Ch.20 - Electrochemistry

Problem 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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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.

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.

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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Using the standard reduction potentials listed in Appendix E, calculate the equilibrium constant for each of the following reactions at 298 K: (c) 10 Br -1aq2 + 2 MnO4-1aq2 + 16 H+1aq2 ¡ 2 Mn2+1aq2 + 8 H2O1l2 + 5 Br21l2

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Open Question

Using the standard reduction potentials listed in Appendix E, calculate the equilibrium constant for each of the following reactions at 298 K: (a) Cu(s) + 2 Ag+(aq) → Cu2+(aq) + 2 Ag(s) (b) 3 Ce4+(aq) + Bi(s) + H2O(l) → 3 Ce3+(aq) + BiO+(aq) + 2 H+(aq) (c) N2H5+(aq) + 4 Fe(CN)6^3- (aq) → N2(g) + 5 H+(aq) + 4 Fe(CN)6^4-(aq)

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?

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Open Question

A voltaic cell is based on the reaction Sn(s) + I2(s) → Sn2+(aq) + 2 I-(aq). Under standard conditions, what is the maximum electrical work, in joules, that the cell can accomplish if 75.0 g of Sn is consumed?

Open Question

(a) In the Nernst equation, what is the numerical value of the reaction quotient, Q, under standard conditions? (b) Can the Nernst equation be used at temperatures other than room temperature?