The standard reduction potential of a calomel half cell is 0.28 v at 25degree c. Calculate half cell potential when 0.1 N KCl solution is used.

To determine the half-cell potential of a calomel electrode when immersed in a 0.1 N KCl solution, we need to consider the Nernst equation, which relates the concentration of ions in solution to the electrode potential. The standard reduction potential of the calomel half-cell is given as 0.28 V at 25°C. Let's break down the calculation step by step.

Understanding the Calomel Electrode

The calomel electrode is a reference electrode made of mercury and mercurous chloride (Hg2Cl2). Its half-reaction can be represented as:

• Hg2Cl2(s) + 2e^- ⇌ 2Hg(l) + 2Cl^-(aq)

In this reaction, the concentration of chloride ions (Cl^-) in the solution affects the potential of the electrode.

Applying the Nernst Equation

The Nernst equation is expressed as:

E = E_° - (RT/nF) * ln(Q)

Where:

• E = half-cell potential
• E_° = standard reduction potential (0.28 V for calomel)
• R = universal gas constant (8.314 J/(mol·K))
• T = temperature in Kelvin (25°C = 298 K)
• n = number of moles of electrons transferred (2 for calomel)
• F = Faraday's constant (96485 C/mol)
• Q = reaction quotient, which in this case is the concentration of Cl^- ions

Calculating the Reaction Quotient

In a 0.1 N KCl solution, the concentration of Cl^- ions is 0.1 M. Therefore, we can substitute this value into the Nernst equation:

Q = [Cl^-]² = (0.1)² = 0.01

Substituting Values into the Nernst Equation

Now, we can plug in the values into the Nernst equation:

E = 0.28 V - (8.314 J/(mol·K) * 298 K / (2 * 96485 C/mol)) * ln(0.01)

Calculating Each Component

First, calculate the term:

(RT/nF) = (8.314 * 298) / (2 * 96485) ≈ 0.0041 V

Next, calculate the natural logarithm:

ln(0.01) = -4.605

Now, substitute these values back into the equation:

E = 0.28 V - (0.0041 * -4.605)

E = 0.28 V + 0.0189 V ≈ 0.2989 V

Final Result

Thus, the half-cell potential of the calomel electrode in a 0.1 N KCl solution is approximately 0.2989 V at 25°C. This calculation illustrates how the concentration of ions in solution can influence the potential of an electrochemical cell, which is crucial in various applications, including electrochemistry and analytical chemistry.