Open Question
If the equilibrium constant for a one-electron redox reaction at 298 K is 8.7 * 10^4, calculate the corresponding ∆G° and E°.
Ch.20 - Electrochemistry
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?
Verified step by step guidance1
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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01:27
Standard Cell Potential
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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01:17The Nernst Equation
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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01:14Equilibrium Constant K
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: (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 (b) if n = 2? (c) if n = 3?
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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
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