A voltaic cell using Cu²+/Cu and Al³+/Al half-cells is set up at standard conditions, and each compartment has a volume of 225 mL. What is the [Al³+] after the cell has delivered 0.120 A for 29.0 hours at 25°C? (E° for Cu²+/ Cu = 0.340 V and Eº for Al³+/AI = -1.660 V.)
A voltaic cell using Cu²+/Cu and Al³+/Al half-cells is set up at standard conditions, and each compartment has a volume of 225 mL. What is the [Al³+] after the cell has delivered 0.120 A for 29.0 hours at 25°C? (E° for Cu²+/ Cu = 0.340 V and Eº for Al³+/AI = -1.660 V.)
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
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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![### Electrochemistry Problem on Voltaic Cells
**Question Overview:**
A voltaic cell using Cu²⁺/Cu and Al³⁺/Al half-cells is set up at standard conditions. Each compartment has a volume of 225 mL. Calculate the concentration of Al³⁺ ions after the cell has delivered 0.120 A for 29.0 hours at 25°C. Use the following standard electrode potentials:
- \( E^° \) for Cu²⁺/Cu = 0.340 V
- \( E^° \) for Al³⁺/Al = -1.660 V
---
**Solution Steps:**
1. **Calculate Total Charge Delivered:**
Convert the current and time into Coulombs:
\[
\text{Charge (Q)} = \text{Current (I)} \times \text{Time (t)}
\]
\[
Q = 0.120 \, \text{A} \times (29.0 \, \text{hours} \times 3600 \, \text{seconds/hour})
\]
2. **Calculate Moles of Electrons:**
Using the formula:
\[
\text{Moles of electrons} = \frac{Q}{F}
\]
where \( F \) is Faraday's constant (96485 C/mol).
3. **Determine Moles of Al³⁺ Reacted:**
Balance the reaction and calculate moles of Al³⁺ formed or reacted.
4. **Calculate Final Concentration of Al³⁺:**
Using:
\[
\text{Concentration} = \frac{\text{Moles}}{\text{Volume (L)}}
\]
**Inputs and Controls:**
- Below the question is a keypad that can be used for inputting answers.
- Additional resources and tips can be accessed by tapping on the designated area.
**Note:**
This problem exemplifies a real-world application of electrochemical principles, combining theoretical knowledge with practical calculations commonly encountered in chemistry and physics studies.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbae483e7-f3a4-4a9a-ba35-bb8b04de3604%2F8b822d1f-503a-4b69-bcea-e3a0a731b868%2Fj0o7luh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Electrochemistry Problem on Voltaic Cells
**Question Overview:**
A voltaic cell using Cu²⁺/Cu and Al³⁺/Al half-cells is set up at standard conditions. Each compartment has a volume of 225 mL. Calculate the concentration of Al³⁺ ions after the cell has delivered 0.120 A for 29.0 hours at 25°C. Use the following standard electrode potentials:
- \( E^° \) for Cu²⁺/Cu = 0.340 V
- \( E^° \) for Al³⁺/Al = -1.660 V
---
**Solution Steps:**
1. **Calculate Total Charge Delivered:**
Convert the current and time into Coulombs:
\[
\text{Charge (Q)} = \text{Current (I)} \times \text{Time (t)}
\]
\[
Q = 0.120 \, \text{A} \times (29.0 \, \text{hours} \times 3600 \, \text{seconds/hour})
\]
2. **Calculate Moles of Electrons:**
Using the formula:
\[
\text{Moles of electrons} = \frac{Q}{F}
\]
where \( F \) is Faraday's constant (96485 C/mol).
3. **Determine Moles of Al³⁺ Reacted:**
Balance the reaction and calculate moles of Al³⁺ formed or reacted.
4. **Calculate Final Concentration of Al³⁺:**
Using:
\[
\text{Concentration} = \frac{\text{Moles}}{\text{Volume (L)}}
\]
**Inputs and Controls:**
- Below the question is a keypad that can be used for inputting answers.
- Additional resources and tips can be accessed by tapping on the designated area.
**Note:**
This problem exemplifies a real-world application of electrochemical principles, combining theoretical knowledge with practical calculations commonly encountered in chemistry and physics studies.
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