calculate the single electrode potential of Zn2+/Zn electrode when the concentration of[Zn+]=0.1 molar and temperature 50°c

To calculate the single electrode potential of the Zn²⁺/Zn electrode, we can use the Nernst equation. This equation relates the concentration of ions in solution to the electrode potential, taking into account temperature and the number of electrons transferred in the half-reaction.

The Nernst Equation

The Nernst equation is given by:

E = E^° - (RT/nF) * ln(Q)

Where:

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

Standard Electrode Potential for Zn

The standard electrode potential (E^°) for the Zn²⁺/Zn couple is approximately -0.76 V. This value is a reference point at standard conditions (1 M concentration, 25°C).

Temperature Conversion

First, we need to convert the temperature from Celsius to Kelvin:

T(K) = T(°C) + 273.15

For 50°C, this gives:

T = 50 + 273.15 = 323.15 K

Calculating the Reaction Quotient (Q)

For the half-reaction:

Zn(s) ⇌ Zn²⁺(aq) + 2e^-

The reaction quotient (Q) is defined as:

Q = [Zn²⁺]/[Zn]

Since solid zinc (Zn) is in its standard state, its activity is 1. Therefore:

Q = [Zn²⁺] = 0.1

Substituting Values into the Nernst Equation

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

• E^° = -0.76 V
• R = 8.314 J/(mol·K)
• T = 323.15 K
• n = 2 (since 2 electrons are transferred)
• F = 96485 C/mol
• Q = 0.1

Now plug these values into the equation:

E = -0.76 - (8.314 * 323.15 / (2 * 96485)) * ln(0.1)

Calculating Each Component

First, calculate the term:

(8.314 * 323.15) / (2 * 96485) ≈ 0.0051 V

Next, calculate ln(0.1):

ln(0.1) ≈ -2.3026

Now substitute this back into the equation:

E = -0.76 - (0.0051 * -2.3026)

E ≈ -0.76 + 0.0117 ≈ -0.7483 V

Final Result

The single electrode potential of the Zn²⁺/Zn electrode at a concentration of 0.1 M and a temperature of 50°C is approximately -0.748 V.