Based on the data given below, the correct order of reducing power is:
`Fe_((aq.))^(3+) + e rarr Fe_((aq.))^(2+), E^(@) = +0.77 V`
`Al_((aq.))^(3+) + 3e rarr Al_((s)), E^(@) = -1.66 V`
`Br_(2(aq.)) + 2e rarr 2Br_((aq.))^(-), E^(@) = +1.08 V`

Options

A. `Br^(-) lt Fe^(2+) lt Al`
B. `Fe^(2+) lt Al lt Br^(-)`
C. `Al^(-) lt Br^(-) lt Fe^(2+)`
D. `Al^(-) lt Fe^(2+) lt Br^(-)`

Explanation

To determine the correct order of reducing power based on the given standard reduction potentials, we will follow these steps:

### Step 1: Understand the Concept of Reducing Power
Reducing power is related to the ability of a species to donate electrons. The higher the standard reduction potential (E°), the stronger the oxidizing agent, and consequently, the weaker the reducing agent. Therefore, to find the order of reducing power, we need to look at the standard reduction potentials provided and convert them to oxidation potentials.

### Step 2: Write Down the Given Standard Reduction Potentials
1. \( \text{Fe}^{3+} + e^- \rightarrow \text{Fe}^{2+}, \quad E^\circ = +0.77 \, \text{V} \)
2. \( \text{Al}^{3+} + 3e^- \rightarrow \text{Al(s)}, \quad E^\circ = -1.66 \, \text{V} \)
3. \( \text{Br}_2(aq) + 2e^- \rightarrow 2\text{Br}^-(aq), \quad E^\circ = +1.08 \, \text{V} \)

### Step 3: Convert Standard Reduction Potentials to Oxidation Potentials
To find the oxidation potential, we take the negative of the standard reduction potential:
1. For \( \text{Fe}^{3+}/\text{Fe}^{2+} \):
\[ E^\circ_{\text{oxidation}} = -0.77 \, \text{V} \]
2. For \( \text{Al}^{3+}/\text{Al} \):
\[ E^\circ_{\text{oxidation}} = +1.66 \, \text{V} \]
3. For \( \text{Br}_2/\text{Br}^- \):
\[ E^\circ_{\text{oxidation}} = -1.08 \, \text{V} \]

### Step 4: Determine the Reducing Power Order
The reducing power is inversely related to the oxidation potential. The higher the oxidation potential (more positive), the weaker the reducing agent. Therefore, we rank the oxidation potentials:
1. \( \text{Al} \) (highest oxidation potential: +1.66 V)
2. \( \text{Fe}^{2+} \) (middle oxidation potential: -0.77 V)
3. \( \text{Br}^- \) (lowest oxidation potential: -1.08 V)

### Step 5: Write the Order of Reducing Power
Based on the above analysis, the order of reducing power from strongest to weakest is:
1. \( \text{Al} \)
2. \( \text{Fe}^{2+} \)
3. \( \text{Br}^- \)

### Conclusion
Thus, the correct order of reducing power is:
**Al > Fe²⁺ > Br⁻**