Faraday's Electrolysis lab report

1. Title and aim

Faraday's Law of Electrolysis: Electrochemical Equivalent of Copper and the Faraday Constant. To verify Faraday's first law of electrolysis by measuring the mass of copper deposited on the cathode of a copper voltameter as a function of total electric charge, determine the electrochemical equivalent of copper (Z) and the Faraday constant (F), and estimate Avogadro's number.

2. Abstract

Five observations were generated from the ideal teaching model over the settings listed below. A straight-line fit gave an estimate of electrochemical equivalent of copper of 0.3293 mg C⁻¹, differing by 0.001% from the model value. The reported scatter comes from scale rounding and any stated model approximation, not measured laboratory noise.

3. Apparatus and fixed settings

• Copper Voltameter Electrolytic Cell: Provides a heavy-walled glass electrolytic vessel with an insulating crossbar supporting two outer electrolytic copper anode plates and a central removable cathode plate immersed in acidified copper sulfate electrolyte solution.
• Four-Decimal Analytical Chemical Balance: Measures the mass of the clean, dry copper cathode plate before and after electrolysis with 0.0001 g (0.1 mg) resolution and high repeatability.
• Regulated DC Power Supply and Sliding Rheostat: Provides an adjustable, filtered direct-current source (0–30 V, 0–3 A) paired with a heavy wirewound rheostat to maintain a strictly constant current (I = 1.000 A) throughout each deposition trial.
• Precision Digital DC Ammeter: Measures and monitors the electrolysis current with 0.001 A resolution (accuracy ±0.2%) to verify constant charge delivery rate.
• Digital Laboratory Chronometer / Timer: Times the duration of electrolysis with 0.01 s precision, enabling exact computation of the total electrical charge Q = I · t.
• Cathode Washing and Desiccating Station: Supplies distilled water wash bottles, high-purity ethanol rinsing baths, and a warm-air desiccator to rinse and dry the deposited copper cathode without surface oxidation prior to weighing.
• Electrolyte composition: 150 g CuSO₄ · 5H₂O, 50 g H₂SO₄, 50 ml ethanol per liter distilled water
• Atomic weight of copper: M = 63.546 g/mol; valence of copper ions: n = 2 (Cu²⁺)
• Reference electrochemical equivalent: Z_ref = 0.00032930 g/C = 0.32930 mg/C
• Theoretical Faraday constant: F = 96485.3 C/mol
• Electrolysis operating current: I = 1.000 A (regulated within ±0.002 A)
• Current density: 15.0 mA/cm² (within optimal 10–20 mA/cm² range for firm adherent deposit)

4. Theory and graph choice

Faraday's laws of electrolysis establish the fundamental quantitative bridge between electrical charge and chemical transformation. In a copper voltameter, passing direct current through an acidified copper sulfate solution causes cupric ions (Cu²⁺) to migrate toward the negative cathode, where each ion captures two electrons to form neutral metallic copper. According to Faraday's first law, the mass of copper deposited is directly proportional to the total electric charge: m = Z · Q = Z · I · t. By measuring the mass gain of a copper cathode across six distinct charge intervals and applying linear regression, students determine the electrochemical equivalent of copper (Z), calculate the Faraday constant (F = M / 2Z), and estimate Avogadro's number.

The calculation fits y = mx + b in SI units. The graph may display scaled axes for readability; those display factors are removed before calculating the physical result. The gradient has units g C⁻¹.

5. Method

1. Clean the copper cathode plate thoroughly using fine emery cloth to remove any oxide film, rinse in distilled water, dip in pure ethanol, and dry gently in a warm-air stream. Once cooled to room temperature, weigh the dry cathode plate on the four-decimal analytical balance and record its initial tare mass m₀ to the nearest 0.0001 g.
2. Connect the circuit in series: DC power supply positive terminal to the voltameter anode plates, central cathode terminal to the digital ammeter, and ammeter through the rheostat and knife switch back to the negative terminal. Insert a dummy test plate, close the switch, adjust the rheostat until the current reads exactly I = 1.000 A, then open the switch and replace the dummy with the weighed cathode.
3. Simultaneously close the knife switch and start the digital chronometer. Monitor the ammeter continuously, making micro-adjustments to the rheostat if needed to maintain current at precisely 1.000 A. Run the electrolysis for an initial duration of 10.0 minutes (t = 600 s, delivering charge Q = 600 C), then open the knife switch and stop the timer simultaneously.
4. Carefully remove the cathode by its stem, handling it only by the dry upper clamp edge. Gently rinse it in a gentle stream of distilled water, immerse in ethanol to displace residual water, and dry in a desiccated warm-air stream for 3 minutes. Allow it to reach thermal equilibrium, weigh on the analytical balance, and record final mass m₁.
5. Repeat the electrolysis procedure for cumulative durations of 20.0 min (1200 C), 30.0 min (1800 C), 40.0 min (2400 C), 50.0 min (3000 C), and 60.0 min (3600 C), cleaning, drying, and re-weighing the cathode after each run to record the net deposited copper mass m = m₁ − m₀.
6. Tabulate the total charge Q (in Coulombs) on the horizontal axis and the deposited copper mass m (in grams) on the vertical axis. Compute ordinary least-squares regression to determine slope Z and intercept b. Calculate the Faraday constant as F = M / (2Z) and Avogadro's number as N_A = F / e.

6. Observations and calculation table

All observations use fixed model settings. Values are rounded only at the instrument reading stage; further calculations use full precision. Repeated physical trials are not claimed.

Download the sample observations (CSV) ↓

7. Worked calculation for one observation

8. Graph, gradient and final calculation

Dots show the sample observations. The line is the ordinary least-squares fit.

9. Uncertainty and comparison

Percentage difference = |estimate − model value| / |model value| × 100 = 0.0014%. Percentage difference is not experimental uncertainty.

For n = 5 observations, Σresidual² = 4.1905e-09; s² = Σresidual²/(n − 2). Gradient standard error = √[s²/Σ(x − x̄)²] = 1.2895e-08. Intercept standard error = √[s²(1/n + x̄²/Σ(x − x̄)²)] = 3.0132e-05.

Propagating only the relevant fit coefficient gives a fit-only standard error of 1.2895e-05 mg C⁻¹. This is a one-standard-error quantity under the regression assumptions. Deterministic rounded model data do not supply a complete physical uncertainty budget.

Atmospheric surface oxidation of the freshly deposited microcrystalline copper during warm-air drying (cuprous oxide Cu₂O formation adding up to +0.2% mass error, mitigated by rapid ethanol rinsing and desiccated drying), mechanical loss of fragile copper dendrites during water washing (minimized by maintaining current density strictly between 10 and 20 mA/cm² to ensure a smooth, coherent adherent deposit), analytical balance zero-point drift and tare buoyancy fluctuations (±0.1 mg balance sensitivity), residual copper sulfate electrolyte salt entrapment in porous deposits, power supply current drift during timed runs (regulated continuously within ±0.002 A), and chronometer switching latency (±0.2 s over 600 s interval, ~0.03%) govern the experimental error budget. Ordinary least-squares regression of deposited mass m against electric charge Q averages out balance quantization and washing variations, with the slope isolating the pure electrochemical equivalent Z and the vertical intercept isolating any baseline tare or oxidation offset.

10. Result and discussion

The observations follow the stated model relationship. Check whether the intercept and residual pattern suggest a systematic offset or a missing approximation. Agreement with the model does not independently verify its input constants.

11. Precautions and limitations

• Clean the cathode plate thoroughly with fine emery paper before the initial weighing to ensure an active, oxide-free copper surface.
• Regulate the rheostat continuously to maintain the current strictly constant at 1.000 A throughout each timed interval.
• Handle the cathode strictly by its dry upper clamping stem; never touch the active deposition surface with fingers.
• Rinse the freshly deposited cathode in distilled water, then dip in alcohol and dry with warm air to prevent oxidation into Cu₂O.
• Ensure the current density remains within 10 to 20 mA/cm² to avoid hydrogen co-evolution and powdery non-adherent deposits.

Calculations assume 100% current efficiency with zero hydrogen gas co-evolution, negligible cuprous ion (Cu⁺) intermediate formation, and ideal analytical balance precision without atmospheric oxidation. Real voltameter deposits can suffer mass loss if spongy dendrites flake off during washing or mass gain if residual sulfate salts are incompletely rinsed or if high-temperature drying oxidizes copper into Cu₂O.

12. Conclusion

The worked example illustrates how to obtain electrochemical equivalent of copper from measurements, graph variables and a fitted coefficient. The estimate is 0.3293 mg C⁻¹. A real experiment must additionally evaluate the apparatus-specific uncertainties and corrections described above.