Determining the realtive strengths of oxidizing and reducing agents
a. Arrange the following oxidizing agents in order of increasing strength unde standard-state conditions: `Br_(2)(1), Fe^(3+)(aq.), Cr_(2)O_(7)^(2-)(aq.)`
b. Arrange the following reducine agents in order of increasing strength under standard state condition: `Al(a), Na(s), Zn(s)`
Strategy: Pick our the half reactions in Table 3.1 that involve the given oxidizing or reducing agents and list them, along with their `E^(@)` value increases (i.e. becomes more positive) whereas the strength of a reducing agent increases as the `E^(@)` value decreases (i.e. becomes more negative).

Explanation

(a). List the half-reation that involve `Br_(2), Fe^(3+)`, and `Cr_(2)O_(7)^(2-)`, in the order in which they occur inTable 3.1
`Cr_(2)O_(7)^(2-)(aq.)+14H^(+)(aq.)+6e^(-)hArr2Cr^(3+)(aq.)+7H_(2)O(1)E^(@)=1.33V`
`Br_(2)(1)+2e^(-)hArr2Br^(-)(aq.)E^(@)=1.09V`
`Fe^(3)(aq.)+e^(-)hArr Fe^(2+)(aq.)E^(@)=0.77V`
We can see that `Cr_(2)O_(7)6(2-)` has the greatest tendency to be reduced (largest `E^(@)`), and `Fe^(3+)` has the least tendency (smallest `E^(@)`). The species that has the freatest tendency to be reduced is the strongest oxidizin agent. So oxidizing strength increases in the `Fe^(3+)ltBr_(2)ltCr_(2)O_(7)^(2-)`:
As a shortcut, cimply note that the strength of the oxidizing agents, listed on the left-side of Table 3.1, increases on moving up in the Table.
(b) List the half reactions that involve `Al(s), Na(s)` and `Zn(s)` in the order in which they occur in Table 3.1:
`Zn^(2+)(aq.) + e^(-) rarr Zn(s) E^(@) = 0.76 V`
`Al^(3+)(aq.) + 3e^(-) rarr Al(s) E^(@) = -1.66 V`
`Na^(+)(aq.) + e^(-) rarr Na(s) E^(@) = -2.71 V`
The last half-reaction has the least tendency to occur in the forward direction (most negative `E^(@)`) and the greatest tendency to occur in the reverse direction. Therefore, `Na` is the strongest reducing agent, and reducing strength increases in the order `Zn lt Al lt Na`. As a shortcut, note that the strength of the reduing agents, listed on the right side of Table 3.1, increases on moving down the table.