2: Charge and Mass of an Electron (Experiment)
- Page ID
- 416880
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Hazard Overview
Chemical Hazards
- Sulfuric acid - corrosive
- Acetone - flammable
- Copper sulfate - environmental hazard
Mechanical Hazards
- Electrolysis setup - electrical hazard
PPE
- 100% cotton lab coat
- Splash goggles
- Nitrile gloves
Dispensary Provided Items
In the Fume Hood
- 1M sulfuric acid
- Acetone
- 1M copper sulfate in 0.8 sulfuric acid
- DI water
- Wash beakers
In the Lab
- The electroplating apparatus will be set up at your lab station
- Copper screens x2
- Tweezers
Introduction
In 1897, J. J. Thomson performed some pioneering experiments on cathode rays, which yielded the first measurement of a physical constant for the electron. He showed that cathode rays were composed of a stream of negatively charged particles, later called electrons, which were deflected by electric and magnetic fields. From his studies, he obtained the charge-to-mass ratio for the electron, which has a currently accepted value of \( {e/m} = 1.7588196 \times {10^{11}} {C/kg} \). Since Thomson's experiment could only give the ratio, a separate experiment was necessary to determine either e or m to have their individual values. Twelve years later, R. A. Millikan succeeded in measuring the charge of the electron with his famous oil drop experiment. The experiment you will perform will also yield a value for the charge of the electron. Given its charge, you can then also calculate the mass of the electron from the accepted value for \( e/m \).
The technique that you will use to determine the electron's charge is based on the electrolysis of an aqueous solution of copper sulfate, \( \ce{CuSO4} \). This solution contains the ions \( \ce{Cu^{2+}(aq)} \) and \( \ce{SO4^{2-} (aq)} \). Elemental copper, \( \ce{Cu} \), can be deposited from this solution onto an electrode, a process called electroplating, by supplying two electrons per \( \ce{Cu^2+} \) ion. The electrons can be supplied by a battery or, as in the present experiment, by a power supply. By measuring the amount of \( \ce{Cu} \) deposited and the total electric charge passed into the solution, the charge per electron can be calculated.
The amount of \( \ce{Cu} \) deposited is determined by weighing the electrode before and after the plating. The total electrical charge, or the number of coulombs passed during the plating, depends on the current and the amount of time it is running. One coulomb is defined as the quantity of charge that crosses in one second a section of a conductor in which there is a constant current of one amp.
\[ Q = I \times t \]
Where \( I \) is the current and is constant, \( Q \) is the total charge in coulombs, and \( t \) is the time during which the current is flowing. If the current is not constant, a measurement of the number of coulombs can be calculated in LabQuest by integrating the current over time. Either method is acceptable for this experiment.
A schematic of an apparatus for the electrolysis of copper is shown in Figure \(\PageIndex{1}\). Two copper-screen electrodes are partially immersed in an acidic electroplating solution containing \( \ce{CuSO4} \) and connected to a power supply. The external power supply produces a constant current to flow through the cell. The current is carried in the external circuit (wires) by the movement of electrons and in the solution by the movement of ions. Note that the movement of positively charged cations in one direction in the solution is equivalent electrically to the movement of negatively charged electrons in the opposite direction in the wires.
Copper cations in the solution migrate to the negative electrode, where they are reduced and deposited as elemental copper, according to the half-reaction:
\[ \ce{Cu^{2+}(aq) + 2e^- -> Cu(s)} \]
The electrode at which the reduction occurs is called the cathode.1 the other electrode, the anode, copper from the electrode is oxidized and goes into solution according to the half-reaction:
\[ \ce{Cu(s) -> Cu^2+(aq) + 2e^-} \]
Ideally, the anode loses mass, and the cathode gains an equal mass, as copper is transferred from the anode into the solution and from the solution to the cathode. However, complicating reactions occur at the anode. You should therefore report the mass gain at the cathode.
Although you will learn more about the requirements of the power supply in a later quarter when you study electrochemistry and thermodynamics, some qualitative comments can be made now. Sufficient voltage must be applied for current to flow through the cell (the electrodes and the solution), namely to overcome the electrical resistance of the cell and any energy barrier for the oxidation/reduction to occur. Once this voltage is exceeded, the current will rise linearly with the applied voltage. Since the current measures the flow of electrons in the connecting wires and of ions in the solution, the rate at which copper is deposited depends on the current. In your experiment, the current stays at a constant and high enough value for the deposition to occur in a reasonable time. This occurs since the concentrations of \( \ce{CuSO4} \) and \( \ce{H2SO4} \) in the solution are large and constant and the electrodes at a fixed separation, so that the resistance of the cell is small and constant. Hence, so long as the power supply delivers a fixed voltage, the current also remains fixed.
Operation of Lab Equipment
For this lab, you will be using the Logger Pro software coupled with a current probe in line with the electrodes. This will allow you to monitor the current versus time for your
experiment.
Experimental Procedure
- Begin by selecting 2 copper screen electrodes from the lab supplies and cleaning them with the following procedure in the fume hoods at the back of the lab:
- Clean your 2 copper screens by using tweezers to place them in the dish containing 1M \( \ce{H2SO4} \) for 2-3 minutes.
- Remove the screens with the tweezers, and dip it in the deionized water dish then swirl a few times.
- Do a final rinse with deionized water under the faucet. Pat dry with paper towels.
- Use the tweezers to swirl the screens in the acetone-containing beaker to remove excess water.
- Once the copper screens have air-dried, they are ready to be weighed.
- Weigh each of your electrodes to the nearest 0.1 mg (0.0001 g) using the analytical balances found at the front of the lab. Be sure to keep track of which electrode is which.
- Fill a 250 mL beaker with about 100 mL of aqueous electroplating solution (it doesn't need to be exact).
- Check your electroplating setup and verify that your lab quest is connected to the PC through the USB.
- Connect your electrodes to the alligator clips hanging above the lab jack.
- Place the beaker with the electroplating solution below the electrodes, and raise it using the lab jack so that the electrodes are about 2/3 covered by the solution. Make sure they don't touch each other or the beaker.
- Launch the Logger Pro software on the desktop of the lab computer. In the Experiment dropdown tab, select Data Collection and set parameters as follows: mode = time-based, 1 sample/second, and the data collection duration to 1800 seconds.
- The power supply should already be on. Plug the wire into the terminal while you start data collection on logger pro. This is a source of uncertainty in the experiment, so try and do these 2 things together as closely as possible.
- The current on the power supply should register as about 0.4 Amps. Adjust it to make it match.
- Keep an eye on the amp measurement on Logger Pro. If it drops, swirl your beaker to remove the bubbles that have built up on the screens.
- After 30 minutes, stop data collection, unplug the wire from the terminal, but leave the power supply on.
- Use the integration feature of the Logger Pro software to calculate the total charge \( Q \) that was used to plate the electrode. See Equation \(\PageIndex{1}\).
- Lower the lab jack, remove the screens, and rinse them with deionized water and acetone before weighing them again to 0.1 mg.
- Repeat the experiment two more times. You don't need to run the full 30 minutes, but ensure that you deposit at least 0.1 g of copper onto the screen. You can estimate the amount of copper deposited per minute from the results of your first trial. Be sure to switch which screen is which in between experiments so that you don't completely use up the copper from one of the copper screens.
Lab Report
Be sure to calculate the following for your lab report:
- Using Avogadro's number, the mass of copper deposited, calculate the total number of electrons transferred. Use the stoichiometry from Equation \(\PageIndex{2}\) to convert moles of \( \ce{Cu^2+} \) to moles of electrons.
- Calculate the charge of 1 electron using the total number of electrons and the total charge (\( Q \)).
- Use the known mass-to-charge ratio from J.J. Thompson's experiment and your measured charge of an electron to calculate the mass of a single electron.
- Calculate the average charge and mass of an electron from your three runs and their 95% confidence limits.
Also, include the answers to the following questions in your lab report.
- Why was it not possible to determine the charge of the electron by this method at the time when Thomson was doing his experiment?
- A constant current of 0.800 A was used to deposit copper at the cathode of a cell. Calculate the grams of \( \ce{Cu} \) deposited in 15.2 minutes.
- If the time and current are each uncertain by 1.0% and the mass of copper is uncertain by 0.10%, what is the uncertainty in the calculated electron charge?
Data Sheet
| Run 1 | Run 2 | Run 3 | |
| Mass of \( \ce{Cu} \) Deposited (g) | |||
| Average Current (amp) | |||
| Time (second) | |||
| Total charge delivered (C) | |||
| Mass of Electron (kg) |
| Average Charge of Electron (coulombs) | |
| Standard Deviation | |
| 95% Confidence Limits | |
| Average Mass of Electron (kg) | |
| Standard Deviation | |
| 95% Confidence Limits |