Calculate The Potential of The Following Concentration Cell at 25

This calculator helps you determine the electromotive force (EMF) of a concentration cell at 25°C using the Nernst equation. The calculation accounts for the difference in ion concentrations between the two half-cells and the number of electrons transferred in the redox reaction.

How to Calculate the Potential of a Concentration Cell

To calculate the potential of a concentration cell, you'll need to know:

The standard reduction potential of the redox couple (E°)
The concentrations of the oxidized and reduced species in each half-cell ([Ox] and [Red])
The number of electrons transferred in the reaction (n)

The Nernst equation relates these factors to the cell potential at any concentration:

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 (298 K at 25°C)
n = Number of electrons transferred
F = Faraday constant (96,485 C/mol)
Q = Reaction quotient ([Red]/[Ox])

For a concentration cell, the standard potential (E°) is typically 0 V because the same redox couple is involved in both half-cells. The potential difference arises solely from the concentration gradient.

Worked Example

Consider a concentration cell with:

Left half-cell: 1.0 M Cu²⁺
Right half-cell: 0.1 M Cu²⁺
Number of electrons transferred (n): 2

Using the Nernst equation:

Calculation Steps

1. Calculate the reaction quotient (Q):

Q = [Cu²⁺]right / [Cu²⁺]left = 0.1 / 1.0 = 0.1

2. Plug values into the Nernst equation:

E = 0 - (8.314 J/mol·K × 298 K / 2 × 96,485 C/mol) × ln(0.1)

3. Simplify the constants:

E = - (0.02569 V) × (-2.3026)

4. Calculate the final potential:

E = 0.0592 V

The calculated potential is 0.0592 V, indicating the right half-cell (with lower Cu²⁺ concentration) is more positive than the left half-cell.

Interpreting the Results

The calculated potential tells you:

The direction of electron flow (from higher to lower potential)
The magnitude of the driving force for the reaction
Whether the cell is spontaneous (E > 0) or non-spontaneous (E < 0)

Important Notes

The Nernst equation assumes ideal conditions and doesn't account for:

Activity coefficients (for concentrated solutions)
Temperature effects beyond the given temperature
Side reactions or impurities

For practical applications, you might need to adjust the calculation for real-world conditions or consider other factors like electrode surface area and solution resistance.

Frequently Asked Questions

What is the difference between standard potential and cell potential?

The standard potential (E°) is the potential measured under standard conditions (1 M concentrations, 25°C). The cell potential (E) is the actual potential under the given concentrations, calculated using the Nernst equation.

Can I use this calculator for any concentration cell?

Yes, this calculator works for any concentration cell where the same redox couple is involved in both half-cells. The standard potential (E°) should be 0 V in these cases.

What units should I use for concentrations?

The calculator accepts concentrations in molarity (M) or molality (m). Make sure both concentrations are in the same units when entering them.

How accurate are the results?

The results are accurate for ideal conditions. For real solutions, you may need to adjust for activity coefficients or other factors not accounted for in the Nernst equation.