For a cell involving one electron at , the equilibrium constant for the cell reaction is :

Question

For a cell involving one electron  at , the equilibrium constant for the cell reaction is :

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🧠 The "Aha!" Moment
This is a core application of the Nernst equation at equilibrium. When a cell reaches equilibrium, its potential () drops to zero, and the standard potential () is purely a function of the equilibrium constant ().

🗺️ The Quantitative Route
1. The Equation: At , the relationship is:
   
2. Setup the Variables:
   - 
   -  (Given)
   - 
3. Plugging it in:
   
4. Solving for K:

⚡ The 30-Second Insight
Notice the numbers!  is exactly ten times . Since , the "power of

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