Chemistry Calculator
Nernst Equation Calculator
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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
Inside a Galvanic Cell
In the classic Daniell cell, zinc is oxidised at the anode and copper ions are reduced at the cathode. Electrons flow through the wire, and the salt bridge keeps both solutions electrically neutral. The Nernst equation tells you how the voltage changes as the ion concentrations change.
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 |
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.