A solution containing 0.20 M Pb²*, 1.5 × 10-6 M Pb** , 1.5 × 10-“ M Mn²+ , 0.20 M MnO, , and 0.88 M HNO, was prepared. For this solution, the balanced reduction half-reactions and overall net reaction shown can occur. 5 [Pb++ + 2e- = Pb²+] 2 [MnO, + 8 H* + 5e-= Mn²+ + 4H,0] 5 Pb** + 2 Mn²* + 8 H,0=5 Pb²* + 2MNO, + 16H* E; = 1.690 V E = 1.507 V Determine Eel, AG", and K for this reaction.

Chemistry
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Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
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Chapter1: Chemical Foundations
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Calculate the value for the cell potential, ?cellEcell, and the free energy, Δ?ΔG, for the given conditions.

 

Calculate the value of ?cellEcell for this system at equilibrium.

 

Determine the pH at which the given concentrations of Pb2+Pb2+ , Pb4+Pb4+ , Mn2+Mn2+ , and MnO−4MnO4− would be at equilibrium.

**Chemistry Problem: Determining Cell Potential and Free Energy**

A solution containing 0.20 M \( \text{Pb}^{2+} \), \( 1.5 \times 10^{-6} \) M \( \text{Pb}^{4+} \), \( 1.5 \times 10^{-6} \) M \( \text{Mn}^{2+} \), 0.20 M \( \text{MnO}_4^- \), and 0.88 M \( \text{HNO}_3 \) was prepared. For this solution, the balanced reduction half-reactions and overall net reaction shown can occur:

1. \( 5[\text{Pb}^{4+} + 2e^- \rightleftharpoons \text{Pb}^{2+}] \)
   - \( E^{o} = 1.690 \, \text{V} \)

2. \( 2[\text{MnO}_4^- + 8 \text{H}^+ + 5e^- \rightleftharpoons \text{Mn}^{2+} + 4 \text{H}_2\text{O}] \)
   - \( E^{o} = 1.507 \, \text{V} \)

**Overall Reaction:**

\[ 5\text{Pb}^{4+} + 2\text{Mn}^{2+} + 8 \text{H}_2\text{O} \rightleftharpoons 5\text{Pb}^{2+} + 2\text{MnO}_4^- + 16 \text{H}^+ \]

---

**Determine \( E_{\text{cell}}^{o} \), \( \Delta G^{o} \), and \( K \) for this reaction.**

\[ E_{\text{cell}}^{o} = \underline{\hspace{5cm}} \, \text{V} \]

\[ \Delta G^{o} = \underline{\hspace{5cm}} \, \text{J} \]

\[ K = \underline{\hspace{6cm}} \]

---

**Calculate the value for the cell potential, \( E_{\text{cell}} \), and the free energy, \( \Delta G \), for the given conditions.**

\[ E_{\text{cell}} = \underline
Transcribed Image Text:**Chemistry Problem: Determining Cell Potential and Free Energy** A solution containing 0.20 M \( \text{Pb}^{2+} \), \( 1.5 \times 10^{-6} \) M \( \text{Pb}^{4+} \), \( 1.5 \times 10^{-6} \) M \( \text{Mn}^{2+} \), 0.20 M \( \text{MnO}_4^- \), and 0.88 M \( \text{HNO}_3 \) was prepared. For this solution, the balanced reduction half-reactions and overall net reaction shown can occur: 1. \( 5[\text{Pb}^{4+} + 2e^- \rightleftharpoons \text{Pb}^{2+}] \) - \( E^{o} = 1.690 \, \text{V} \) 2. \( 2[\text{MnO}_4^- + 8 \text{H}^+ + 5e^- \rightleftharpoons \text{Mn}^{2+} + 4 \text{H}_2\text{O}] \) - \( E^{o} = 1.507 \, \text{V} \) **Overall Reaction:** \[ 5\text{Pb}^{4+} + 2\text{Mn}^{2+} + 8 \text{H}_2\text{O} \rightleftharpoons 5\text{Pb}^{2+} + 2\text{MnO}_4^- + 16 \text{H}^+ \] --- **Determine \( E_{\text{cell}}^{o} \), \( \Delta G^{o} \), and \( K \) for this reaction.** \[ E_{\text{cell}}^{o} = \underline{\hspace{5cm}} \, \text{V} \] \[ \Delta G^{o} = \underline{\hspace{5cm}} \, \text{J} \] \[ K = \underline{\hspace{6cm}} \] --- **Calculate the value for the cell potential, \( E_{\text{cell}} \), and the free energy, \( \Delta G \), for the given conditions.** \[ E_{\text{cell}} = \underline
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