Book cover for General Chemistry: Principles and Modern Applications

General Chemistry: Principles and Modern Applications

Ralph H. Petrucci, F. Geoffrey Herring, Jeffry D. Madura, Carey Bissonnette

ISBN #9780132931281

11th Edition

3,230 Questions

293,395 Students Helped

Homework Questions

Summary

Learning Objectives

Key Concepts

Example Problems

Explanations

Common Mistakes

Summary

This chapter provides an in-depth understanding of electrochemistry through the measurement and analysis of electrode potentials, the practical relationships between cell potential, Gibbs free energy, and reaction equilibrium, and the impact of ion concentration variations on cell voltage via the Nernst equation. Additionally, applications such as battery operation and corrosion highlight the industrial and environmental relevance of these concepts.

Learning Objectives

1

Explain the concept and measurement of electrode potentials and standard electrode potentials.

2

Understand the relationship between cell potential (Ecell), Gibbs free energy (?G°), and the equilibrium constant (K).

3

Apply the Nernst equation to determine how concentration changes affect cell potential.

4

Analyze the working principles of batteries and understand the chemical basis of corrosion.

Key Concepts

CONCEPT

DEFINITION

Electrode Potential

The voltage difference between an electrode and its surrounding solution, measured relative to a reference electrode.

Standard Electrode Potential (E°)

The electrode potential measured under standard conditions (1 M concentration, 1 atm pressure, and 25°C) against the standard hydrogen electrode.

Cell Potential (Ecell)

The overall voltage of an electrochemical cell, calculated as the difference between the cathode and anode potentials.

Nernst Equation

An equation that relates the cell potential to the standard cell potential and the activities (or concentrations) of the reactants and products: Ecell = E°cell - (RT/nF) ln Q.

Gibbs Free Energy (ΔG°)

A thermodynamic quantity that is related to the cell potential via ΔG° = -nFE°cell, linking the electrochemical process with chemical spontaneity.

Activation Energy

The minimum energy required to initiate a chemical reaction, often discussed in kinetics but also important in understanding reaction mechanisms at electrodes.

Corrosion

An electrochemical process that leads to the deterioration of metals, often involving unwanted voltaic cells.

Example Problems

Example 1

From the observations listed, estimate the value of $E^{\circ}$ for the half-cell reaction $\mathrm{M}^{2+}(\mathrm{aq})+2 \mathrm{e}^{-} \longrightarrow \mathrm{M}(\mathrm{s})$ (a) The metal M reacts with HNO $_{3}(\mathrm{aq}),$ but not with $\mathrm{HCl}(\mathrm{aq}) ; \mathrm{M}$ displaces $\mathrm{Ag}^{+}(\mathrm{aq}),$ but not $\mathrm{Cu}^{2+}(\mathrm{aq})$ (b) The metal M reacts with HCl(aq), producing $\mathrm{H}_{2}(\mathrm{g}),$ but displaces neither $\mathrm{Zn}^{2+}(\text { aq })$ nor $\mathrm{Fe}^{2+}(\mathrm{aq}).$

Example 2

You must estimate $E^{\circ}$ for the half-cell reaction $\operatorname{In}^{3+}(\mathrm{aq})+$ $3 \mathrm{e}^{-} \longrightarrow \operatorname{In}(\mathrm{s}) .$ You have no electrical equipment, but you do have all of the metals listed in Table 19.1 and aqueous solutions of their ions, as well as $\operatorname{In}(\mathrm{s})$ and $\operatorname{In}^{3+}(\text { aq }) .$ Describe the experiments you would perform and the accuracy you would expect in your result.

Example 3

$E_{\text {cell }}^{\circ}=0.201 \mathrm{V}$ for the reaction $$\begin{aligned} 3 \mathrm{Pt}(\mathrm{s})+12 \mathrm{Cl}^{-}(\mathrm{aq})+2 \mathrm{NO}_{3}^{-}(\mathrm{aq})+8 \mathrm{H}^{+}(\mathrm{aq}) & \longrightarrow \\ 3\left[\mathrm{PtCl}_{4}\right]^{2-}(\mathrm{aq})+2 \mathrm{NO}(\mathrm{g})+4 \mathrm{H}_{2} \mathrm{O}(1) \end{aligned}$$ What is $E^{\circ}$ for the reduction of $\left[\mathrm{PtCl}_{4}\right]^{2-}$ to $\mathrm{Pt}$ in acidic solution?

Example 4

Ascorbic acid ($\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6},$ also commonly known as vitamin $C,$ can be used to reduce a wide variety oftransition metal ions. Given that $E_{\text {cell }}^{\circ}=0.71 \mathrm{V}$ for the reaction $\quad \mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6}(\mathrm{aq})+2 \mathrm{Fe}^{3+}(\mathrm{aq}) \rightarrow \mathrm{C}_{6} \mathrm{H}_{6} \mathrm{O}_{6}(\mathrm{aq})$ $+2 \mathrm{Fe}^{2+}(\mathrm{aq})+2 \mathrm{H}^{+}(\mathrm{aq}),$ what is $E^{\circ}$ for the half-cell reaction $\mathrm{C}_{6} \mathrm{H}_{6} \mathrm{O}_{6}(\mathrm{aq})+2 \mathrm{H}^{+}(\mathrm{aq})+2 \mathrm{e}^{-} \rightarrow \mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6}(\mathrm{aq}) ?$

Example 5

Given that $E_{\text {cell }}^{r}$ for the aluminum-air battery is 2.71 V, what is $E^{\circ}$ for the reduction half-cell reaction $\left[\mathrm{Al}(\mathrm{OH})_{4}\right]^{-}(\mathrm{aq})+3 \mathrm{e}^{-} \longrightarrow \mathrm{Al}(\mathrm{s})+4 \mathrm{OH}^{-}(\mathrm{aq}) ?$ [Hint: Refer to cell reaction (19.28).]

Step-by-Step Explanations

QUESTION

How do you calculate the cell potential (Ecell) of an electrochemical cell when the concentrations are not at standard state?

STEP-BY-STEP ANSWER:

Step 1: Identify the standard cell potential E°cell from standard electrode potentials of the cathode and anode.
Step 2: Write the reaction quotient Q using the concentrations (or pressures) of the reactants and products.
Step 3: Substitute the known values into the Nernst equation: Ecell = E°cell - (RT/nF)*ln Q. Use appropriate temperature and constant values (R = 8.314 J/mol·K, F = 96485 C/mol).
Step 4: Calculate the value of (RT/nF)*ln Q and subtract from E°cell.
Step 5: The final number obtained is the cell potential under the given non-standard conditions.
Final Answer: The resulting voltage from the calculation is the cell potential, Ecell.

Calculating Ecell using the Nernst Equation

QUESTION

How is the standard cell potential related to Gibbs free energy and the equilibrium constant of the reaction?

STEP-BY-STEP ANSWER:

Step 1: Recall the relationship between standard Gibbs free energy and cell potential: ΔG° = -nFE°cell.
Step 2: Recognize that ΔG° is also given by ΔG° = -RT ln K, where K is the equilibrium constant.
Step 3: Equate the two expressions to relate E°cell and K: -nFE°cell = -RT ln K.
Step 4: Rearrange to solve for the equilibrium constant: ln K = (nFE°cell)/(RT).
Step 5: Exponentiate both sides to find K: K = exp((nFE°cell)/(RT)).
Final Answer: The standard cell potential determines both ΔG° and K through the relationships ΔG° = -nFE°cell and K = exp((nFE°cell*nF)/(RT)).

Relating Ecell to ΔG° and K

Common Mistakes

Mixing up the sign conventions when calculating cell potentials from electrode potentials.
Forgetting to use standard conditions when determining E°, thereby misapplying the Nernst equation.
Confusing the relationship between ?G° and Ecell, particularly with respect to the sign (negative relationship).
Neglecting the effect of temperature on cell potential calculations using the Nernst equation.