(19) Consider the following redox reaction that occurs in a voltaic cell: Cr2+ (aq) + Cu²+ (aq) → Cr³+ (aq) + Cut (aq) If the cell is operating at 25°C, what is the value of the equilibrium constant (Keq)? (A) 1.41 x 10¹1 1.19 x 1018 5.53 x 105 2.79 x 1033 1.81 x 10-6 (B) (C) (D) (E)
(19) Consider the following redox reaction that occurs in a voltaic cell: Cr2+ (aq) + Cu²+ (aq) → Cr³+ (aq) + Cut (aq) If the cell is operating at 25°C, what is the value of the equilibrium constant (Keq)? (A) 1.41 x 10¹1 1.19 x 1018 5.53 x 105 2.79 x 1033 1.81 x 10-6 (B) (C) (D) (E)
Chemistry
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ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter18: Electrochemistry
Section: Chapter Questions
Problem 133CWP: Consider a galvanic cell based on the following half-reactions: a. What is the expected cell...
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![### Redox Reaction in a Voltaic Cell
**Problem Statement:**
Consider the following redox reaction that occurs in a voltaic cell:
\[ \text{Cr}^{2+} (\text{aq}) + \text{Cu}^{2+} (\text{aq}) \rightarrow \text{Cr}^{3+} (\text{aq}) + \text{Cu}^{+} (\text{aq}) \]
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) \( 1.81 \times 10^{6} \)
---
**Explanation:**
To determine the equilibrium constant (\(K_{eq}\)) for the given redox reaction at 25°C, it's essential to understand the relationship between the cell potential and the equilibrium constant. At standard conditions (25°C or 298 K):
\[ \Delta G^\circ = -RT \ln K_{eq} \]
For a voltaic cell:
\[ \Delta G^\circ = -nFE^\circ_{cell} \]
Where:
- \( \Delta G^\circ \) is the standard Gibbs free energy change.
- \( R \) is the universal gas constant (8.314 J/mol·K).
- \( T \) is the temperature in Kelvin (25°C = 298 K).
- \( n \) is the number of moles of electrons transferred in the balanced redox equation.
- \( F \) is the Faraday constant (96485 C/mol).
- \( E^\circ_{cell} \) is the standard cell potential.
By equating the equations for \( \Delta G^\circ \):
\[ -nFE^\circ_{cell} = -RT \ln K_{eq} \]
Simplifying and solving for \( K_{eq} \):
\[ \ln K_{eq} = \frac{nFE^\circ_{cell}}{RT} \]
\[ K_{eq} = e^{\left( \frac{nFE^\circ_{cell}}{RT} \right)} \]
Given these relationships, you](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc94d9e95-0e25-4757-a170-f111f0abbe77%2Ff06a861c-ce3d-4121-b3e8-ea98f6d0ef97%2Fl70okp9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Redox Reaction in a Voltaic Cell
**Problem Statement:**
Consider the following redox reaction that occurs in a voltaic cell:
\[ \text{Cr}^{2+} (\text{aq}) + \text{Cu}^{2+} (\text{aq}) \rightarrow \text{Cr}^{3+} (\text{aq}) + \text{Cu}^{+} (\text{aq}) \]
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) \( 1.81 \times 10^{6} \)
---
**Explanation:**
To determine the equilibrium constant (\(K_{eq}\)) for the given redox reaction at 25°C, it's essential to understand the relationship between the cell potential and the equilibrium constant. At standard conditions (25°C or 298 K):
\[ \Delta G^\circ = -RT \ln K_{eq} \]
For a voltaic cell:
\[ \Delta G^\circ = -nFE^\circ_{cell} \]
Where:
- \( \Delta G^\circ \) is the standard Gibbs free energy change.
- \( R \) is the universal gas constant (8.314 J/mol·K).
- \( T \) is the temperature in Kelvin (25°C = 298 K).
- \( n \) is the number of moles of electrons transferred in the balanced redox equation.
- \( F \) is the Faraday constant (96485 C/mol).
- \( E^\circ_{cell} \) is the standard cell potential.
By equating the equations for \( \Delta G^\circ \):
\[ -nFE^\circ_{cell} = -RT \ln K_{eq} \]
Simplifying and solving for \( K_{eq} \):
\[ \ln K_{eq} = \frac{nFE^\circ_{cell}}{RT} \]
\[ K_{eq} = e^{\left( \frac{nFE^\circ_{cell}}{RT} \right)} \]
Given these relationships, you
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