In the Classroom edited by
JCE DigiDemos: Tested Demonstrations
Ed Vitz Kutztown University Kutztown, PA 19530
A Fast Coulometric Estimation of Avogadro’s Number submitted by:
Nicholas C. Thomas Department of Chemistry, Auburn University at Montgomery, Montgomery, AL 36124-4023;
[email protected] checked by:
Carole Bennett Sickles High School, 7950 Gunn Highway, Tampa, FL 33604-1112
Many methods can be used to determine Avogadro’s number. These include X-ray diffraction, radioactive decay, electrochemical studies, and surface film methods (1). While these methods may be accurate, they are often not convenient to reproduce as classroom demonstrations. For instance, an electrochemical method using a Hoffman apparatus requires at least 50 minutes to collect data (2). Once set up, the procedure presented below yields Avogadro’s number in just a few minutes and uses materials available in any high school or college. Despite the simplicity of this demonstration, values of around 6.0 × 1023 can consistently be obtained with an error generally less than 5%. Materials The following materials are needed for the demonstration: 1 L beaker; 500 mL of 0.5 M sulfuric acid; a buret; an ammeter; a 6 V lantern battery; two pieces of insulated copper wire (heavy gauge, each about 15 in. long); two wires with alligator clips on each end; a few drops of food coloring; and a small piece of white cardboard. Procedure Place the acid and a few drops of food coloring in the beaker and stir to mix. Fill the buret to the top with acid and, with hands protected with rubber gloves, hold a finger over the top of the buret, invert it, and quickly immerse the top of the buret in the beaker of acid. A small quantity of air in the buret is okay.1 Clamp the buret to a stand so that the end of the buret is about an inch below the surface of the acid. Tape a piece of white cardboard behind the buret so the level of colored acid is clearly visible. Place one of the pieces of insulated wire, with about an inch of exposed copper, into the acid and up into the inverted buret. Make sure all the exposed copper wire is in the buret so that all the evolved hydrogen will be collected. This copper “electrode” will be the cathode and must be connected to the negative battery terminal. Place the other piece of insulated wire in the acid solution in the beaker with about an inch of exposed wire (the anode) completely immersed. Both wires can be anchored to the beaker with large paperclips or clothes pegs. Slowly open the buret tap so that the level of acid drops to the 50.00 mL graduation mark. Using a thick black felt tipped pen, mark this level on the cardboard so the level is easily seen. All the above steps can be performed before class. To begin the demonstration connect the ammeter and battery in series with the electrolysis apparatus and collect the www.JCE.DivCHED.org
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evolved hydrogen for five minutes. Mark the new level of acid on the cardboard so that the volume of evolved hydrogen is clearly visible. During this time the theory and calculations may be presented. CAUTION: There is an explosive mixture of hydrogen and air in the buret—no flames or sparks! Discussion Hydrogen is generated at the cathode (2H+ + 2e− → H2) but no oxygen is seen at the reactive copper anode (Cu → Cu2+ + 2e−). Calculations were done as described previously (2) with typical results as follows. By using the gas equation pV = nRT, the amount of hydrogen gas (in mol) that is produced may be calculated: n =
(0.970 atm) (0.00965 L) L atm 0.0821 (296 K) mol K
= 3.85 × 10 −4 mol H2
where R = 0.0821 (L atm)兾(mol K) and the pressure (0.970 atm) has been corrected for water vapor pressure at a temperature of 296 Kelvin for 0.00965 liters of hydrogen formed. Since two moles of electrons are required to generate each mole of hydrogen, 7.70 × 104 moles of electrons are transferred. To obtain the number of electrons transferred, the current (0.240 A) is multiplied by the time (300.0 s) and divided by the charge on one electron (1.60 × 1019 C兾e−):
(0.240 C/s)(300.0 s) no. e − 20 − transfered = 1.60 × 10 −19 C/e − = 4.50 × 10 e Using simple ratios, Avogadro’s number—the number of electrons produced from 1 mole of hydrogen—is determined. no. e − per mol =
4.50 × 10 20 e− 7.70 × 10
−4
mol e
−
= 5.84 × 10 23 e− /mol
Note 1. Alternatively, the buret can filled by attaching a rubber hose to the buret tip and applying a vacuum with a water aspirator to draw up the acid into the buret.
Literature Cited 1. Kolb, Doris. J. Chem. Educ. 1978, 55, 728–732. 2. Szell, Thomas; Dennis, David; Jouas, Jean-Pierre; Wong, Mabel. J. Chem. Educ. 1980, 57, 735–736.
Vol. 84 No. 10 October 2007
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Journal of Chemical Education
1667
