Chemistry Calculator
Nernst Equation Calculator
The Nernst equation converts standard cell potential (E°) into real-world cell potential (E) by accounting for temperature and how far the reaction has progressed (Q). Use this calculator to estimate cell voltage under non-standard conditions.
Nernst Equation
Calculate cell potential from E°, T, n, and Q
Results
Enter values to calculate E
What is the Nernst equation?
In electrochemistry, standard potentials (E°) are defined for idealized conditions (typically 1 M solutions, 1 bar gases, pure solids/liquids, and 25°C). Real cells almost never operate exactly at those conditions.
The Nernst equation adjusts E° using the reaction quotient Q, which summarizes the current ratio of products to reactants. As Q increases, the driving force typically decreases, reducing cell potential.
Electrochemistry Formulas & Laws
Depending on your textbook preference, the Nernst equation uses one of two logarithmic modes:
Where R is the gas constant, F is Faraday’s constant, n is electrons transferred, T is temperature in kelvin, and Q is the reaction quotient.
Standard Reduction Potentials at 25°C (298.15 K)
Standard half-cell reduction potential references for common redox couples:
| Half-Reaction | Standard Potential (E°) |
|---|---|
| F₂ (g) + 2e⁻ → 2F⁻ | +2.87 V |
| Ag⁺ + e⁻ → Ag (s) | +0.80 V |
| Cu²⁺ + 2e⁻ → Cu (s) | +0.34 V |
| 2H⁺ + 2e⁻ → H₂ (g) | 0.00 V (SHE) |
| Zn²⁺ + 2e⁻ → Zn (s) | -0.76 V |
| Li⁺ + e⁻ → Li (s) | -3.04 V |
Textbook Voltage Correction Factor at 25°C
At room temperature (25°C), the term (2.303RT/F) simplifies to a constant 0.05916 V. Use this table to check the resulting division coefficient based on electron count:
| Transferred Electrons (n) | Correction Term Coefficient |
|---|---|
| 1 electron (n = 1) | 0.05916 V |
| 2 electrons (n = 2) | 0.02958 V |
| 3 electrons (n = 3) | 0.01972 V |
| 4 electrons (n = 4) | 0.01479 V |
Benefits of Using the Nernst Equation Calculator
Example Calculations
Example Scenario 1 — Room temperature, Q = 10
E° = 1.10 V, T = 25°C, n = 2, Q = 10
At 25°C: E = E° − (0.05916 / n) × log10(Q)
E = 1.10 − (0.05916 / 2) × log10(10)
E = 1.10 − 0.02958 × 1 = 1.07042 V
Example Scenario 2 — Products low (Q < 1)
E° = 0.80 V, T = 25°C, n = 2, Q = 0.01
log10(0.01) = −2
E = 0.80 − (0.05916 / 2) × (−2)
E = 0.80 + 0.05916 = 0.85916 V
Example Scenario 3 — Higher temperature increases correction
E° = 1.23 V, T = 60°C, n = 2, Q = 100
Higher T increases (RT/nF), so the correction grows
For Q = 100, log10(Q) = 2
E will be lower than E° by a larger amount than at 25°C
Frequently Asked Questions
- What does the Nernst equation calculate?
- It calculates the cell potential (E) under non-standard conditions by correcting the standard potential (E°) using temperature, electron transfer (n), and the reaction quotient (Q).
- What is the reaction quotient Q?
- Q is the ratio of products to reactants (raised to stoichiometric powers) using activities or effective concentrations. Q must be positive and dimensionless.
- What does n mean in the Nernst equation?
- n is the number of electrons transferred in the balanced redox reaction. It controls how strongly E changes with Q and temperature.
- Why is 25°C often special in electrochemistry?
- At 25°C (298.15 K), the Nernst equation is often written in base-10 form: E = E° − (0.05916/n) log10(Q). This is just a convenient constant for room temperature.
- How does the Nernst equation relate to the Gibbs free energy?
- The cell potential is related to free energy by delta G = -nFE. Thus, the Nernst equation can also calculate free energy shifts under non-standard conditions.
- What happens to the cell potential when Q equals 1?
- When Q = 1, the log or ln term becomes 0, and the cell potential E is exactly equal to the standard potential E°.
- What happens to the cell potential when the reaction reaches equilibrium?
- At equilibrium, the cell potential E = 0 and the reaction quotient Q equals the equilibrium constant K. The equation simplifies to E° = (RT/nF) * ln(K).
- Can the reaction quotient Q be equal to zero or negative?
- No, concentrations and activities must be positive, so Q is always strictly greater than zero. A value of Q = 0 would theoretically yield infinite cell potential, which is physically impossible.
- What values of R and F are used in this calculator?
- This calculator uses the exact gas constant R = 8.314462618 J/(mol·K) and Faraday's constant F = 96485.33212 C/mol.
- Is the Nernst equation applicable to biological cell membranes?
- Yes, it is widely used in neurophysiology to calculate the resting equilibrium membrane potential for individual ions like Na+, K+, and Cl- across cell membranes.