Calculate the emf of the following cell at 298 K:

Fe₃|Fe²⁺(0.001M)||H⁺(1M)|H₂(1 bar), Pt

(Given: E_cell⁰ = +0.44V)

To calculate the electromotive force (emf) of the given electrochemical cell at 298 K, we can use the Nernst equation. This equation allows us to determine the cell potential under non-standard conditions by taking into account the concentrations of the reactants and products involved in the redox reactions.

Understanding the Components of the Cell

The cell notation provided is:

• Fe₃ | Fe²⁺(0.001 M)
• ||
• H⁺(1 M) | H₂(1 bar), Pt

This indicates that we have a half-cell involving iron ions and a hydrogen half-cell. The standard cell potential (E°) is given as +0.44 V.

Applying the Nernst Equation

The Nernst equation is expressed as:

E = E° - (RT/nF) * ln(Q)

Where:

• E = cell potential under non-standard conditions
• E° = standard cell potential (+0.44 V)
• R = universal gas constant (8.314 J/(mol·K))
• T = temperature in Kelvin (298 K)
• n = number of moles of electrons transferred in the reaction
• F = Faraday's constant (96485 C/mol)
• Q = reaction quotient

Determining the Reaction Quotient (Q)

For the given cell, the half-reaction for the reduction of Fe³⁺ to Fe²⁺ can be represented as:

Fe³⁺ + e⁻ ⇌ Fe²⁺

In this case, the number of electrons transferred (n) is 1. The reaction quotient (Q) can be calculated using the concentrations of the species involved:

Q = [Fe²⁺] / [Fe³⁺]

Assuming that the concentration of Fe³⁺ is in a saturated state, we can denote it as 1 M for simplicity. Thus:

Q = 0.001 / 1 = 0.001

Calculating the Cell Potential (E)

Now, we can substitute the values into the Nernst equation:

E = 0.44 V - (8.314 J/(mol·K) * 298 K / (1 * 96485 C/mol)) * ln(0.001)

Calculating the term:

• RT/F = (8.314 * 298) / 96485 ≈ 0.008314 V
• ln(0.001) ≈ -6.907755

Substituting these values back into the equation gives:

E = 0.44 V - (0.008314 * -6.907755)

E = 0.44 V + 0.0575 V

E ≈ 0.4975 V

Final Result

The emf of the cell at 298 K is approximately 0.498 V. This value indicates the potential difference that can drive the electrochemical reaction under the specified conditions.