To find the standard potential of `M^(3+)//M` electrode , the following cell is constituted : `Pt|M|M^(3+((.001moLL^(-1)|| Ag ^(+) ((0.01moLL^(-1))|` Ag. The emf of the cell is found to be 0.421 volt at 298 K. The standard potential of half reaction `M^(3+)+ 3e^(-) to M` at 298 K will be :
(Given `E_(Ag^(+)//Ag^(@)` at 298 K = 0.80 Volt)

Options

A. (0.32Volt)
B. (0.66Volt)
C. (0.38VOlt)
D. (1.28Volt)

Explanation

To find the standard potential of the half-reaction \( M^{3+} + 3e^- \rightarrow M \) at 298 K, we can follow these steps:

### Step 1: Write the Nernst Equation
The Nernst equation relates the cell potential (E) to the standard electrode potential (\( E^0 \)) and the concentrations of the reactants and products:
\[ E_{cell} = E^0_{cell} - \frac{0.059}{n} \log Q \]
where \( n \) is the number of moles of electrons transferred, and \( Q \) is the reaction quotient.
...