Determining Reactant Concentrations from Cell Potential

Introduction to Determining Reactant Concentrations from Cell Potential

In electrochemistry, the relationship between the concentration of reactants and the cell potential is crucial for understanding how electrochemical cells function. The Nernst equation allows us to calculate the cell potential under non-standard conditions and can be rearranged to find the concentrations of reactants based on measured cell potentials. Here, we present three diverse examples to illustrate this concept in practical scenarios.

Example 1: Determining Concentration of Copper(II) Ions in a Copper-Zinc Cell

In a standard galvanic cell comprised of copper and zinc electrodes, we want to determine the concentration of copper(II) ions
([Cu²⁺]) in the solution. This can be useful in applications like electroplating, where knowing the ion concentration is critical for optimal plating.

Using the Nernst equation, we have:

E = E° - (RT/nF) * ln(Q)

Where:

• E = cell potential (measured in volts)
• E° = standard cell potential (0.34 V for Cu²⁺/Cu)
• R = universal gas constant (8.314 J/(mol·K))
• T = temperature in Kelvin (assumed to be 298 K)
• n = number of electrons transferred (2 for Cu²⁺/Cu)
• F = Faraday’s constant (96485 C/mol)
• Q = reaction quotient, calculated as [Cu²⁺]/[Zn²⁺]

Assuming we know the concentration of zinc ions
([Zn²⁺]) is 0.10 M and we measure the cell potential (E) to be 0.20 V. Rearranging the equation to solve for [Cu²⁺]:

1. Calculate Q: Q = [Cu²⁺]/[Zn²⁺]

2. Plug in the values:

   • 0.20 V = 0.34 V - (0.0257/2) * ln([Cu²⁺]/0.10)

3. Solve for [Cu²⁺]:

   • [Cu²⁺] = 0.034 M (after rearranging and solving the equation)

This calculation helps in applications where copper ion concentration directly impacts the electroplating quality.

Example 2: Concentration of Iron(III) Ions in a Redox Reaction

In a laboratory setting, you are conducting a redox reaction involving iron(III) ions and iron(II) ions. The goal is to determine the concentration of
[Fe³⁺] in a solution after measuring the cell potential. This is particularly relevant in environmental chemistry, where tracking ion concentrations can indicate pollution levels.

The Nernst equation is again utilized:

E = E° - (RT/nF) * ln([Fe²⁺]/[Fe³⁺])

Assume the standard potential (E°) for the Fe³⁺/Fe²⁺ couple is +0.77 V. If we measure the cell potential (E) to be +0.50 V and know the concentration of iron(II) ions
([Fe²⁺]) is 0.05 M, we can determine the concentration of iron(III) ions:

1. Rearranging gives:

   • 0.50 V = 0.77 V - (0.0257/1) * ln(0.05/[Fe³⁺])

2. Solve for [Fe³⁺]:

   • [Fe³⁺] = 0.21 M (after rearranging and solving the equation)

This example highlights the importance of understanding ion concentrations in both laboratory and environmental contexts.

Example 3: Assessing Chloride Ion Concentration in a Silver Chloride Cell

In this example, we are working with a silver chloride cell, where silver ions
([Ag⁺]) and chloride ions
([Cl⁻]) are involved. Determining the concentration of chloride ions in a solution is essential for applications in food safety and water quality assessment.

Using the Nernst equation:

E = E° - (RT/nF) * ln([Ag⁺]/[Cl⁻])

The standard potential for the Ag⁺/Ag and Cl⁻/Cl couple is 0.80 V. If the measured cell potential (E) is 0.60 V and the concentration of silver ions
([Ag⁺]) is 0.10 M, we can find the chloride ion concentration:

1. Rearranging gives:

   • 0.60 V = 0.80 V - (0.0257/1) * ln(0.10/[Cl⁻])

2. Solve for [Cl⁻]:

   • [Cl⁻] = 0.15 M (after rearranging and solving the equation)

This example underscores the relevance of ion concentration measurements in ensuring safety and compliance in food and water industries.