Question

An Ag/AgCl electrode dipping into 1.00 M HCl has a standard reduction potential of 0.2223 V. The half-reaction is AgCl(s) e- Ag(s) Cl-(aq) A second Ag/AgCl electrode is dipped into a solution containing Cl- at an unknown concentration. The cell generates a potential of 0.0530 V, with the electrode in the solution of unknown concentration having a negative charge. What is the molar concentration of Cl- in the unknown solution

Answer 1

The molar concentration of Cl⁻ in the unknown solution is approximately 2.81 x 10⁻¹⁰ M.

How to find molar concentration?

The Nernst equation relates the potential of a cell to the standard potential, concentration of reactants and products, and temperature. For this system, the equation is:

E = E° - (RT/nF) ln([Cl⁻]/[AgCl])

where:

E = cell potential (0.0530 V)

E° = standard reduction potential (0.2223 V)

R = gas constant (8.314 J/mol·K)

T = temperature (assumed to be 298 K)

n = number of electrons transferred (1)

F = Faraday constant (96485 C/mol)

[Cl⁻] = molar concentration of Cl- in the unknown solution

[AgCl] = concentration of AgCl

Rearrange the equation to isolate [Cl⁻]:

ln([Cl-]/[AgCl]) = (E° - E) / (RT/nF)

Plug in the known values:

ln([Cl-]/[AgCl]) = (0.2223 V - 0.0530 V) / ((8.314 J/mol·K × 298 K) / (1 × 96485 C/mol))

Simplify and solve for [Cl⁻]:

ln([Cl⁻]/[AgCl]) ≈ -0.0675

[Cl⁻]/[AgCl] = exp(-0.0675)

≈ 0.937

Since [AgCl] is assumed constant, [Cl⁻] ≈ 0.937 × [AgCl].

The solubility product (Ksp) of AgCl is 2.8 x 10⁻¹⁰. Assuming ideal behavior, the concentration of AgCl can be approximated by:

[Ag⁺] × [Cl⁻] = Ksp

Since AgCl is saturated in both solutions, assume [Ag⁺] is the same in both electrodes. Therefore:

[Ag⁺] × [Cl⁻] ≈ 2.8 x 10⁻¹⁰

[Cl⁻] ≈ 2.8 x 10⁻¹⁰ / [Ag+]

Substitute this expression for [Cl⁻] in the previous equation:

0.937 × ([2.8 x 10⁻¹⁰] / [Ag⁺]) ≈ [Cl⁻]

[Ag⁺] ≈ 3 x 10⁻¹⁰

Finally, calculate the concentration of Cl⁻ in the unknown solution:

[Cl⁻] ≈ 0.937 × 3 x 10⁻¹⁰

≈ 2.81 x 10⁻¹⁰ M

Therefore, the molar concentration of Cl⁻ in the unknown solution is approximately 2.81 x 10⁻¹⁰ M.