According to the standard reduction potentials:
`Pb^(2+)(aq) + 2e^(-) rightarrow Pb(s)` `E^(@) = -0.13V`
`Fe^(2+)(aq) + 2e^(-) rightarrow Fe(s)` `E^(@) = -0.44`
`Zn^(2+)(aq) + 2e^(-) rightarrow Zn(s)` `E^(@) = -0.76V`
Which species will reduce `Mn^(3+)` to `Mn^(2+) [E^(@) = 1.51V` but will NOT reduce `Cr^(3+) to Cr^(2+) [E^(@) = -0.40V]`

Options

A. Pb only
B. Zn only
C. Pb and Fe only
D. Pb, Fe, and Zn

Answer

To determine which species can reduce \( \text{Mn}^{3+} \) to \( \text{Mn}^{2+} \) but cannot reduce \( \text{Cr}^{3+} \) to \( \text{Cr}^{2+} \), we need to analyze the standard reduction potentials given for the reactions.

### Step 1: Identify the standard reduction potentials
We have the following standard reduction potentials:
- \( \text{Mn}^{3+} + e^- \rightarrow \text{Mn}^{2+} \) with \( E^\circ = 1.51 \, \text{V} \)
- \( \text{Cr}^{3+} + e^- \rightarrow \text{Cr}^{2+} \) with \( E^\circ = -0.40 \, \text{V} \)
- \( \text{Pb}^{2+} + 2e^- \rightarrow \text{Pb} \) with \( E^\circ = -0.13 \, \text{V} \)
- \( \text{Fe}^{2+} + 2e^- \rightarrow \text{Fe} \) with \( E^\circ = -0.44 \, \text{V} \)
- \( \text{Zn}^{2+} + 2e^- \rightarrow \text{Zn} \) with \( E^\circ = -0.76 \, \text{V} \)

### Step 2: Determine which species can reduce \( \text{Mn}^{3+} \)
To reduce \( \text{Mn}^{3+} \) to \( \text{Mn}^{2+} \), we need a species with a standard reduction potential that is **lower** than \( 1.51 \, \text{V} \).

- \( \text{Pb}^{2+} \) has \( E^\circ = -0.13 \, \text{V} \) (lower than \( 1.51 \, \text{V} \))
- \( \text{Fe}^{2+} \) has \( E^\circ = -0.44 \, \text{V} \) (lower than \( 1.51 \, \text{V} \))
- \( \text{Zn}^{2+} \) has \( E^\circ = -0.76 \, \text{V} \) (lower than \( 1.51 \, \text{V} \))

All these species can reduce \( \text{Mn}^{3+} \).

### Step 3: Determine which species cannot reduce \( \text{Cr}^{3+} \)
To not reduce \( \text{Cr}^{3+} \) to \( \text{Cr}^{2+} \), we need a species with a standard reduction potential that is **higher** than \( -0.40 \, \text{V} \).

- \( \text{Pb}^{2+} \) has \( E^\circ = -0.13 \, \text{V} \) (higher than \( -0.40 \, \text{V} \))
- \( \text{Fe}^{2+} \) has \( E^\circ = -0.44 \, \text{V} \) (not higher than \( -0.40 \, \text{V} \))
- \( \text{Zn}^{2+} \) has \( E^\circ = -0.76 \, \text{V} \) (not higher than \( -0.40 \, \text{V} \))

### Conclusion
The only species that can reduce \( \text{Mn}^{3+} \) to \( \text{Mn}^{2+} \) but cannot reduce \( \text{Cr}^{3+} \) to \( \text{Cr}^{2+} \) is \( \text{Pb}^{2+} \).

### Final Answer
**The species that will reduce \( \text{Mn}^{3+} \) to \( \text{Mn}^{2+} \) but will NOT reduce \( \text{Cr}^{3+} \) to \( \text{Cr}^{2+} \) is \( \text{Pb}^{2+} \).**