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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 (\(E_{cell} = E°_{cell} - \frac{RT}{nF} \ln{Q}\)), 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°, 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°C), and a pressure of 1 atm. By convention, E° values are measured relative to the standard hydrogen electrode (SHE), which is assigned a value of zero volts. A positive E° 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°_cell) and the concentrations of the reacting species. The Nernst equation is given by: \[E_{cell} = E°_{cell} - \frac{RT}{nF} \ln{Q}\] 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

Consider a galvanic cell based on the following half-reactions: $$\begin{array}{ll}{\text {}} & { \mathscr{E}^{\circ}(\mathbf{V}) } \\ \hline {\mathrm{Au}^{3+}+3 \mathrm{e}^{-} \longrightarrow \mathrm{Au}} & {1.50} \\\ {\mathrm{Mg}^{2+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{Mg}} & {-2.37}\end{array}$$ a. What is the standard potential for this cell? b. A nonstandard cell is set up at \(25^{\circ} \mathrm{C}\) with \(\left[\mathrm{Mg}^{2+}\right]=\) \(1.00 \times 10^{-5} \mathrm{M}\) . The cell potential is observed to be 4.01 \(\mathrm{V}\) . Calculate \(\left[\mathrm{Au}^{3}+\right]\) in this cell.

What reactions take place at the cathode and the anode when each of the following is electrolyzed? (Assume standard conditions.) a. 1.0 \(M \mathrm{NiBr}_{2}\) solution b. 1.0 \(M \mathrm{AlF}_{3}\) solution c. 1.0 \(M \mathrm{MnI}_{2}\) solution

Consider the following galvanic cell: Calculate the \(K_{s p}\) value for \(\mathrm{Ag}_{2} \mathrm{SO}_{4}(s) .\) Note that to obtain silver ions in the right compartment (the cathode compartment), excess solid \(\mathrm{Ag}_{2} \mathrm{SO}_{4}\) was added and some of the salt dissolved.

Assign oxidation numbers to all the atoms in each of the following: a. \(\mathrm{HNO}_{3} \quad\) g. \(\mathrm{PbSO}_{4}\) b. \(\mathrm{CuCl}_{2} \quad\) h. \(\mathrm{PbO}_{2}\) c. \(\mathrm{O}_{2} \quad\) i. \(\mathrm{Na}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\) d. \(\mathrm{H}_{2} \mathrm{O}_{2} \quad\) j. \(\mathrm{CO}_{2}\) e. $\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} \quad \mathrm{k} .\left(\mathrm{NH}_{0}\right)_{2} \mathrm{Ce}\left(\mathrm{SO}_{4}\right)_{3}$ f. \(\mathrm{Ag} \quad\) l. \(\mathrm{Cr}_{2} \mathrm{O}_{3}\)

A galvanic cell is based on the following half-reactions at $25^{\circ} \mathrm{C} :$ $$\begin{array}{c}{\mathrm{Ag}^{+}+\mathrm{e}^{-} \longrightarrow \mathrm{Ag}} \\\ {\mathrm{H}_{2} \mathrm{O}_{2}+2 \mathrm{H}^{+}+2 \mathrm{e}^{-} \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}}\end{array}$$ Predict whether \(\mathscr{E}_{\text{cell}}\) is larger or smaller than \(\mathscr{E}^{\circ}_{\text{cell}}\) for the following cases. a. [Ag1] 5 1.0 a. $\left[\mathrm{Ag}^{+}\right]=1.0 M,\left[\mathrm{H}_{2} \mathrm{O}_{2}\right]=2.0 M,\left[\mathrm{H}^{+}\right]=2.0 \mathrm{M}$ b. $\left[\mathrm{Ag}^{+}\right]=2.0 \mathrm{M},\left[\mathrm{H}_{2} \mathrm{O}_{2}\right]=1.0 M,\left[\mathrm{H}^{+}\right]=1.0 \times 10^{-7} \mathrm{M}$
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