Write the Nernst equation and calculate the EMF of the following cell at 298 K. Mg(s) / Mg2+ (0.001 M) // Cu²+ (0.0001 M) / Cu(s) Eº = -2.37 V Eº Cu² /Cu = 0.34 V; Mg/Mg
Write the Nernst equation and calculate the EMF of the following cell at 298 K. Mg(s) / Mg2+ (0.001 M) // Cu²+ (0.0001 M) / Cu(s) Eº = -2.37 V Eº Cu² /Cu = 0.34 V; Mg/Mg
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
Related questions
Question
![**Problem:**
Write the Nernst equation and calculate the EMF of the following cell at 298 K.
Cell representation: Mg(s) / Mg²⁺ (0.001 M) // Cu²⁺ (0.0001 M) / Cu(s)
Given:
- \( E^\circ_{\text{Cu}^{2+}/\text{Cu}} = 0.34 \, \text{V} \)
- \( E^\circ_{\text{Mg}^{2+}/\text{Mg}} = -2.37 \, \text{V} \)
**Solution:**
To calculate the EMF, we need to apply the Nernst equation.
**Nernst Equation:**
\[ E = E^\circ - \frac{RT}{nF} \ln Q \]
Where:
- \( E \) is the cell potential under non-standard conditions
- \( E^\circ \) is the standard cell potential
- \( R \) is the universal gas constant \((8.314 \, \text{J mol}^{-1} \text{K}^{-1})\)
- \( T \) is the temperature in Kelvin \((298 \, \text{K})\)
- \( n \) is the number of moles of electrons transferred in the reaction
- \( F \) is Faraday's constant \((96485 \, \text{C mol}^{-1})\)
- \( Q \) is the reaction quotient
**Standard Cell Potential Calculation:**
\[ E^\circ_{\text{cell}} = E^\circ_{\text{Cu}^{2+}/\text{Cu}} - E^\circ_{\text{Mg}^{2+}/\text{Mg}} \]
\[ E^\circ_{\text{cell}} = 0.34 \, \text{V} - (-2.37 \, \text{V}) \]
\[ E^\circ_{\text{cell}} = 2.71 \, \text{V} \]
**Reaction Quotient \( Q \):**
\[ Q = \frac{[\text{Mg}^{2+}]}{[\text{Cu}^{2+}]} \]
\[ Q = \frac{0.001}{0.0001} \]
\[ Q = 10 \]
**Applying the Nernst Equation:**
For this reaction, the number of electrons \(](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fab37e650-bdc6-40e6-877e-651c5d53a140%2F431dd69d-ad1c-4b33-9c03-4cf44808e294%2Fudaopj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem:**
Write the Nernst equation and calculate the EMF of the following cell at 298 K.
Cell representation: Mg(s) / Mg²⁺ (0.001 M) // Cu²⁺ (0.0001 M) / Cu(s)
Given:
- \( E^\circ_{\text{Cu}^{2+}/\text{Cu}} = 0.34 \, \text{V} \)
- \( E^\circ_{\text{Mg}^{2+}/\text{Mg}} = -2.37 \, \text{V} \)
**Solution:**
To calculate the EMF, we need to apply the Nernst equation.
**Nernst Equation:**
\[ E = E^\circ - \frac{RT}{nF} \ln Q \]
Where:
- \( E \) is the cell potential under non-standard conditions
- \( E^\circ \) is the standard cell potential
- \( R \) is the universal gas constant \((8.314 \, \text{J mol}^{-1} \text{K}^{-1})\)
- \( T \) is the temperature in Kelvin \((298 \, \text{K})\)
- \( n \) is the number of moles of electrons transferred in the reaction
- \( F \) is Faraday's constant \((96485 \, \text{C mol}^{-1})\)
- \( Q \) is the reaction quotient
**Standard Cell Potential Calculation:**
\[ E^\circ_{\text{cell}} = E^\circ_{\text{Cu}^{2+}/\text{Cu}} - E^\circ_{\text{Mg}^{2+}/\text{Mg}} \]
\[ E^\circ_{\text{cell}} = 0.34 \, \text{V} - (-2.37 \, \text{V}) \]
\[ E^\circ_{\text{cell}} = 2.71 \, \text{V} \]
**Reaction Quotient \( Q \):**
\[ Q = \frac{[\text{Mg}^{2+}]}{[\text{Cu}^{2+}]} \]
\[ Q = \frac{0.001}{0.0001} \]
\[ Q = 10 \]
**Applying the Nernst Equation:**
For this reaction, the number of electrons \(
Expert Solution
Step 1
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Introduction to Chemical Engineering Thermodynami…
Chemical Engineering
ISBN:
9781259696527
Author:
J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:
McGraw-Hill Education
Elementary Principles of Chemical Processes, Bind…
Chemical Engineering
ISBN:
9781118431221
Author:
Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:
WILEY
Elements of Chemical Reaction Engineering (5th Ed…
Chemical Engineering
ISBN:
9780133887518
Author:
H. Scott Fogler
Publisher:
Prentice Hall
Introduction to Chemical Engineering Thermodynami…
Chemical Engineering
ISBN:
9781259696527
Author:
J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:
McGraw-Hill Education
Elementary Principles of Chemical Processes, Bind…
Chemical Engineering
ISBN:
9781118431221
Author:
Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:
WILEY
Elements of Chemical Reaction Engineering (5th Ed…
Chemical Engineering
ISBN:
9780133887518
Author:
H. Scott Fogler
Publisher:
Prentice Hall
Industrial Plastics: Theory and Applications
Chemical Engineering
ISBN:
9781285061238
Author:
Lokensgard, Erik
Publisher:
Delmar Cengage Learning
Unit Operations of Chemical Engineering
Chemical Engineering
ISBN:
9780072848236
Author:
Warren McCabe, Julian C. Smith, Peter Harriott
Publisher:
McGraw-Hill Companies, The