9: Voltaic Cells
- Page ID
- 516593
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)1. Prerequisite Math & Theory
- Cell Potential: \(E_\text{cell} = E_\text{cathode} - E_\text{anode}\). At standard states (\(1.0\text{ M}\) ion concentrations, \(25\,^\circ\text{C}\)):
\[ E^\circ_\text{cell} = E^\circ_\text{cathode} - E^\circ_\text{anode} \]
- Spontaneous Direction: The metal species with the more positive (higher) standard reduction potential (\(E^\circ\)) spontaneously undergoes reduction and serves as the cathode.
- Concentration Cells (Nernst Equation): When both half-cells utilize the same metal electrode and electrolyte species, \(E^\circ_\text{cell} = 0\text{ V}\). The overall cell potential is driven solely by concentration differences: \[ E_\text{cell} = E^\circ_\text{cell} - \frac{0.0592\text{ V}}{n}\log Q \] where \(Q = \frac{[\text{dilute}]}{[\text{concentrated}]}\).
2. Required Technical Skills
- Connecting and zeroing Vernier Voltage Probes for low-voltage electrochemical measurements.
- Polishing metal electrodes (copper, zinc, and unknown strips) with steel wool to remove oxide layers prior to immersion.
3. Critical Safety
- Heavy metal waste (copper, zinc, and unknown metal salt solutions) must be collected in designated waste containers. Do not pour down the drain.
- To construct a semi-microscale \(\mathrm{Cu/Zn}\) voltaic cell and measure its potential (\(E_\text{cell}\)) using a voltage probe.
- To measure the cell potential of two voltaic cells constructed with unknown metal electrodes and identify the unknown metals using standard reduction potential tables.
- To construct a copper concentration cell, observe its spontaneous potential, and verify the Nernst equation model.
INTRODUCTION
In electrochemistry, a voltaic (galvanic) cell is an electrochemical system in which a spontaneous oxidation-reduction reaction generates electrical energy. A voltaic cell consists of two separate half-cells: an oxidation half-cell occurring at the anode (negative terminal) and a reduction half-cell occurring at the cathode (positive terminal). Electrical neutrality between the two solutions is maintained by a salt bridge containing an inert electrolyte such as \(\mathrm{KNO_3}\).
In Parts A and B of this experiment, you will construct semi-microscale voltaic cells in a 24-well plate using metal strips immersed in \(0.10\text{ M}\) aqueous solutions of their respective metal nitrates. You will measure the cell potential of a standard \(\mathrm{Cu/Zn}\) cell and two cells pairing copper with unknown metal electrodes (\(\text{X}\) and \(\text{Y}\)). By observing lead polarities and measured cell potentials, you will determine the reduction potentials of the unknown metals and identify them from an activity series.
In Part C, you will explore a concentration cell. In a concentration cell, both half-cells utilize identical copper electrodes and \(\mathrm{Cu^{2+}}\) ions, but at different concentrations (\(0.050\text{ M}\) vs. \(1.0\text{ M}\)). The system generates voltage as it spontaneously works to equalize \(\mathrm{Cu^{2+}}\) concentrations across the half-cells.
Concentration cells demonstrate that concentration gradients can drive spontaneous current flow:
- Drive Mechanism: Thermodynamics favors equalizing concentrations. Electrons flow from the dilute half-cell (anode, where \(\mathrm{Cu(s) \rightarrow Cu^{2+}(aq) + 2e^-}\)) to the concentrated half-cell (cathode, where \(\mathrm{Cu^{2+}(aq) + 2e^- \rightarrow Cu(s)}\)).
- Nernst Prediction: Because \(E^\circ_\text{cell} = 0\text{ V}\), the theoretical potential is given by \(E_\text{cell} = -\frac{0.0592}{2}\log\left(\frac{0.050}{1.0}\right) \approx +0.038\text{ V}\).
Cell Potential:
\[ E_\text{cell} = E_\text{cathode} - E_\text{anode} \]
Standard Cell Potential:
\[ E^\circ_\text{cell} = E^\circ_\text{cathode} - E^\circ_\text{anode} \]
Nernst Equation at \(25\,^\circ\text{C}\) (\(298.15\text{ K}\)):
\[ E_\text{cell} = E^\circ_\text{cell} - \frac{0.0592\text{ V}}{n}\log Q \]
- 9.1: Voltaic Cells - Experiment
- This page details safety measures, necessary equipment, and chemicals for experiments with voltaic cells. It outlines procedures to determine the standard electrode potential of a Cu/Zn cell and compares two unknown cells to copper, utilizing a logic matrix to rank the unknown metals by reducing strength. Additionally, it provides steps for preparing and testing a copper concentration cell and highlights proper chemical disposal practices.
- 9.2: Voltaic Cells - Pre-lab
- This page teaches students how to calculate the theoretical standard cell potential for a galvanic cell with zinc and copper electrodes. It includes steps for writing a balanced equation, completing half-reaction tables with standard reduction potentials, and applying the Nernst equation with varying ion concentrations. A logic check helps assess the reduction potential of an unknown metal compared to copper, illustrating practical uses of standard reduction potentials.
- 9.3: Voltaic Cells - Data and Report
- This page details a laboratory exercise in electrochemistry, focusing on copper/zinc concentration cells and analyzing unknown metals. Participants measure cell potentials, identify unknowns using standard reduction potentials, and compare measured averages to theoretical values calculated via the Nernst equation. Post-lab questions prompt reflection on accuracy through percent error and percent difference calculations, reinforcing the importance of validating experimental models.