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Ch.20 - Electrochemistry
All textbooksBrown 14th EditionCh.20 - ElectrochemistryProblem 57b,c
Chapter 20, Problem 57b,c

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 (b) if n = 2? (c) if n = 3?

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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: E° = (RT/nF) * ln(K).
Recognize that at 298 K, the Nernst equation simplifies to: E° = (0.0592 V/n) * log(K).
Substitute the given values into the simplified equation: 0.177 V = (0.0592 V/3) * log(K).
Solve for log(K) by rearranging the equation: log(K) = (0.177 V * 3) / 0.0592 V.
Calculate K by taking the antilogarithm (base 10) of the result from the previous step: K = 10^(log(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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Standard Cell Potential

Nernst Equation

The Nernst equation relates the cell potential to the concentrations of the reactants and products at non-standard conditions. It can be used to calculate the equilibrium constant (K) for a reaction by connecting E° to the Gibbs free energy change, allowing for the determination of K when E° and the number of electrons transferred (n) are known.
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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. It is a dimensionless value that reflects the extent to which a reaction proceeds; a large K indicates a reaction favoring products, while a small K suggests a preference for reactants. K can be derived from the standard cell potential using the relationship K = e^(nFE°/RT).
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Related Practice
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)

Textbook Question

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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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?