Following information are known abot a metal `M :`
`I.` A salt of metal M is used in the manufacture of gunpowder.
`II.` The superoxide of metal M is used as an air purifier in submarines.
`III.` The hydroxide of metal M is used for the absorption of gases like `CO_(2),SO_(2)`, etc. in eudiometry.
Identify the metal M `:`

Options

A. Sodium
B. Calcium
C. Magnesium
D. Potassium

Explanation

To identify the metal \( M \) based on the provided information, we can analyze each statement step by step.

### Step 1: Analyze the first statement
The first statement mentions that a salt of metal \( M \) is used in the manufacture of gunpowder. The primary component of traditional gunpowder is potassium nitrate (\( KNO_3 \)). This suggests that metal \( M \) could be potassium.

**Hint:** Consider common compounds used in gunpowder and identify the metal present in those compounds.

### Step 2: Analyze the second statement
The second statement states that the superoxide of metal \( M \) is used as an air purifier in submarines. The superoxide of potassium is potassium superoxide (\( KO_2 \)), which is known to absorb carbon dioxide (\( CO_2 \)) and release oxygen. This aligns with the description provided.

**Hint:** Look for metals that form superoxides and are used in applications related to air purification.

### Step 3: Analyze the third statement
The third statement indicates that the hydroxide of metal \( M \) is used for the absorption of gases like \( CO_2 \) and \( SO_2 \) in eudiometry. Potassium hydroxide (\( KOH \)) is commonly used for absorbing these gases in various chemical processes, including eudiometry.

**Hint:** Identify hydroxides that are commonly used for gas absorption and check if they correspond to the metal identified in previous steps.

### Conclusion
Based on the analysis of all three statements, the common metal identified is potassium (\( K \)). Therefore, the metal \( M \) is:

**Answer:** Potassium (\( K \))