Calculating half-reaction potential: Using the data in Table 3.1, find the standard potential of the half-reaction for the reduction of iron from the `+3` to the `0` oxidation state.
Strategy: Write the desired half-cell reaction:
`Fe^(3+)(aq.)+3e^(-)hArrFe(s)`
Inspect the table for half-reactions that include these oxidantion states of iron.

Explanation

The required half reactions are
`{:(Fe^(3+)(aq.)+e^(-)hArr Fe^(2+)(aq.)" "E^(@)=0.77V),(Fe^(2+)(aq.)+2e^(-)hArr Fe(s)" "E^(@)=-0.44V):}`
We see that the two half-reactions should be added to product the desired half-reaction. The `E^(@)` of the new half-reaction can be calculated by using Equation (3.13):
`E_(T)^(@) = (n_1E_1^(@)+n_2E_2^(@))/(n_(T))`
`= ((1)(0.77 V) + (2)(-0.044 V))/(3)`
`= -0.036`