Nernst Equation Calculator
Calculate cell potential under non-standard conditions using the Nernst equation.
Nernst Equation Calculator
Calculate non-standard cell potentials
Solve For
Parameters
V
V
K
mol
Nernst Equation
The Nernst equation relates the reduction potential of an electrochemical reaction (half-cell or full cell reaction) to the standard electrode potential, temperature, and activities (often approximated by concentrations) of the chemical species undergoing reduction and oxidation.
Understanding the Nernst Equation
Calculating Cell Potential Under Real-World Conditions.
What is the Nernst Equation?
The Nernst Equation is a fundamental equation in electrochemistry that relates the reduction potential of an electrochemical reaction (a half-cell or a full cell reaction) to the standard electrode potential, temperature, and the concentrations of the reacting species.
It is used to calculate the cell potential (E_cell) under non-standard conditions.
The standard cell potential (E°_cell) is calculated assuming all concentrations are 1 M and pressure is 1 atm. The Nernst equation allows us to determine the voltage of a cell in a real-world scenario where concentrations are not 1 M.
Example: As a battery discharges, the concentration of reactants decreases and the concentration of products increases. The Nernst equation explains why the battery's voltage drops as it is used.
The Formula for the Nernst Equation
The general form of the Nernst equation is:
E_cell = E°_cell - (RT / nF) * ln(Q)
It can also be expressed using base-10 logarithm, which is often more convenient at standard temperature (298 K or 25°C):
E_cell = E°_cell - (0.0592 / n) * log(Q)
Example:This equation shows that the actual cell potential deviates from the standard potential based on the ratio of products to reactants.
Components of the Equation
Each part of the Nernst equation is a critical variable:
E_cell: The cell potential under non-standard conditions, in Volts (V).
E°_cell: The standard cell potential, in Volts (V).
R: The ideal gas constant (8.314 J/(mol·K)).
T: The absolute temperature in Kelvin (K).
n: The number of moles of electrons transferred in the balanced redox reaction.
F: Faraday's constant (≈ 96,485 C/mol), the charge of one mole of electrons.
Q: The reaction quotient, which is the ratio of the concentrations of the products to the concentrations of the reactants, each raised to the power of its stoichiometric coefficient. Q = [Products]ᶜ / [Reactants]ᵃ.
Example:The term (RT/nF) or (0.0592/n) represents the correction factor that adjusts the standard potential for the given concentrations.
Real-World Application: Concentration Cells and pH Meters
The Nernst equation is not just a theoretical tool; it has direct practical applications.
Nerve Impulses: The transmission of signals in our nervous system relies on the movement of ions (like Na⁺ and K⁺) across nerve cell membranes. The potential difference (membrane potential) that drives this is described by the Nernst equation.
Concentration Cells: A concentration cell is a special type of galvanic cell constructed from two half-cells of the same material but with different ion concentrations. Since the electrodes are the same, E°_cell is zero. The voltage is generated solely by the tendency of the concentrations to equalize, as predicted by the Nernst equation.
pH Meters: A pH meter works by measuring the potential difference across a special glass electrode that is permeable to H⁺ ions. The meter uses the Nernst equation to convert this measured voltage into a pH reading, as the voltage is directly dependent on the concentration of H⁺ ions.
Example:A pH meter is a real-life Nernstian device, turning a concentration difference into a measurable voltage.
Key Summary
- The **Nernst Equation** calculates the cell potential (voltage) under **non-standard conditions**.
- The formula is **E_cell = E°_cell - (RT/nF)ln(Q)**.
- It shows that cell potential depends on the standard potential, temperature, and the ratio of product to reactant concentrations (Q).
- This equation is fundamental to understanding nerve impulses, pH meters, and why battery voltage drops with use.
Practice Problems
Problem: A zinc-copper cell has a standard potential (E°_cell) of 1.10 V. The reaction is Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s). What is the cell potential at 25°C if [Cu²⁺] = 0.5 M and [Zn²⁺] = 1.5 M?
1. Identify 'n' (moles of electrons transferred). 2. Calculate the reaction quotient Q. 3. Use the simplified Nernst equation at 25°C.
Solution: In this reaction, n=2. Q = [Zn²⁺] / [Cu²⁺] = 1.5 / 0.5 = 3. E_cell = 1.10 V - (0.0592 / 2) * log(3) ≈ 1.10 - (0.0296 * 0.477) ≈ 1.10 - 0.014 = 1.086 V.
Problem: What happens to the cell potential in the problem above as the reaction proceeds?
As the reaction proceeds, [Zn²⁺] will increase and [Cu²⁺] will decrease. Analyze how this affects Q and the overall E_cell.
Solution: The ratio Q = [Zn²⁺] / [Cu²⁺] will get larger. This means that log(Q) will also get larger. According to the Nernst equation, a larger log(Q) term will be subtracted from E°_cell, causing the overall cell potential (E_cell) to decrease. This continues until the battery reaches equilibrium (dies) and E_cell is zero.
Frequently Asked Questions
Why are solids and liquids not included in the reaction quotient, Q?
The concentration (or more accurately, the activity) of a pure solid or a pure liquid is considered to be constant and is defined as 1. Therefore, they do not affect the value of Q and are omitted from the expression.
What is the relationship between the Nernst equation and the equilibrium constant (K)?
When a reaction reaches equilibrium, the cell potential (E_cell) is zero, and the reaction quotient (Q) becomes equal to the equilibrium constant (K). By setting E_cell = 0 and Q = K in the Nernst equation, you can derive a direct relationship: E°_cell = (RT/nF)ln(K).
Why is it important to use Kelvin for temperature?
The Nernst equation is derived from fundamental thermodynamic principles where temperature must be an absolute scale. Using Celsius would not work because it has an arbitrary zero point and can be negative, which is physically meaningless in this context.
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