Calculation of Standard Reduction Potential for M2/M Couple

To calculate the standard reduction potential for the M2/M couple, we need to consider the given potential of the cell for the reaction M + 2H- -> H2 + M2, which is 1.5 V.

Step 1: Identify the Half-Reactions
In this cell, we have two half-reactions:
1. Oxidation half-reaction: M -> M2+ + 2e-
2. Reduction half-reaction: 2H+ + 2e- -> H2

Step 2: Write the Balanced Equation for the Cell Reaction
By combining the two half-reactions, we obtain the balanced equation for the cell reaction as follows:
M + 2H+ -> H2 + M2+

Step 3: Identify the Nernst Equation
The Nernst equation relates the standard reduction potential (E°) to the concentrations of the reactants and products in the cell. The Nernst equation for the M2/M couple can be written as:
E = E° - (RT/nF) * ln(Q)

Where:
- E is the cell potential
- E° is the standard reduction potential
- R is the gas constant (8.314 J/mol·K)
- T is the temperature in Kelvin
- n is the number of electrons transferred in the balanced equation (2 in this case)
- F is the Faraday constant (96,485 C/mol)
- Q is the reaction quotient

Step 4: Calculate the Reaction Quotient (Q)
The reaction quotient (Q) is calculated by substituting the concentrations of the reactants and products at a given point in the cell reaction. Since the standard reduction potential is determined under standard conditions, the concentrations of all species are 1 M. Therefore, Q = 1.

Step 5: Calculate the Standard Reduction Potential (E°)
To calculate the standard reduction potential (E°), we need to rearrange the Nernst equation and solve for E°:
E° = E + (RT/nF) * ln(Q)

Since E is given as 1.5 V, we can substitute the values into the equation:
E° = 1.5 V + (8.314 J/mol·K * T / (2 * 96,485 C/mol) * ln(1)

Step 6: Simplify the Equation
To simplify the equation, we can substitute the value of ln(1) which is 0:
E° = 1.5 V + (8.314 J/mol·K * T / (2 * 96,485 C/mol) * 0

Therefore, the standard reduction potential (E°) for the M2/M couple is 1.5 V.

Explanation:
The standard reduction potential for the M2/M couple is calculated by using the Nernst equation, which relates the cell potential to the standard reduction potential, temperature, and reaction quotient. By rearranging the equation and substituting the given values, we can determine the standard reduction potential. In this case, the given potential of the cell for the reaction M + 2H- -> H2 + M2 is 1.5 V,