The standard reduction potential for the half cell `:`
`NO_(3)^(c-)(aq)+2H^(c-) +e^(-) rarr NO_(2)(g)+H_(2)O` is `0.78V`.
`a.` Calculate the reduction potential in `8M H^(o+)`.
`b.` What will be the reduction potential of the half cell in a neutral solution ? Assume all the other species to be at unit concentration.

Explanation

To solve the problem step by step, we will use the Nernst equation to calculate the reduction potentials for the given half-cell reaction in two different conditions.

### Given:
- Standard reduction potential (E°) = 0.78 V
- Half-cell reaction:
\[ \text{NO}_3^{-} (aq) + 2 \text{H}^{+} (aq) + e^{-} \rightarrow \text{NO}_2 (g) + \text{H}_2\text{O} \]
...