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Calculate the standard reduction potential for Ba2+ (aq) + 2 e- -> Ba(s) given that ∆G° = 16.7 kJ for the reaction Ba2+(aq) + 2Cl-(aq) -> BaCl2(s). Use any necessary data from Appendices B and D.
Ch.19 - Electrochemistry
Chapter 19, Problem 159
Consider a galvanic cell that utilizes the following half-reactions:
(b) What are the values of E° and the equilibrium constant K for the cell reaction at 25 °C?
Verified step by step guidance1
Identify the half-reactions involved in the galvanic cell and write their standard reduction potentials (E°).
Use the Nernst equation to calculate the standard cell potential (E°cell) by combining the half-reactions.
Write the overall balanced equation for the cell reaction.
Use the relationship between E°cell and the equilibrium constant K: E°cell = (RT/nF)lnK, where R is the gas constant, T is the temperature in Kelvin, n is the number of moles of electrons transferred, and F is Faraday's constant.
Solve for the equilibrium constant K using the calculated E°cell and the given temperature of 25 °C (298 K).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Galvanic Cell
A galvanic cell is an electrochemical cell that converts chemical energy into electrical energy through spontaneous redox reactions. It consists of two half-cells, each containing an electrode and an electrolyte. The flow of electrons from the anode to the cathode generates an electric current, and the cell potential (E°) can be calculated using standard reduction potentials.
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The Galvanic Cell
Standard Electrode Potential (E°)
The standard electrode potential (E°) is a measure of the tendency of a chemical species to be reduced, measured under standard conditions (1 M concentration, 1 atm pressure, and 25 °C). It is expressed in volts and is used to predict the direction of electron flow in electrochemical cells. The overall cell potential can be determined by subtracting the anode potential from the cathode potential.
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01:27Standard Cell Potential
Equilibrium Constant (K)
The equilibrium constant (K) is a dimensionless value that expresses the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. In electrochemistry, K can be related to the cell potential (E°) using the Nernst equation, indicating the extent to which a reaction favors products over reactants. A larger K value suggests a more favorable reaction.
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Related Practice
Textbook Question
A concentration cell has the same half-reactions at the anode and cathode, but a voltage results from different concentrations in the two electrode compartments.
(b) A similar cell has 0.10 M Cu2+ in both compartments. When a stoichiometric amount of ethylenediamine (NH2CH2CH2NH2) is added to one compartment, the measured cell potential is 0.179 V. Calculate the formation constant Kf for the complex ion Cu(NH2CH2CH2CH2)22+. Assume there is no volume change.
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Textbook Question
Consider the redox titration (Section 4.13) of 120.0 mL of 0.100 M FeSO4 with 0.120 M K2Cr2O7 at 25 °C, assuming that the pH of the solution is maintained at 2.00 with a suitable buffer. The solution is in contact with a platinum electrode and constitutes one half-cell of an electrochemical cell. The other half-cell is a standard hydrogen electrode. The two half-cells are connected with a wire and a salt bridge, and the progress of the titration is monitored by measuring the cell potential with a voltmeter. (a) Write a balanced net ionic equation for the titration reaction, assuming that the products are Fe3+ and Cr3+.
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Textbook Question
The nickel–iron battery has an iron anode, an NiO(OH) cathode, and a KOH electrolyte. This battery uses the follow-ing half-reactions and has an E° value of 1.37 V at 25 °C.
(b) Calculate ∆G° (in kilojoules) and the equilibrium con-stant K for the cell reaction at 25 °C.
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Textbook Question
Experimental solid-oxide fuel cells that use butane (C4H10) as the fuel have been reported recently. These cells contain composite metal/metal oxide electrodes and a solid metal oxide electrolyte. The cell half-reactions are (b) Use the thermodynamic data in Appendix B to calculate the values of E° and the equilibrium constant K for the cell reaction at 25 °C. Will E° and K increase, decrease, or remain the same on raising the temperature?
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Textbook Question
Experimental solid-oxide fuel cells that use butane (C4H10) as the fuel have been reported recently. These cells contain composite metal/metal oxide electrodes and a solid metal oxide electrolyte. The cell half-reactions are (c) How many grams of butane are required to produce a constant current of 10.5 A for 8.00 h? How many liters of gaseous butane at 20 °C and 815 mm Hg pressure are required?
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