Ch.19 - Electrochemistry

Problem 99

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Chapter 19, Problem 99

What is the Fe2+: Sn2+ concentration ratio in the following cell at 25 °C if the measured cell potential is 0.35 V?

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Identify the half-reactions for the cell. The cell consists of Fe2+/Fe and Sn2+/Sn half-cells.

Write the standard reduction potentials for each half-reaction: Fe2+ + 2e- -> Fe (E° = -0.44 V) and Sn2+ + 2e- -> Sn (E° = -0.14 V).

Determine the overall cell reaction and calculate the standard cell potential (E°cell) using E°cell = E°cathode - E°anode.

Use the Nernst equation to relate the cell potential (Ecell) to the concentrations: Ecell = E°cell - (RT/nF) * ln(Q), where Q is the reaction quotient.

Solve for the concentration ratio [Fe2+]/[Sn2+] by rearranging the Nernst equation and substituting the given Ecell and calculated E°cell.

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Key Concepts

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

Nernst Equation

The Nernst Equation relates the cell potential to the concentrations of the reactants and products in an electrochemical cell. It is expressed as E = E° - (RT/nF) ln(Q), where E is the cell potential, E° is the standard cell potential, R is the gas constant, T is the temperature in Kelvin, n is the number of moles of electrons transferred, F is Faraday's constant, and Q is the reaction quotient. This equation allows us to calculate the concentration ratio of ions based on the measured cell potential.

Cell Potential

Cell potential, or electromotive force (EMF), is the voltage generated by an electrochemical cell when it is operating. It indicates the tendency of the cell to drive an electrochemical reaction. The measured cell potential can provide insights into the relative concentrations of the reactants and products, which is essential for determining the concentration ratio of Fe2+ to Sn2+ in this specific cell.

Reaction Quotient (Q)

The reaction quotient (Q) is a dimensionless number that reflects the ratio of the concentrations of products to reactants at any point in a reaction, not necessarily at equilibrium. For the given cell, Q can be expressed as [Fe2+]/[Sn2+]. By substituting Q into the Nernst Equation, we can solve for the concentration ratio of Fe2+ to Sn2+ based on the measured cell potential.

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Reaction Quotient Q

Related Practice

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Textbook Question

A galvanic cell has an iron electrode in contact with 0.10 M FeSO4 and a copper electrode in contact with a CuSO4 solu-tion. If the measured cell potential at 25 °C is 0.67 V, what is the concentration of Cu2+ in the CuSO4 solution?

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Textbook Question

The Nernst equation applies to both cell reactions and half-reactions. For the conditions specified, calculate the potential for the following half-reactions at 25 °C. (b)

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Textbook Question

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