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Chapter 18: Problem 16

Is the following statement true or false? Concentration cells work because standard reduction potentials are dependent on concentration. Explain.

Short Answer

Expert verified
The statement is false. Concentration cells work because the actual cell potential, described by the Nernst equation (\(E_{cell} = E掳_{cell} - \frac{RT}{nF} \ln{Q}\)), is dependent on the concentration of the reacting species. The standard reduction potentials, determined under standard conditions, serve as reference values for the redox tendency of the species involved but do not directly depend on concentration.

Step by step solution

01

Understanding Concentration Cells

A concentration cell is a type of electrochemical cell, where both the half-cells (anode and cathode) have the same chemical species but at different concentrations. The cell generates its voltage because of the difference in concentrations of the reacting species. The overall cell reaction involves the transfer of ions from one half-cell to the other, resulting in a measurable voltage across the electrodes.
02

Understanding Standard Reduction Potentials

Standard reduction potential, denoted by E掳, is a measure of the tendency of a chemical species to acquire electrons and get reduced. These potentials are determined under standard conditions, which include a fixed ion concentration of 1 M, a temperature of 298.15 K (25掳C), and a pressure of 1 atm. By convention, E掳 values are measured relative to the standard hydrogen electrode (SHE), which is assigned a value of zero volts. A positive E掳 value suggests a species has a greater tendency to get reduced, while a negative value indicates a lesser tendency.
03

Relationship between Concentration and Standard Reduction Potentials

To understand the impact of concentration on the cell potential, we apply the Nernst equation, which relates the actual cell potential (E_cell) to the standard cell potential (E掳_cell) and the concentrations of the reacting species. The Nernst equation is given by: \[E_{cell} = E掳_{cell} - \frac{RT}{nF} \ln{Q}\] Here, R is the gas constant, T is the absolute temperature, n is the number of electrons transferred, F is the Faraday constant, and Q is the reaction quotient of the cell. The equation illustrates that the actual cell potential depends on the concentrations of the reacting species and varies with changes in concentration.
04

Analyzing the Statement

The given statement claims that concentration cells work because standard reduction potentials are dependent on the concentration. This statement is not entirely accurate. Concentration cells work because the actual cell potential, described by the Nernst equation, is dependent on the concentration. The standard reduction potential is determined under standard conditions (1 M concentration) and serves as a reference point. However, the actual cell potential is influenced by the differences in concentration between the half-cells, which drives the cell voltage.
05

Conclusion

The given statement is false. Concentration cells work because the actual cell potential, described by the Nernst equation, is dependent on the concentration of the reacting species. In contrast, the standard reduction potentials are determined under standard conditions and serve as reference values for the redox tendency of the species involved.

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Most popular questions from this chapter

A zinc-copper battery is constructed as follows at \(25^{\circ} \mathrm{C} :\) $$\mathrm{Zn}\left|\mathrm{Zn}^{2+}(0.10 M)\right|\left|\mathrm{Cu}^{2+}(2.50 M)\right| \mathrm{Cu}$$ The mass of each electrode is 200. g. a. Calculate the cell potential when this battery is first connected. b. Calculate the cell potential after 10.0 A of current has flowed for 10.0 h. (Assume each half-cell contains 1.00 L of solution.) c. Calculate the mass of each electrode after 10.0 h. d. How long can this battery deliver a current of 10.0 A before it goes dead?

Calculate \(\mathscr{E}^{\circ}\) and \(\Delta G^{\circ}\) for the reaction $$2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g)$$ at 298 \(\mathrm{K}\) . Using thermodynamic data in Appendix \(4,\) estimate \(\mathscr{E}^{\circ}\) and \(\Delta G^{\circ}\) at \(0^{\circ} \mathrm{C}\) and \(90 .^{\circ} \mathrm{C}\) . Assume \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) do not depend on temperature.

What is electrochemistry? What are redox reactions? Explain the difference between a galvanic and an electrolytic cell.

An electrochemical cell consists of a standard hydrogen electrode and a copper metal electrode. If the copper electrode is placed in a solution of 0.10\(M \mathrm{NaOH}\) that is saturated with \(\mathrm{Cu}(\mathrm{OH})_{2},\) what is the cell potential at \(25^{\circ} \mathrm{C} ?\left[\text { For } \mathrm{Cu}(\mathrm{OH})_{2}\right.\) \(K_{\mathrm{sp}}=1.6 \times 10^{-19} . ]\)

The black silver sulfide discoloration of silverware can be removed by heating the silver article in a sodium carbonate solution in an aluminum pan. The reaction is $$3 \mathrm{Ag}_{2} \mathrm{S}(s)+2 \mathrm{Al}(s) \rightleftharpoons 6 \mathrm{Ag}(s)+3 \mathrm{S}^{2-}(a q)+2 \mathrm{Al}^{3+}(a q)$$ a. Using data in Appendix \(4,\) calculate \(\Delta G^{\circ}, K,\) and \(\mathscr{E}^{\circ}\) for the above reaction at \(25^{\circ} \mathrm{C} .\left[\text { For } \mathrm{Al}^{3+}(a q), \Delta G_{\mathrm{f}}^{\circ}=-480 . \mathrm{kJ} / \mathrm{mol.}\right]\) b. Calculate the value of the standard reduction potential for the following half-reaction: $$2 \mathrm{e}^{-}+\mathrm{Ag}_{2} \mathrm{S}(s) \longrightarrow 2 \mathrm{Ag}(s)+\mathrm{S}^{2-}(a q)$$
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