Calculate `K_(sp)` if `(PbSO_(4))E_(cell)` at 298 K of this electrode is 0.236 V
`Pb(s)|PbSO_(4)(s)|underset(0.01M)(Na_(2)SO_(4)(aq))||underset(0.1M)(Pb(NO_(3))|Pb(s))`
`E_(cell)=E_(cell)^(@)-(0.059)/(2)log[(0.01)/(0.1)]`
`0.236=E_(cell)^(@)+(0.059)/(2)`
`E_(cell)^(@)=0.236-0.03=0.206-0.059log[K_(sp)]`

Explanation

To calculate the solubility product constant (Ksp) for lead(II) sulfate (PbSO4) based on the given cell potential (E_cell) and the Nernst equation, we can follow these steps:

### Step 1: Write down the Nernst equation
The Nernst equation relates the cell potential to the standard cell potential and the concentrations of the reactants and products. The equation is given as:
\[ E_{cell} = E_{cell}^0 - \frac{0.059}{n} \log \left( \frac{[Pb^{2+}][SO_4^{2-}]}{[PbSO_4]} \right) \]
where \( n \) is the number of electrons transferred in the reaction. For the dissolution of PbSO4, \( n = 2 \).
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