### Electrochemistry: Calculating the Equilibrium Constant**Given the following half-reactions:**\[ \text{AlF}_6^{3-} + 3e^- \rightarrow \text{Al} + 6\text{F}^- \hspace{1cm} E^\circ = -2.07\,V \]\[ \text{Al}^{3+} + 3e^- \rightarrow \text{Al} \hspace{1cm} E^\circ = -1.66\,V \]**Calculate the equilibrium constant at 25°C for the reaction:**\[ \text{Al}^{3+}(aq) + 6\text{F}^-(aq) \leftrightarrow \text{AlF}_6^{3-}(aq) \](Enter your answer to two significant figures.)\[ K = \_\_\_\_\_\_ \]---#### Detailed Explanation:- The provided half-reactions are used to determine the cell potential (\(E^\circ_{\text{cell}}\)).- The cell potential is calculated by determining the difference between the reduction potentials of the cathode and anode reactions.- Using the Nernst equation, the equilibrium constant (\(K\)) can be found from the cell potential.For more information on electrochemical cells and the Nernst equation, please refer to our extensive resources and detailed guides.

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Given the following actions: AIF +3e Al + 6F A13+ + 3e - Al 3- E = -2.07 V %3D E = -1.66 V %3D Calculate the equilibrium constant at 25°C for the reaction A1s+ (aq) + 6F (aq) AIF6 (aq) (Enter your answer to two significant figures.) K= %3D

Given the following actions: AIF +3e Al + 6F A13+ + 3e - Al 3- E = -2.07 V %3D E = -1.66 V %3D Calculate the equilibrium constant at 25°C for the reaction A1s+ (aq) + 6F (aq) AIF6 (aq) (Enter your answer to two significant figures.) K= %3D

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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Question

### Electrochemistry: Calculating the Equilibrium Constant

**Given the following half-reactions:**

\[ \text{AlF}_6^{3-} + 3e^- \rightarrow \text{Al} + 6\text{F}^- \hspace{1cm} E^\circ = -2.07\,V \]

\[ \text{Al}^{3+} + 3e^- \rightarrow \text{Al} \hspace{1cm} E^\circ = -1.66\,V \]

**Calculate the equilibrium constant at 25°C for the reaction:**

\[ \text{Al}^{3+}(aq) + 6\text{F}^-(aq) \leftrightarrow \text{AlF}_6^{3-}(aq) \]

(Enter your answer to two significant figures.)

\[ K = \_\_\_\_\_\_ \]

---

#### Detailed Explanation:

- The provided half-reactions are used to determine the cell potential (\(E^\circ_{\text{cell}}\)).
- The cell potential is calculated by determining the difference between the reduction potentials of the cathode and anode reactions.
- Using the Nernst equation, the equilibrium constant (\(K\)) can be found from the cell potential.

For more information on electrochemical cells and the Nernst equation, please refer to our extensive resources and detailed guides.

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