Calculate The Voltage for The Following Cell Zn Zn2

The voltage of an electrochemical cell can be calculated using the Nernst equation, which relates the cell potential to the standard reduction potential and the activities of the species involved. This calculator helps determine the voltage for a Zn/Zn² cell under different conditions.

Introduction

When a zinc electrode is immersed in a solution containing Zn²⁺ ions, a redox reaction occurs:

Redox Reaction

Zn(s) → Zn²⁺(aq) + 2e⁻

Zn²⁺(aq) + 2e⁻ → Zn(s)

The voltage of the cell depends on the standard reduction potential of the zinc half-cell and the activities of the zinc ions in solution. The Nernst equation allows us to calculate the cell potential under non-standard conditions.

Nernst Equation Formula

Nernst Equation

E = E° - (RT/nF) * ln(Q)

Where:

E = Cell potential (V)
E° = Standard reduction potential (V)
R = Gas constant (8.314 J/mol·K)
T = Temperature (K)
n = Number of electrons transferred
F = Faraday constant (96,485 C/mol)
Q = Reaction quotient

The standard reduction potential for the Zn²⁺/Zn half-reaction is +0.763 V at 25°C. The reaction quotient Q is defined as:

Reaction Quotient

Q = [Zn²⁺]

Worked Example

Let's calculate the voltage for a Zn/Zn² cell with [Zn²⁺] = 0.1 M at 25°C.

Given Values

E° = 0.763 V
[Zn²⁺] = 0.1 M
T = 298 K (25°C)
n = 2

Using the Nernst equation:

Calculation

E = 0.763 - (8.314 × 298 / (2 × 96,485)) × ln(0.1)

E = 0.763 - (4.76) × (-2.3026)

E = 0.763 + 10.98

E ≈ 1.853 V

The calculated voltage for this cell is approximately 1.853 V.

Standard Reduction Potentials

The standard reduction potential (E°) is the potential of a half-cell under standard conditions (1 M concentration, 1 atm pressure, 25°C). For the Zn²⁺/Zn half-reaction:

Half-Reaction	Standard Reduction Potential (V)
Zn²⁺ + 2e⁻ → Zn	+0.763

This value is crucial for calculating cell potentials under non-standard conditions.

Effect of Concentration

The concentration of Zn²⁺ ions affects the cell potential. Higher concentrations of Zn²⁺ ions result in a more positive cell potential because the reaction quotient Q increases, making the ln(Q) term more negative (since Q < 1).

Key Points

Increasing [Zn²⁺] increases the cell potential
The relationship is logarithmic
Temperature also affects the cell potential

Frequently Asked Questions

What is the standard reduction potential for the Zn²⁺/Zn half-reaction?: The standard reduction potential for Zn²⁺ + 2e⁻ → Zn is +0.763 V at 25°C.
How does the concentration of Zn²⁺ affect the cell potential?: Increasing the concentration of Zn²⁺ ions increases the cell potential because it makes the reaction quotient Q larger, which makes the ln(Q) term more negative (since Q < 1).
What is the Nernst equation used for?: The Nernst equation is used to calculate the cell potential under non-standard conditions based on the standard reduction potential and the activities of the species involved.
What units are used in the Nernst equation?: The Nernst equation uses volts (V) for potential, moles (mol) for concentrations, joules per mole per kelvin (J/mol·K) for the gas constant, coulombs per mole (C/mol) for the Faraday constant, and kelvin (K) for temperature.
How does temperature affect the cell potential?: Temperature affects the cell potential through the RT term in the Nernst equation. Higher temperatures increase the RT term, which can either increase or decrease the cell potential depending on the sign of the ln(Q) term.