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A friend wants you to invest in a new battery she has designed that produces 24 V in a single voltaic cell. Why should you be wary of investing in such a battery?
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Ch.19 - Electrochemistry
Tro4th EditionChemistry: A Molecular ApproachISBN: 9780134112831
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TOC.tableOfContents
- Ch.1 - Matter, Measurement & Problem Solving136
- Ch.2 - Atoms & Elements112
- Ch.3 - Molecules, Compounds & Chemical Equations159
- Ch.4 - Chemical Quantities & Aqueous Reactions140
- Ch.5 - Gases118
- Ch.6 - Thermochemistry106
- Ch.7 - Quantum-Mechanical Model of the Atom62
- Ch.8 - Periodic Properties of the Elements103
- Ch.9 - Chemical Bonding I: The Lewis Model104
- Ch.10 - Chemical Bonding II: Molecular Shapes & Valence Bond Theory89
- Ch.11 - Liquids, Solids & Intermolecular Forces73
- Ch.12 - Solids and Modern Material59
- Ch.13 - Solutions110
- Ch.14 - Chemical Kinetics140
- Ch.15 - Chemical Equilibrium78
- Ch.16 - Acids and Bases155
- Ch.17 - Aqueous Ionic Equilibrium176
- Ch.18 - Free Energy and Thermodynamics108
- Ch.19 - Electrochemistry118
- Ch.20 - Radioactivity and Nuclear Chemistry82
- Ch.21 - Organic Chemistry150
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Capitolo 19, Problema 112
The cell potential of this electrochemical cell depends on the gold concentration in the cathode half-cell. Pt(s) | H2(g, 1.0 atm) | H+(aq, 1.0 M) || Au3+(aq, ? M) | Au(s) What is the concentration of Au3+ in the solution if Ecell is 1.22 V?
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Identify the half-reactions for the electrochemical cell. The anode half-reaction involves hydrogen: \( \text{H}_2(g) \rightarrow 2\text{H}^+(aq) + 2e^- \). The cathode half-reaction involves gold: \( \text{Au}^{3+}(aq) + 3e^- \rightarrow \text{Au}(s) \).
Write the Nernst equation for the cell potential: \( E_{cell} = E^\circ_{cell} - \frac{RT}{nF} \ln Q \), where \( Q \) is the reaction quotient.
Determine the standard cell potential \( E^\circ_{cell} \) using standard reduction potentials: \( E^\circ_{cell} = E^\circ_{cathode} - E^\circ_{anode} \). Use standard reduction potentials for \( \text{Au}^{3+}/\text{Au} \) and \( \text{H}^+/\text{H}_2 \).
Calculate the reaction quotient \( Q \) using the Nernst equation: \( Q = \frac{1}{[\text{Au}^{3+}]} \) since the concentration of \( \text{H}^+ \) is 1.0 M and \( \text{H}_2 \) is at 1.0 atm.
Rearrange the Nernst equation to solve for \( [\text{Au}^{3+}] \): \( [\text{Au}^{3+}] = \exp\left(\frac{nF(E^\circ_{cell} - E_{cell})}{RT}\right) \). Substitute known values to find the concentration of \( \text{Au}^{3+} \).
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Nernst Equation
The Nernst Equation relates the cell potential (E) of an electrochemical cell to the concentrations of the reactants and products. It is expressed as E = E° - (RT/nF) ln(Q), where 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 cell potential under non-standard conditions, which is essential for determining the concentration of Au3+ in this scenario.
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01:17
The Nernst Equation
Standard Electrode Potentials
Standard electrode potentials (E°) are measured under standard conditions (1 M concentration, 1 atm pressure, and 25°C) and provide a reference for predicting the direction of redox reactions. Each half-reaction has a specific E° value, which can be used to calculate the overall cell potential. In this question, knowing the standard reduction potential for the Au3+/Au couple is crucial for determining the concentration of Au3+ when the cell potential is given.
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01:27Standard Cell Potential
Reaction Quotient (Q)
The reaction quotient (Q) is a measure of the relative concentrations of products and reactants at any point in a reaction. It is calculated using the formula Q = [products]/[reactants], where the concentrations are raised to the power of their coefficients in the balanced equation. In this electrochemical cell, Q will include the concentration of Au3+ and the concentration of H+ ions, and it is essential for applying the Nernst Equation to find the unknown concentration of Au3+ when the cell potential is specified.
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00:49Reaction Quotient Q
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