To distinguish between nitrate salts of Mn²⁺ and Cu²⁺, we need to analyze their chemical properties and test behaviors. Let's evaluate each option step by step.

Step 1: Evaluate Option 1 - Flame Test

Mn²⁺ does not produce a characteristic green color in the flame test. Manganese compounds typically impart a pale green or no distinct color, but it is not a reliable test for identification. Copper compounds, however, produce a blue-green flame. This option is incorrect because Mn²⁺ does not show a characteristic green color.

Step 2: Evaluate Option 2 - Reduction Potential

The standard reduction potential for Cu²⁺/Cu is $E^{\circ }=+0.34V$, while for Mn²⁺/Mn it is $E^{\circ }=-1.18V$. Clearly, Cu²⁺/Cu has a higher reduction potential, meaning copper ions are more easily reduced than manganese ions. This is a factual statement but not a practical distinguishing test in a lab setting, as it requires electrochemical measurements rather than simple observation.

Step 3: Evaluate Option 3 - H₂S in Faintly Basic Medium

In a faintly basic medium, Mn²⁺ does not form a precipitate with H₂S because manganese sulfide (MnS) is soluble in acidic or neutral conditions but may precipitate in basic conditions; however, it is not a common test for distinction. Cu²⁺ forms a black precipitate of CuS in both acidic and basic media. This option is incorrect because Mn²⁺ does not reliably form a precipitate in faintly basic medium with H₂S, and Cu²⁺ would also precipitate.

Step 4: Evaluate Option 4 - H₂S in Acidic Medium

In acidic medium, Cu²⁺ forms a black precipitate of CuS with H₂S, while Mn²⁺ does not form a precipitate because MnS is soluble in acidic conditions. This is a standard qualitative analysis test where group II cations (like Cu²⁺) precipitate as sulfides in acidic medium, while group IV cations (like Mn²⁺) do not. Thus, this option is correct and practical for distinction.

Conclusion

Only option 4 is correct for distinguishing Mn²⁺ and Cu²⁺ nitrate salts using a simple lab test. Option 2 is theoretically true but not practical for immediate distinction.

Related Topics

Qualitative Analysis: This involves identifying ions based on precipitation, solubility, and other reactions. Understanding group separation and specific tests for cations is key.

Solubility Rules: Knowledge of which compounds precipitate under certain conditions (e.g., sulfides in acidic vs. basic media) is essential.

Electrochemistry: Reduction potentials indicate the tendency of ions to gain electrons, influencing reactivity and stability.

Key Formulae

Standard Reduction Potential: $E^{\circ }$ values compare the ease of reduction.

Precipitation Reaction: e.g., ${\mathrm{Cu}}^{2+}+H_{2}S\to \mathrm{CuS}\downarrow +2H^{+}$ (in acidic medium).