Calculate the reduction potential using the Nernst equation.
    Enter the standard reduction potential \(E^{\circ}\), temperature \(T\) (K), number of electrons \(n\), and the reaction quotient \(Q\).

    * All values should be in SI units.

    Step 1: Enter Parameters

    Example: 0.00 V

    Default: 298.15 K (25°C)

    Example: 2

    Example: 1 (for standard conditions)

    Derived Equation:
    $$E = E^{\\circ} – \\frac{RT}{nF} \\ln Q$$
    where \(R = 8.314\\,\\text{J/(mol·K)}\) and \(F = 96485\\,\\text{C/mol}\).


    Example:
    For \(E^{\\circ} = 0.00\\,\\text{V}\), \(T = 298.15\\,\\text{K}\), \(n = 2\), and \(Q = 1\), the reduction potential is calculated.

    Electrochemistry Tutorial: Using a Nernst Equation Calculator

    Electrochemical cells rarely operate under standard‑state conditions (1 M, 1 bar, 25 °C). The Nernst equation corrects the standard electrode potential (\(E^\circ\)) for actual temperature and reactant/product activities, giving the instantaneous cell potential \(E\). Accurate potentials are critical in batteries, corrosion studies, sensors, and biochemical redox reactions. This tutorial explains the Nernst equation, shows how temperature and concentration affect \(E\), and demonstrates the online Nernst‑equation calculator.

    What Is the Nernst Equation?

    • General form: \( E = E^\circ – \frac{RT}{nF}\ln Q \)
    • 25 °C simplification: \( E = E^\circ – \frac{0.05916}{n}\log_{10} Q \)
    • Variables:
      • \(E\) – cell/electrode potential (V)
      • \(E^\circ\) – standard potential (V)
      • \(R = 8.314\;\text{J mol}^{-1}\text{K}^{-1}\)
      • \(T\) – temperature (K)
      • \(n\) – electrons transferred
      • \(F = 96485\;\text{C mol}^{-1}\)
      • \(Q\) – reaction quotient \(\displaystyle Q = \frac{\prod a_{\text{products}}^{\nu}}{\prod a_{\text{reactants}}^{\nu}}\)
    • Big Idea: Increasing oxidant concentration or decreasing reductant concentration raises \(Q\) and lowers \(E\); temperature amplifies this effect.

    Why Concentration and Temperature Matter

    The factor \(\tfrac{RT}{nF}\) grows with temperature, so non‑standard concentrations shift potentials more at higher \(T\). Batteries therefore deliver different voltages in cold vs hot conditions, and biochemical redox couples vary with intracellular pH and ion gradients.

    How to Calculate E with the Nernst Equation

    1. Write the balanced redox half‑reaction or full cell reaction.
    2. Identify n, the number of electrons transferred.
    3. Insert known \(E^\circ\) from a table of standard potentials.
    4. Compute \(Q\) from ion activities (≈ molar concentrations for dilute aqueous solutions).
    5. Choose temperature \(T\) (in kelvin).
    6. Evaluate \(E = E^\circ – (RT/nF)\ln Q\) or at 25 °C, \(E = E^\circ – 0.05916\,\log_{10}Q / n\).

    How to Use the Online Nernst Equation Calculator

    1. Open Nernst Equation Calculator.
    2. Enter the standard potential E° (in volts).
    3. Specify the number of electrons n.
    4. Select the temperature or leave at 25 °C.
    5. Enter activities/concentrations for each oxidized and reduced species (the form auto‑builds the correct \(Q\)).
    6. Click Calculate E to display the actual potential and a step‑by‑step breakdown.

    Example Problems

    Example 1 — Zn/Cu Galvanic Cell

    Cell: \(\text{Zn}^{2+}(1\,\text M)\;|\;\text{Zn}\;||\;\text{Cu}^{2+}(0.010\,\text M)\;|\;\text{Cu}\)
    Overall: \(\text{Zn} + \text{Cu}^{2+} \rightarrow \text{Zn}^{2+} + \text{Cu}\) (\(n = 2\))
    \(E^\circ = 1.10\;\text V\). \(Q = \frac{a_{\text{Zn}^{2+}}}{a_{\text{Cu}^{2+}}} = \frac{1}{0.010} = 100\).
    \(E = 1.10 – 0.05916/2 \,\log_{10} 100 = 1.10 – 0.02958\times2 = 1.04\;\text V\).

    Example 2 — Ag⁺/Ag Half‑Cell

    \(\text{Ag}^{+} + e^- \leftrightharpoons \text{Ag}\) (\(n = 1\)); \(E^\circ = 0.799\;\text V\). At \([\text{Ag}^+] = 0.020\,\text M\) and 25 °C:
    \(Q = 0.020\). \(E = 0.799 – 0.05916 \,\log_{10}(0.020) = 0.799 + 0.077 \approx 0.876\;\text V\).

    Example 3 — Effect of Temperature

    For the Ag⁺/Ag half‑cell above at 40 °C (313 K):
    \(E = 0.799 – \dfrac{8.314 \times 313}{1 \times 96485}\ln 0.020 \approx 0.862\;\text V\). Higher temperature slightly reduces the potential.

    Frequently Asked Questions

    Why use log₁₀ sometimes and ln other times?

    The fundamental equation uses natural log (ln). Converting to log₁₀ introduces the factor 2.303 so the term becomes 0.05916 V /  at 25 °C.

    Can activities be replaced by concentrations?

    For dilute aqueous solutions (< 0.1 M), activities ≈ concentrations. In high‑ionic‑strength media use activity coefficients for accuracy.

    What if the calculated E is negative?

    A negative potential means the reaction, as written, is not spontaneous under the given conditions; reversing the cell changes the sign.

    How does pH enter the Nernst equation?

    If H+ (or OH‑) appears in the redox reaction, its activity (linked to pH) contributes to \(Q\), coupling electrochemistry with acid–base equilibria.

     
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