spurious results will be obtained.  As always, measure all temperatures to 0.1C and all masses to 0.001g.

  1. Carefully clean and dry a 150 mL beaker, a 250 mL beaker, and a large 155mm test tube.
  2. Remove two Alka-Seltzer tablet from their hermetically sealed packet and weight them.
  3. Use a clean (use paper towels only, NO water) mortar and pestle to grind the tablets into a fine power.
  4. Accurately weigh an empty gelatin capsule.  Note:  make sure your hands are dry and that you close the bottle containing the capsules IMMEDIATELY!  Gelatin starts dissolving when it comes in contact with moisture.
  5. Take the capsule apart and use your scoopula to fill the larger portion with your powdered Alka-Seltzer.
  6. Put the two parts of the capsule back together, carefully blow off any power than may be sticking to the outside and reweigh.
  7. Add a magnetic stir bar to your test tube and place it upright in your 150 mL beaker.  Use a repipetter to add 10.0 mL of 6M HCl to the test test.
  8. Weigh the beaker, test tube, stir bar and HCl.
  9. Fill your water bottle to about half an inch below the 'full line' with distilled water and place it on the magnetic stirrer motor.
  10. Weigh your clean, dry 250 mL beaker.
  11. Place it on a your iron ring with the wire gauze,  and position it so it can catch all of the water from the water bottle.
  12. Remove the top from your water bottle and place the test tube/stir bar/HCl in the bottle, it should float.
  13. Quickly drop the Alka-Seltzer filled gelatin capsule into the test tube and seal the water bottle.  Be sure that the top is on tight or some of the carbon dioxide will escape.  Make sure the spout of the water bottle is pointed into the 250 mL beaker.
  14. Now adjust the magnetic stirrer motor to agitate the capsule and HCl.  It may take a minute or two for the capsule to dissolve and the reaction to begin.
  15. As the reaction proceeds you should see a 'foam' produced.  At the same time, water will be displaced from the water bottle into the 250 mL beaker.
  16. Keep adjusting the rate of the magnetic stirrer up and down for about 10 minutes or until all of the 'foam' has disappeared and no more water is being generated.
  17. After the reaction is complete, weigh the 250 mL beaker.  By difference, you now have the mass of water generated. 
  18. Open the water bottle and carefully remove the test tube/stirrer/HCl.  Use a paper towel to wipe off any water from the outside of the test tube.
  19. Place the test tube upright in the same 150 mL beaker and reweigh.  By difference, you now have the mass of CO2 generated.
  20. Record the temperature of the water in the bottle (to 0.1C).  You can use a C.R.C. or this Table of Water Density to find the density of water at this temperature.  You will use this to convert the grams of water you obtained in Step #19 into mL.  This is the volume of CO2 generated. 
  21. Record the barometric pressure in the lab (How to read an Eco-Celli barometer).
  22. Clean the test tube thoroughly to remove any remnants of the gelatin capsule.  Rinse with distilled water and thoroughly dry with paper towels.
  23. Repeat Step #4-22 until you have at least three GOOD trials.  You can perform a simple calculation to determine if a given trial is 'good' or not.  Divide the amount of water generated by the mass of CO2 generated.  This value should be in the range of 500-600 and should not vary by more than 10-20 units from trial to trial.  If it does, you have made some mistakes and will have to run additional trial(s).
Calculations:

For EACH trial, calculate the following from your data (show all calculations):

Conclusion:
(Updated 9/13/13 by C.R. Snelling)