Results and calculations

Purpose

The purpose of this lab was to construct various galvanic cells and corresponding ionic solutions and through known relations measure and/or calculate previously unknown values such as electric cell potential, electrolyte concentrations or secondary reaction constants.

Theory

A galvanic cell is basically the exchange of electrons between two half-cells, consisting of elements with different reduction potentials and their corresponding ionic solutions. By knowing these reduction potentials and concentrations of the corresponding electrolyte solutions we can calculate the reaction constants through the Nernst equation:

E = Cell voltage (V)

E⁰ = Reduction potential in standard conditions (V)

R = The gas constant; 8.314 j/mol*K)

T = Temperature (K), here assumed to be 298 K

n = Number of electrons involved in the balanced redox-reaction

F = Faradys constant, the charge of one mole electrons (96485 C)

Q = Reaction ratio

The reaction with highest E₀ becomes the positive pole in the cell since it has a higher ability of gaining electrons.

Procedure

The lab was divided into five separate parts, A-E. Each of these consisted in creating a galvanic cell by putting different pieces of metal in beakers with ionic solutions and connecting these through cords to a multimeter. The beakers were connected through a piece of cloth, soaked with electrolyte solution (NH₄⁺, NO₃^-), closing the circuit. Further details for each part will be described below.

Results and calculations

Part A: Daniell element, Copper-Zinc.

Two half-cells were made. The negative pole consisted of Zn(s) / Zn²⁺(aq) and the positive pole was made of Cu(s) / Cu²⁺(aq). The ionic solutions were prepared as follows:

The appropriate amount of two salts was calculated. These were then diluted in water whereon the solutions were put in separate beakers.

n = m/M, n = cV => m = cVM

Desired concentration, c = 0.01 M

Volume, V = 0.025 dm³

Molar mass, M (ZnSO₄.7H₂O) = 287 g/mol

Molar mass, M (CuSO₄.5H₂O) = 250 g/mol

Used mass, m (ZnSO₄.7H₂O) = 0.01 mol/dm³ * 0.025 dm³ * 287 g/mol = 0.0718 g

Used mass, m (CuSO₄.5H₂O) = 0.01 mol/dm³ * 0.025 dm³ * 250 g/mol = 0.0625 g

A galvanic element with these solutions and solid copper and zinc as poles was created. The cell potential was measured and theoretical values were calculated.

Anode:

Zn(s) à Zn²⁺(aq) + 2e^- E⁰ = -0.76 V

Calculated E_- (Zinc cell):

Cathode:

Cu²⁺(aq) + 2e^- à Cu(s) E⁰ = 0.34 V

Calculated E₊ (Copper cell):

Redox:

Zn(s) + Cu²⁺(aq) à Cu(s) + Zn²⁺(aq)
Cell schedule:

Zn(s) | Zn²⁺(aq) (0.01M) || Cu²⁺(aq) (0.01M) | Cu(s)

sd d﷽﷽﷽﷽﷽nstam genom formeln:

cloth was use as a salt bridge to transport the ions between the solutions. ter genom formeln:

sd d﷽﷽﷽﷽﷽nstam genom formeln:

cloth was use as a salt bridge to transport the ions between the solutions. ter genom formeln:

Measured E_cell = 0.9019 V

Part B: Copper-Silver.

This part was analog to part A, except zinc was changed for silver. The cell potential was measured and theoretical values were calculated.

Anode:

Cu(s) à Cu²⁺(aq) + 2e^- E⁰ = 0.34 V

Calculated E_- (Copper cell):

Cathode:

Ag⁺(aq) + e^- à Ag(s) E⁰ = 0.80 V

Calculated E₊ (Silver cell):

Redox:

Cu(s) + 2Ag⁺(aq) à Cu²⁺(aq) + 2Ag(s)
Cell schedule:

Cu(s) | Cu²⁺(aq) (0.01M) || Ag⁺(aq) (0.01M) | Ag(s)

sd d﷽﷽﷽﷽﷽nstam genom formeln:

cloth was use as a salt bridge to transport the ions between the solutions. ter genom formeln:

sd d﷽﷽﷽﷽﷽nstam genom formeln:

cloth was use as a salt bridge to transport the ions between the solutions. ter genom formeln:

Measured E_cell = 0.37 V

Part C: Silver and zinc.

This part was executed in analogy with the previous parts A and B, but with silver and zinc for the half-cells.

Anode:

Zn(s) à Zn²⁺(aq) + 2e^- E⁰ = -0.76 V

Calculated E_- (Zinc cell):

Cathode:

Ag⁺(aq) + e^- à Ag(s) E⁰ = 0.80 V

Calculated E₊ (Silver cell):

Redox:

Zn(s) + 2Ag⁺(aq) à 2Ag(s) + Zn²⁺(aq)
Cell schedule:

Zn(s) | Zn²⁺(aq) (0.01M) || Ag⁺(aq) (0.01M) | Ag(s)

sd d﷽﷽﷽﷽﷽nstam genom formeln:

cloth was use as a salt bridge to transport the ions between the solutions. ter genom formeln:

sd d﷽﷽﷽﷽﷽nstam genom formeln:

cloth was use as a salt bridge to transport the ions between the solutions. ter genom formeln:

Measured E_cell = 1.33 V

Part D: Determination of the complex-constant for the synthesis of a tetra-amine complex from modified Daniell element.

A Daniell element like the one in part A was constructed, with one big difference: The zinc half-cell electrolyte was changed into a mix of the original zinc-solution (10 cm³) and NH₃(aq) (10 cm³, 4 mol/dm³). In this solution, the vast majority of the zinc ions build complexes with the ammoniac:

Zn²⁺(aq) + 4NH₃(aq) ↔ Zn(NH₃)₄²⁺(aq)

Because of this, the amount of free zinc ions becomes unknown, but can be calculated from the Nernst equation. Also, the equilibrium constant of the reaction above can be derived.

Cathode:

Cu²⁺(aq) + 2e^- à Cu(s) E⁰ = 0.34 V

Calculated E₊ (Copper cell):

sd d﷽﷽﷽﷽﷽nstam genom formeln:

cloth was use as a salt bridge to transport the ions between the solutions. ter genom formeln:

sd d﷽﷽﷽﷽﷽nstam genom formeln:

cloth was use as a salt bridge to transport the ions between the solutions. ter genom formeln:

Measured E_cell = 1.3 V

Anode:

Zn(s) à Zn²⁺(aq) + 2e^- E⁰ = -0.76 V

The equilibrium constant for the following reaction can now be calculated:

Zn(NH₃)₄²⁺(aq) ↔ Zn²⁺(aq) + 4NH₃(aq)

Given from lab manual:

· [Zn²⁺] + [Zn(NH₃)₄²⁺] = [Zn²⁺]_total ≈ 0.005 mol/dm³

à [Zn(NH₃)₄²⁺] = [Zn²⁺]_total - [Zn²⁺] = 0.005 – 1.72 * 10^-9 mol/dm³ ≈ 0.005 mol/dm³

· [NH₃] + 4[Zn(NH₃)₄²⁺] = [NH₃]_total = 2 mol/dm³, from preparation.

à [NH₃] = 2 – 4 * 0.005 mol/dm³ = 1.98 mol/dm³

This value of K_c indicates that the reaction is pushed far to the right, implying that almost all of the zinc ions in the solution have reacted with ammoniac molecules.

Redox for cell:

Zn(s) + Cu²⁺(aq) à Cu(s) + Zn²⁺(aq)
Cell schedule:

Zn(s) | Zn²⁺(aq) (1.72 * 10^-9 M) || Cu²⁺(aq) (0.01M) | Cu(s)

Part E: Deriving the solubility product for AgCl.

In this part, two identical half-cells were made, consisting of Ag(s) in Ag⁺-solution (20 cm³, 0.01 M), and connected by the same salt bridge as in part A-D. The electric potential was measured (E_base = 6.15 V). Next, a solution of Cl^-(aq) (20 cm³, 1.00 M) was added to one of the half cells, causing a precipitate as follows:

Ag⁺(aq) + Cl^-(aq) ↔ AgCl(s)

This reaction strongly reduces the amount of available free silver ions. The cell potential was measured again: E_cell = 0.4098 V

This value was the used in order to calculate the solubility product (the K-value) for the reaction above.

Half-cell with just silver (Cathode):

Ag⁺(aq) + e^- à Ag(s) E⁰ = 0.80 V

Calculated E₊ (Silver cell):

The concentration [Ag⁺] is lower in the Ag⁺/Cl^- half-cell due to the produced precipitate, which yields a lower reduction potential as compared to the half-cell above. Hence, the silver half-cell is the cathode in this galvanic element.

Knowing this, the Nernst equation can be used to calculate the concentration of free silver ions in the Ag⁺/Cl^- half-cell.

Anode:

Ag(s) à Ag⁺(aq) + e^- E⁰ = 0.80 V

The solubility product, K_s, for the silver chloride is derived as follows:

Ag⁺(aq) + Cl^-(aq) ↔ AgCl(s)

The stoichiometric ratio between Ag⁺ and Cl^- is 1:1.

n(Ag⁺)_before = cV = 0.01 mol/dm³ * 0.02 dm³ = 0.2 * 10^-3 mol

n(Ag⁺)_after = [Ag⁺(aq)] * V = 1.175 * 10^-9 mol/dm³ * 0.04 dm³ = 4.7 * 10^-11 mol

n(Cl^-)_precipitate = n(Ag⁺)_precipitate = n(Ag⁺)_before - n(Ag⁺)_after = 0.1999 * 10^-3 mol

n(Cl^-)_before = cV = 1 mol/dm³ * 0.02 dm³ = 0.02 mol

n(Cl^-)_after = n(Cl^-)_before - n(Cl^-)_precipitate = 0.0198 mol

[Cl^-(aq)] = n(Cl^-)_after / V_after = 0.0198 mol / 0.04 dm³ = 0.495 mol/dm³

These calculations give an approximated value of [Cl^-(aq)], based on the assumption that the amount of silver ions produced from the oxidation of the pole was too small to matter at the time the galvanic cell potential was measured.

Cell schedule:

Ag(s) | Ag⁺(aq) (1.175 * 10^-9 M) || Ag⁺(aq) (0.01M) | Ag(s)

Discussion

In all of the parts A-C, both theoretical and measured values show that the bigger the difference between the reduction potential of the half-cell elements, the greater the cell voltage.

Measured values were always smaller than the corresponding theoretical values, although reasonably close. This could be an effect of poor contact or conductivity within the circuits or the presence of impurities within the cells. There is always, of course, a risk that sloppy measuring when preparing the electrolytes could have affected the results.

In part E, the increasing amount of Ag⁺-ions will push the reaction further towards the production of the precipitate, for as long as there is still available Cl^--ions in the solution. The precipitate production gives the galvanic cell longer life-time since it maintains the concentration differences between the half-cells to some extent. At some point, the whole cell will reach equilibrium.

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