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Ch.20 - Electrochemistry
Brown - Chemistry: The Central Science 14th Edition
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Not the one you use?Change textbook
All textbooksBrown 14th EditionCh.20 - ElectrochemistryProblem 57a
Chapter 20, Problem 57a

A cell has a standard cell potential of +0.177 V at 298 K. What is the value of the equilibrium constant for the reaction
(a) if n = 1?

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1
Identify the relationship between the standard cell potential (E°) and the equilibrium constant (K) using the Nernst equation at standard conditions.
Use the formula: E° = (RT/nF) * ln(K), where R is the universal gas constant (8.314 J/mol·K), T is the temperature in Kelvin (298 K), n is the number of moles of electrons transferred in the reaction, and F is Faraday's constant (96485 C/mol).
Rearrange the formula to solve for the equilibrium constant (K): ln(K) = (nF * E°) / (RT).
Substitute the given values into the equation: n = 1, E° = 0.177 V, R = 8.314 J/mol·K, T = 298 K, and F = 96485 C/mol.
Calculate ln(K) using the substituted values, and then find K by taking the exponential of ln(K).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Standard Cell Potential

The standard cell potential (E°) is the measure of the voltage produced by an electrochemical cell under standard conditions (1 M concentration, 1 atm pressure, and 298 K). It indicates the tendency of a chemical reaction to occur spontaneously; a positive E° suggests a spontaneous reaction, while a negative E° indicates non-spontaneity.
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Nernst Equation

The Nernst equation relates the cell potential to the concentrations of the reactants and products in an electrochemical reaction. It can be used to calculate the equilibrium constant (K) by connecting E° to the Gibbs free energy change (ΔG°) and the reaction quotient (Q), allowing for the determination of K at equilibrium.
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Equilibrium Constant (K)

The equilibrium constant (K) quantifies the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. It is derived from the standard cell potential and reflects the extent to which a reaction proceeds; a larger K indicates a greater tendency for products to form, while a smaller K suggests a preference for reactants.
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Related Practice
Textbook Question

A voltaic cell utilizes the following reaction: Al1s2 + 3 Ag+1aq2 ¡ Al3+1aq2 + 3 Ag1s2 What is the effect on the cell emf of each of the following changes? (a) Water is added to the anode half-cell, diluting the solution.

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Textbook Question

At 298 K a cell reaction has a standard cell potential of +0.17 V. The equilibrium constant for the reaction is 5.5 × 105. What is the value of n for the reaction?

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Textbook Question

Using the standard reduction potentials listed in Appendix E, calculate the equilibrium constant for each of the following reactions at 298 K:

(a) Fe(s) + Ni2+(aq) → Fe2+(aq) + Ni(s)

(b) Co(s) + 2 H+(aq) → Co2+(aq) + H2(g)

(c) 10 Br-(aq) + 2 MnO4-(aq) + 16 H+(aq) → 2 Mn2+(aq) + 8 H2O(l) + 5 Br2(l)

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