Nernst Equation Calculator

About Nernst Equation Calculator

The Nernst equation adjusts standard cell potential for non-standard conditions. At equilibrium, E = 0 and Q = K.

How to use this calculator

1. Enter the standard cell potential, usually written as \(E^\circ\).
2. Enter the temperature \(T\), the number of electrons transferred \(n\), and the reaction quotient \(Q\).
3. Use the calculator to find the cell potential \(E\) under the given conditions.
4. Check whether the result is higher or lower than \(E^\circ\), which tells you how the conditions affect the cell.

The formula explained

The Nernst equation computes the cell potential \(E\) for non-standard conditions. It adjusts the standard potential \(E^\circ\) by a term involving temperature, the reaction quotient \(Q\), and the number of electrons \(n\).

• E = cell potential under the given conditions
• \(E^\circ\) = standard cell potential
• R = gas constant, \(8.314\ \text{J} / (\text{mol} \cdot \text{K})\)
• T = temperature in kelvin
• n = number of electrons transferred in the balanced redox reaction
• F = Faraday constant, about \(96485\ \text{C} / \text{mol}\)
• Q = reaction quotient, based on the current concentrations or partial pressures

Step by step method

1. Write down the values for \(E^\circ\), \(T\), \(n\), and \(Q\).
2. Substitute them into \(E = E^\circ - \frac{RT}{nF}\ln Q\).
3. Evaluate \(\ln Q\) and then calculate the correction term \(\frac{RT}{nF}\ln Q\).
4. Subtract that correction from \(E^\circ\) to get the cell potential \(E\).

Worked example

Problem. Find the cell potential for a reaction with \(E^\circ = 1.10\ \text{V}\), \(T = 298\ \text{K}\), \(n = 2\), and \(Q = 10\).

1. Start with \(E = E^\circ - \frac{RT}{nF}\ln Q\).
2. Substitute the values: \(E = 1.10 - \frac{(8.314)(298)}{(2)(96485)}\ln(10)\).
3. Since \(\ln(10) \approx 2.303\), the correction is about \(0.0296\ \text{V}\), so \(E \approx 1.10 - 0.0296 = 1.0704\ \text{V}\).

Tips and common mistakes

• Make sure temperature is in kelvin, not degrees Celsius.
• A larger \(Q\) usually lowers \(E\) when \(Q > 1\), while a smaller \(Q\) can raise \(E\).

Frequently asked questions