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Ch.20 - Electrochemistry
All textbooksTro 5th EditionCh.20 - ElectrochemistryProblem 104
Chapter 20, Problem 104

Consider the reaction shown here occurring at 25°C. Cr(s) + Cd2+(aq) → Cr2+(aq) + Cd(s) Determine E°cell, K, and ∆G°rxn for the reaction and complete the table.
[Cd2+] [Cr2+] Q Ecell 𝚫Grxn
1.00 1.00
1.00 1.00 × 10-5
1.00 × 10-5 1.00
4.18 × 10-4 1.00
Table showing concentrations and values for electrochemical cell calculations in electrochemistry.

Verified step by step guidance
1
Step 1: Write the half-reactions for the given redox reaction. For Cr(s) to Cr2+(aq) and Cd2+(aq) to Cd(s).
Step 2: Determine the standard reduction potentials (E°) for each half-reaction from a standard reduction potential table.
Step 3: Calculate the standard cell potential (E°cell) using the formula E°cell = E°cathode - E°anode.
Step 4: Calculate the reaction quotient (Q) for each set of concentrations using the formula Q = [products]/[reactants].
Step 5: Use the Nernst equation to calculate the cell potential (Ecell) for each set of concentrations: Ecell = E°cell - (RT/nF) * ln(Q).

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Key Concepts

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

Electrochemical Cell

An electrochemical cell is a device that converts chemical energy into electrical energy through redox reactions. It consists of two electrodes, an anode where oxidation occurs, and a cathode where reduction takes place. The flow of electrons from the anode to the cathode generates an electric current, which can be harnessed for work.
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Nernst Equation

The Nernst equation relates the cell potential (E) of an electrochemical cell to the standard cell potential (E°) and the reaction quotient (Q). It is expressed as E = E° - (RT/nF)ln(Q), 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. This equation allows for the calculation of cell potential under non-standard conditions.
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Gibbs Free Energy (ΔGrxn)

Gibbs free energy (ΔGrxn) is a thermodynamic quantity that indicates the spontaneity of a reaction. It is defined as ΔGrxn = ΔH - TΔS, where ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy. A negative ΔGrxn indicates a spontaneous reaction, while a positive value suggests non-spontaneity. The relationship between ΔGrxn and cell potential (Ecell) is given by ΔGrxn = -nFEcell.
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