What is the cell potential for the reaction at 49 °C when [Fe²+] = 3.80 M and [Mg²+] = 0.210 M. Express your answer to three significant figures and include the appropriate units. ▸ View Available Hint(s) μA E= Value Submit y Units Mg(s) + Fe²+ (aq) →Mg²+ (aq) + Fe(s) ?

Chemistry
10th Edition
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
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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**Learning Goal:**
To learn how to use the Nernst equation.

The standard reduction potentials listed in any reference table are only valid at the common reference temperature of 25 °C and standard conditions of 1 M for solutions and 1 atm for gases. To calculate the cell potential at nonstandard conditions, one uses the Nernst equation:

\[ E = E^o - \frac{2.303RT}{nF} \log_{10} Q \]

Where:
- \( E \) is the potential in volts.
- \( E^o \) is the standard potential at 25 °C in volts.
- \( R = 8.314 \, \text{J/(K·mol)} \) is the gas constant.
- \( T \) is the temperature in kelvins.
- \( n \) is the number of moles of electrons transferred.
- \( F = 96,500 \, \text{C/mol e}^-\) is the Faraday constant.
- \( Q \) is the reaction quotient.

At the common reference temperature of 298 K, substituting each constant into the equation the result is:

\[ E = E^o - \frac{0.0592 \, \text{V}}{n} \log_{10} Q \]
Transcribed Image Text:**Learning Goal:** To learn how to use the Nernst equation. The standard reduction potentials listed in any reference table are only valid at the common reference temperature of 25 °C and standard conditions of 1 M for solutions and 1 atm for gases. To calculate the cell potential at nonstandard conditions, one uses the Nernst equation: \[ E = E^o - \frac{2.303RT}{nF} \log_{10} Q \] Where: - \( E \) is the potential in volts. - \( E^o \) is the standard potential at 25 °C in volts. - \( R = 8.314 \, \text{J/(K·mol)} \) is the gas constant. - \( T \) is the temperature in kelvins. - \( n \) is the number of moles of electrons transferred. - \( F = 96,500 \, \text{C/mol e}^-\) is the Faraday constant. - \( Q \) is the reaction quotient. At the common reference temperature of 298 K, substituting each constant into the equation the result is: \[ E = E^o - \frac{0.0592 \, \text{V}}{n} \log_{10} Q \]
**Title: Determining Electrochemical Cell Potential**

**Introduction:**

In this task, we aim to calculate the cell potential for a given reaction under specific conditions.

**Reaction:**

\[ \text{Mg(s)} + \text{Fe}^{3+}(\text{aq}) \rightarrow \text{Mg}^{2+}(\text{aq}) + \text{Fe(s)} \]

**Conditions:**

- Temperature: \(4^\circ \text{C}\)
- Concentration of \( \text{Fe}^{3+} \) = \(3.80 \, \text{M} \)
- Concentration of \( \text{Mg}^{2+} \) = \(0.210 \, \text{M} \)

**Objective:**

Express the answer to three significant figures and include the appropriate units.

**Instructions:**

1. Use the standard reduction potentials for magnesium and iron to calculate the overall cell potential.
2. Consider Nernst equation adjustments for the given concentrations and temperature.

**Input Fields:**

- Enter the calculated potential value and select the proper units in the input boxes provided.

**Resources:**

- View available hints for guidance.

**Graph/Diagram:**

There are no graphs or diagrams associated with this calculation task.

**Tools:**

A toolset including undo, redo, calculator, and help is available to facilitate the calculation.

**Submission:**

- After calculating, enter the value in the form \(E =\) [Value] [Units].

**Conclusion:**

To solve, apply electrochemical principles, considering concentration effects on the cell potential at the given temperature. 

Click "Submit" once done.
Transcribed Image Text:**Title: Determining Electrochemical Cell Potential** **Introduction:** In this task, we aim to calculate the cell potential for a given reaction under specific conditions. **Reaction:** \[ \text{Mg(s)} + \text{Fe}^{3+}(\text{aq}) \rightarrow \text{Mg}^{2+}(\text{aq}) + \text{Fe(s)} \] **Conditions:** - Temperature: \(4^\circ \text{C}\) - Concentration of \( \text{Fe}^{3+} \) = \(3.80 \, \text{M} \) - Concentration of \( \text{Mg}^{2+} \) = \(0.210 \, \text{M} \) **Objective:** Express the answer to three significant figures and include the appropriate units. **Instructions:** 1. Use the standard reduction potentials for magnesium and iron to calculate the overall cell potential. 2. Consider Nernst equation adjustments for the given concentrations and temperature. **Input Fields:** - Enter the calculated potential value and select the proper units in the input boxes provided. **Resources:** - View available hints for guidance. **Graph/Diagram:** There are no graphs or diagrams associated with this calculation task. **Tools:** A toolset including undo, redo, calculator, and help is available to facilitate the calculation. **Submission:** - After calculating, enter the value in the form \(E =\) [Value] [Units]. **Conclusion:** To solve, apply electrochemical principles, considering concentration effects on the cell potential at the given temperature. Click "Submit" once done.
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