Diagnosing Galvanic Cell Readings That Do Not Match the Nernst Equation
Four student groups build Zn-Cu galvanic cells. Each uses a zinc strip in ZnSO4 solution, a copper strip in CuSO4 solution, and a salt bridge of 1.0 M KNO3 in agar. Group 1 uses 1.0 M solutions in both half-cells and reads 0.94 V. Group 2 uses 0.0010 M CuSO4 and 1.0 M ZnSO4 and reads 1.01 V. Group 3 uses 1.0 M solutions but its zinc strip was polished only with a paper towel and its copper strip is covered with a dark oxide film; it reads 0.78 V. Group 4 uses 1.0 M solutions and a voltmeter with a 10 MΩ input; its reading fluctuates between 1.06 and 1.09 V. Standard potentials are E°(Cu2+/Cu) = +0.34 V and E°(Zn2+/Zn) = -0.76 V. The teacher must decide which readings are consistent with the Nernst equation and which indicate a cell-construction problem.
1. Calculate the expected cell potential for Group 1 and Group 2 at 25 °C and compare with their readings.
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For the cell Zn(s) + Cu2+(aq) → Zn2+(aq) + Cu(s), E°cell = 0.34 V - (-0.76 V) = 1.10 V. The Nernst equation is E = E° - (0.0592 V / 2) log([Zn2+]/[Cu2+]) at 25 °C. Group 1 has equal concentrations, so Q = 1 and E = 1.10 V. Its reading of 0.94 V is 0.16 V below the predicted value, which is too large to explain by concentration alone. Group 2 has Q = 1.0 / 0.0010 = 1000, so log Q = 3 and E = 1.10 V - (0.0592 / 2)(3) = 1.10 - 0.0888 = 1.01 V. Its reading matches the prediction within rounding. Group 2 therefore supports the Nernst equation; Group 1 does not.
2. Group 1's reading is far below its calculated value. Identify the most likely category of error and describe one diagnostic test.
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Group 1's discrepancy is not a concentration effect because both solutions are 1.0 M. The likely category is a cell-construction or measurement problem: poor electrical contact, a salt bridge that is not making ionic contact, high internal resistance, or electrode surfaces that are not clean. A diagnostic test is to remake the cell with freshly polished zinc and copper strips, fresh solutions, and a new salt bridge, then measure again with the same voltmeter. If the reading rises toward 1.10 V, the original problem was in the cell hardware or surfaces. The teacher could also measure the potential of each half-cell against a reference or check the salt bridge for cracks and air gaps. Students should not attribute the 0.94 V reading to a lower thermodynamic driving force until these artifacts are ruled out.
3. Group 3 reports 0.78 V and concludes that the reaction is less spontaneous than predicted. Evaluate this conclusion and state what the teacher should require before accepting it.
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The conclusion is premature. A dark oxide film on copper and an improperly cleaned zinc surface can increase resistance and introduce overpotential, so the measured terminal voltage is not a clean thermodynamic cell potential. Group 3's value is far below the Nernst prediction and below Group 1's already-low value, which suggests surface or contact problems rather than a real change in E°. The teacher should require the group to polish both electrodes until shiny, use fresh solutions, confirm that the salt bridge is in contact with both solutions, and repeat the measurement. If the voltage rises toward 1.10 V, the original conclusion is invalid. If it remains low after these controls, the teacher should check the voltmeter and connections before discussing spontaneity. The distinction between thermodynamic cell potential and measured voltage under load or resistance is the key judgment.