Cell Potential (Non-Standard Conditions)

Related Examples and Practice Problems

Additional Worked Out Examples/ Practice

  • Identifying classification types: Differentiation between elements, compounds or mixtures and homogeneous and heterogenous mixtures

  • Separation techniques: Selected and explaining limitation of appropriate separation

  • Relating Properties to Composition: Predicting classification based on descriptive properties

Topic Summary & Highlights
and Help Videos

Core Concept

The voltage of an electrochemical cell when the concentrations, pressures, or temperatures differ from standard conditions (1 M,1 atm, 25°C).

Significance: Real-world electrochemical reactions rarely occur under standard conditions, so understanding how to adjust for non-standard conditions is critical.

Practice Tips

  • Cell potential depends on concentration, pressure, and temperature.

  • Use the Nernst equation to adjust $E_{\text{cell}}$​ for non-standard conditions.

  • The reaction quotient (Q) determines whether the cell potential is higher or lower than $E^°_{\text{cell}}$​.

  • Mastery of the Nernst equation is essential for understanding real-world electrochemical systems.

Topic Overview Podcast

Topic Related Resources

 LABORATORY 
 DEMONSTRATIONS 
 ACTIVITIES 
 VIRTUAL SIMULATIONS 

The Nernst Equation

The Nernst equation calculates the cell potential (E<sub>cell</sub>) under non-standard conditions:

$E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{RT}{nF} \ln Q$

Where:

  • $E_{\text{cell}}$: Cell potential under non-standard conditions (V)

  • $E°_{\text{cell}}$: Standard cell potential (V)

  • R: Gas constant (8.314 J/mol·K)

  • T: Temperature (Kelvin)

  • n: Number of moles of electrons transferred

  • F: Faraday’s constant (96,485 C/mol)

  • Q: Reaction quotient (ratio of products to reactants)

Key Concepts

Reaction Quotient (Q):

$Q = \frac{[\text{products}]^{\text{coefficients}}}{[\text{reactants}]^{\text{coefficients}}}$

Concentrations of solids and pure liquids are not included in Q.

Effect of Q on $E_{\text{cell}}$:

  • Q < 1: Reactants dominate; ln Q < 0, $E_{\text{cell}}$ > E°<sub>cell</sub>

  • Q = 1: Standard conditions; $E_{\text{cell}}$ = E°<sub>cell</sub>

  • Q > 1: Products dominate; ln Q > 0, $E_{\text{cell}}$ < E°<sub>cell</sub>

Temperature Dependence:

Higher temperatures amplify the effect of ln Q due to the $\frac{RT}{nF}$ term.

Standard Conditions vs. Nonstandard Conditions
Condition Standard Conditions Nonstandard Conditions
Concentration of Aqueous Solutions Aqueous solutions of reactant(s) and product(s) are equal to 1.0 M. At least one of the aqueous solutions is NOT equal to 1.0 M.
Partial Pressure of Gases (if gases are present) Partial pressures of gaseous reactant(s) and/or product(s) are equal to 1.0 atm. At least one of the gaseous substances has a partial pressure that is NOT equal to 1.0 atm.
Temperature Temperature is 298 K. Temperature is NOT 298 K.
Reaction Quotient \( Q \) \( Q \) is equal to 1.0. It is likely that \( Q \) is NOT equal to 1.0.

Simplified Nernst Equation at 25°C

At 25∘C25^\circ \text{C}25∘C (T=298 KT = 298 \, \text{K}T=298K):

Ecell=Ecell∘−0.0592nlog⁡QE_{\text{cell}} = E^\circ_{\text{cell}} - \frac{0.0592}{n} \log QEcell​=Ecell∘​−n0.0592​logQ

This simplifies calculations when temperature is standard.

Steps to Calculate EcellE_{\text{cell}}Ecell​

  1. Write the Half-Reactions:

    • Identify the oxidation and reduction reactions.

  2. Determine E°_{\text{cell}}$:

    • Use the standard reduction potential table:
      $E°_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}}$

  3. Calculate Q:

    • Use the concentrations or pressures of the reactants and products.

  4. Apply the Nernst Equation:

    • Plug values into the Nernst equation to find $E_{\text{cell}}$.

Example CalculationProblem: Calculate the cell potential for the following reaction under non-standard conditions:

Zn(s) + Cu²⁺(aq, 0.010 M) → Zn²⁺(aq, 1.0 M) + Cu(s)

Given:

  • E°<sub>cell</sub> = +1.10 V

  • n = 2

Solution:

1. Calculate Q:

Q = [Zn²⁺] / [Cu²⁺] = 1.0 / 0.010 = 100

2. Use the Simplified Nernst Equation:

E<sub>cell</sub> = E°<sub>cell</sub> - (0.0592/n) log Q E<sub>cell</sub> = 1.10 - (0.0592/2) log(100) E<sub>cell</sub> = 1.10 - (0.0296)(2) E<sub>cell</sub> = 1.10 - 0.0592 E<sub>cell</sub> = 1.04 V

Conclusion: The cell potential under these conditions is 1.04 V.

Video Resources