Determination of Electron Charge Using a Wee Bit o Electrolysis Background and Theory: The purpose of this laboratory is to study and measure the electric charge of an electron. In 1832 Michael Faraday, who we will hear a lot about this semester, observed that the quantity of material undergoing oxidation/reduction during electrolysis is related to the quantity of electrical charge passing through the cell. We will use this observation to estimate the size of the electric charge. A cell for electrolysis is used that has a copper anode and a Copper (II) Sulfate (CuSO4) solution. The cathode in our case is an iron nail. A reduction reaction takes place at the cathode according to the following equation: 1) Cu 2+ + 2e- Cu Let s quickly review what this means: copper ions are extracted from the solution and, with the addition of two electrons from the power supply, they are plated to the cathode. To state this another way, for every two electrons supplied from the electric circuit, one copper atom is oxidized from the anode. From the point of view of Faraday's Law of Electrolysis: 2) 1 mole of ions + 2 moles of electrons 1 mole of atoms or 3) 63.55 g (Cu ions) + 2 (faraday/e) 1 63.55 g (Cu atoms) Thus, we can relate the mass of Cu atoms plated to the cathode to the charge that moves during the process as follows: 31.77 grams of copper are plated for each 96,487 coulombs (=6.023 x 10 23 electrons/mol x 1.602 x 10-19 coulombs/electron = 1 faraday) of electric charge. 2 1 The faraday is a somewhat archaic unit for the magnitude of the electric charge per mole of electrons. Although still used occasionally in electrochemistry, it has typically been replaced by the Coulomb, but is included here for historical purposes. 2 Pasco Scientific, Activity C29, 1999 WCUPA Physics 1 1/25/10
By measuring the change of mass, Δm, of the copper anode before and after the experiment, we can determine the mass of Cu atoms plated to the cathode. And by measuring the total amount of charge transferred, Q, it is possible to determine the size of the electron charge, e. The total charge transferred divided by the electron charge is equal to the number of electrons transferred: 4) Q e = N e Note that the number of moles of copper transferred is equal to the change of mass, Δm, divided by the molar mass of copper (M=63.55 g): 5) n moles = Δm M And the number of ions of copper transferred is equal to the number of moles transferred times Avogadro's Number NA: 6) N Cu = N A Δm M Since, according to equation 2), the number of electrons transferred is equal to twice the number of copper ions: 7) N e = 2N A Δm M By setting equations 4) and 7) equal to each other, one can rearrange the known quantities to solve for the charge of the electron. We know you want to participate and do some algebra, so we will leave that step for you!! WCUPA Physics 2 1/25/10
Procedure: PHY180 Laboratory Getting Started: 1) Ensure that the Pasco ScienceWorkshop 750 Interface is plugged in and connected to the computer via a USB cable. 2) Turn on 750 Interface (LEDs should light up). 3) On your desktop, Double-click on DataStudio then click on Create Experiment. a) If the DataStudio does not recognize the 750 interface, click on Choose Interface and select ScienceWorkshop 750. Setting up the Experiment: In this experiment, you are measuring Δm, the change in mass of the anode. Therefore, before you proceed further, you must determine the mass of your copper coil anode (to the nearest 1 mg). In order to avoid leaving deposits on the scale, use an index card underneath your anode. Zero the scale with the card first without the copper anode and then mass the anode. 3 Note the uncertainty in your measurement. Setup the experiment as shown in the figure (without the blue copper (II) sulfate solution). To suspend the nail and the copper anode in the beaker, poke two holes into an index card and feed the nail and copper wire through the holes. The nail and the copper wire can touch the side of the glass beaker, but must not touch each other. Final Preparation for Data Collection: Finally, you must setup DataStudio to provide a voltage between the nail and the copper wire and to measure the flow of charge through the solution. Set up DataStudio to drive the Power Amplifier from analog channel A. To do this, click on channel A on the picture of the 750 interface and select Power Amplifier from the drop down list. A Signal Generator window should pop-up. Set the signal generator parameters to: 1) Amplitude: 3 volts 2) Waveform: DC voltage 3 We do not want to know the weight, so we are not weighing our anode. We want to know the mass so we are massing it! WCUPA Physics 3 1/25/10
3) Be certain auto is selected so that it will send a voltage out only when the start button is pressed. 4) Click on Measurements and Sample Rate if it is not already selected and choose 10 Hz sampling. 5) Check the box to Measure Output Voltage and Measure Output Current. 6) You can X the window when you are done with the settings. You will be collecting current data over an hour. Find Graph under Displays on the bottom left of the screen and drag it onto Current, Ch A. This will show the data collected PHY180 Laboratory Once you have done this much, you are ready to kindly ask your instructor for the copper (II) sulfate solution. Place the electrodes into the solution such that they do not touch each other. Then press the Start button in Data Studio. Allow the data collection to proceed for approximately an hour. Do NOT drink the blue!! Data Analysis: Integrate the current graph using the Data Studio's ability to calculate the area under a curve. In the graph window turn on statistics by selecting Σ. Make sure Area is selected under Σ. Recall that the area under the curve is the integral of ydx. Thus, the integrated current is the charge that was transferred. In equation form, we have current (I) defined as, I = dq dt, and therefore Q = While You Wait: Idt. Graph of Current vs. Time showing integrated area. 1) Determine the expression for finding the charge of an electron (e). 2) Which variables in the expression are determined from the experiment? 3) Which variables (or constants) in the expression are already known? Write down the values including their uncertainties and make sure to cite your source. (e.g. NA = 6.02 10 23 ± 0.3% 4 ) 4 Halliday, D, R. Resnick, and J. Walker. 2008. Fundamentals of Physics (Eighth Edition). Hoboken, NJ: John Wiley & Sons. p. 508. (Note: 0.02/6.02=0.3%) WCUPA Physics 4 1/25/10
Write-up: Credits: 4) Work on the Error Analysis worksheet you downloaded from the website. Use write-up template provided at the end of this handout. PHY180 Laboratory This lab is based on a lab written by Dr. Harold Skelton of West Chester University, and Pasco Scientific's Activity C29, 1999. The current version has been updated by Dr. Kevin Aptowicz and Dr. Matthew M. Waite. WCUPA Physics 5 1/25/10
Determination of Electron Charge using Electrolysis Author: your name Coauthors: your lab partner(s) name(s) Abstract: The abstract should be concise and precise, no more than a paragraph or so. Within the abstract you are trying to answer four questions, and in doing so gain the attention of a prospective reader: (1) what is the purpose of the experiment? (2) what were the methods used? (3) what were the results obtained?, and (4) what was the conclusion of the experiment? WCUPA Physics 6 1/25/10
DATA Use a table similar to the one below to organize all the values that will be used to determined the charge of an electron. Absolute Fractional Variable Value Uncertainty Uncertainty DATA ANALYSIS Here is a minimum list of questions you should address in the data analysis section. These should be answered in the body of a paragraph, NOT as a numbered list of answers!! What is your calculated value for e including the uncertainty? Make sure to write it with the correct number of significant digits. What is the discrepancy between your value and the accepted value (cite source)? Do you think this is significant? If it is significant, discuss what you think the source of this large discrepancy is. What is the limiting factor in minimizing the uncertainty? How could you change the experiment to improve your result? REFERENCES Include any references you used in making your calculations and/or completing this laboratory experiment. APPENDIX Error Propagation Calculations [This part does not need to be typed, but can be neatly hand-written.] WCUPA Physics 7 1/25/10