(19) Consider the following redox reaction that occurs in a voltaic cell: Cr2+ (aq) + Cu2+ (aq) → Cr³+ (aq) + Cu+ (aq) If the cell is operating at 25°C, what is the value of the equilibrium constant (Kea)? (A) 1.41 x 10¹1 (B) 1.19 x 1018 (C) 5.53 x 105 (D) 2.79 x 1033 (E) 1.81 x 10-6
(19) Consider the following redox reaction that occurs in a voltaic cell: Cr2+ (aq) + Cu2+ (aq) → Cr³+ (aq) + Cu+ (aq) If the cell is operating at 25°C, what is the value of the equilibrium constant (Kea)? (A) 1.41 x 10¹1 (B) 1.19 x 1018 (C) 5.53 x 105 (D) 2.79 x 1033 (E) 1.81 x 10-6
Chemistry
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Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
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Chapter1: Chemical Foundations
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Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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![**Problem (19): Equilibrium Constant Calculation for a Voltaic Cell**
Consider the following redox reaction that occurs in a voltaic cell:
\[ \text{Cr}^{2+} (\text{aq}) + \text{Cu}^{2+} (\text{aq}) \rightarrow \text{Cr}^{3+} (\text{aq}) + \text{Cu}^{+} (\text{aq}) \]
**Question:**
If the cell is operating at 25°C, what is the value of the equilibrium constant (K_eq)?
**Options:**
- (A) \( 1.41 \times 10^{11} \)
- (B) \( 1.19 \times 10^{18} \)
- (C) \( 5.53 \times 10^{5} \)
- (D) \( 2.79 \times 10^{33} \)
- (E) \( 1.81 \times 10^{-6} \)
---
This problem requires an understanding of redox reactions and the calculation of equilibrium constants in electrochemical cells. The equilibrium constant, \( K_{eq} \), varies based on the Gibbs free energy change (ΔG°) for the reaction, which is linked to the cell potential (E°cell) by the following relationship:
\[ \Delta G° = -nFE°_{cell} \]
Where:
- \( \Delta G° \) is the standard Gibbs free energy change.
- \( n \) is the number of moles of electrons transferred in the reaction.
- \( F \) is the Faraday constant (\( 96,485 \, \text{C/mol} \)).
- \( E°_{cell} \) is the standard cell potential.
The relationship between the equilibrium constant \( K_{eq} \) and the Gibbs free energy is given by:
\[ \Delta G° = -RT \ln(K_{eq}) \]
Where:
- \( R \) is the universal gas constant (\( 8.314 \, \text{J/mol·K} \)).
- \( T \) is the temperature in Kelvin (\( 298 \, \text{K} \) for 25°C).
These equations allow for calculating \( K_{eq} \) based on \( E°_{cell} \). However, direct calculation isn't demonstrated here, the options listed are potential values of \(](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc94d9e95-0e25-4757-a170-f111f0abbe77%2F2ee007e8-7277-4179-b8c5-674f412289d3%2Fn8q4mfm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem (19): Equilibrium Constant Calculation for a Voltaic Cell**
Consider the following redox reaction that occurs in a voltaic cell:
\[ \text{Cr}^{2+} (\text{aq}) + \text{Cu}^{2+} (\text{aq}) \rightarrow \text{Cr}^{3+} (\text{aq}) + \text{Cu}^{+} (\text{aq}) \]
**Question:**
If the cell is operating at 25°C, what is the value of the equilibrium constant (K_eq)?
**Options:**
- (A) \( 1.41 \times 10^{11} \)
- (B) \( 1.19 \times 10^{18} \)
- (C) \( 5.53 \times 10^{5} \)
- (D) \( 2.79 \times 10^{33} \)
- (E) \( 1.81 \times 10^{-6} \)
---
This problem requires an understanding of redox reactions and the calculation of equilibrium constants in electrochemical cells. The equilibrium constant, \( K_{eq} \), varies based on the Gibbs free energy change (ΔG°) for the reaction, which is linked to the cell potential (E°cell) by the following relationship:
\[ \Delta G° = -nFE°_{cell} \]
Where:
- \( \Delta G° \) is the standard Gibbs free energy change.
- \( n \) is the number of moles of electrons transferred in the reaction.
- \( F \) is the Faraday constant (\( 96,485 \, \text{C/mol} \)).
- \( E°_{cell} \) is the standard cell potential.
The relationship between the equilibrium constant \( K_{eq} \) and the Gibbs free energy is given by:
\[ \Delta G° = -RT \ln(K_{eq}) \]
Where:
- \( R \) is the universal gas constant (\( 8.314 \, \text{J/mol·K} \)).
- \( T \) is the temperature in Kelvin (\( 298 \, \text{K} \) for 25°C).
These equations allow for calculating \( K_{eq} \) based on \( E°_{cell} \). However, direct calculation isn't demonstrated here, the options listed are potential values of \(
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