Identify the metal `M` whose extraction is based on the following reactions:
`MS +2O_(2)rarr MSO_(4)`
`2MS +3O_(2)rarr 2MO +2SO_(2)`
`MS +2MO rarr 3M +SO_(2)`
`MS +MSO_(4) rarr 2M +2SO_(2)`

Options

A. `Mg`
B. `Pb`
C. `Sn`
D. `Fe`

Answer

To identify the metal \( M \) based on the given reactions, we will analyze each reaction step by step.

### Step 1: Analyze the first reaction
The first reaction is:
\[ MS + 2O_2 \rightarrow MSO_4 \]

This indicates that the metal \( M \) reacts with oxygen to form a metal sulfate \( MSO_4 \). This is a typical reaction for metal sulfides being oxidized.

### Step 2: Analyze the second reaction
The second reaction is:
\[ 2MS + 3O_2 \rightarrow 2MO + 2SO_2 \]

Here, we see that two moles of the metal sulfide \( MS \) react with oxygen to form metal oxide \( MO \) and sulfur dioxide \( SO_2 \). This suggests a reduction process where the metal sulfide is being oxidized.

### Step 3: Analyze the third reaction
The third reaction is:
\[ MS + 2MO \rightarrow 3M + SO_2 \]

In this reaction, the metal sulfide \( MS \) reacts with the metal oxide \( MO \) to produce the metal \( M \) and sulfur dioxide \( SO_2 \). This indicates a self-reduction process, where the metal oxide contributes to the reduction of the metal sulfide.

### Step 4: Analyze the fourth reaction
The fourth reaction is:
\[ MS + MSO_4 \rightarrow 2M + 2SO_2 \]

This reaction shows that the metal sulfide \( MS \) reacts with the metal sulfate \( MSO_4 \) to produce the metal \( M \) and sulfur dioxide \( SO_2 \). This is another self-reduction process.

### Conclusion
From the analysis of the reactions, it is clear that the metal \( M \) is involved in multiple self-reduction processes, which is characteristic of lead (Pb) extraction from its sulfide ore (lead sulfide, \( PbS \)). The reactions indicate that lead is oxidized to lead sulfate and lead oxide, and then reduced back to lead metal.

Thus, the metal \( M \) is **Lead (Pb)**.