Which of the following is a formula of methanides:
(a) `Be_(2)C`
(b) `CaC_(2)`
(c) `Mg_(2)C_(3)`
(d) `Al_(4)C_(3)`

Options

A. only a,d
B. only a,b
C. only c,d
D. only b,d

Explanation

To determine which of the given options is a formula of methanides, we need to understand what methanides are. Methanides are derivatives of methane (CH₄) that contain the methanide ion (C⁴⁻). Let's analyze each option step by step.

### Step 1: Analyze Option (a) Be₂C
- **Chemical Name**: Beryllium carbide
- **Reaction with Water**:
\[ \text{Be}_2\text{C} + 4\text{H}_2\text{O} \rightarrow 2\text{Be(OH)}_2 + \text{CH}_4 \]
- **Conclusion**: The reaction produces methane (CH₄), which indicates that it can be associated with the methanide ion (C⁴⁻). Therefore, Be₂C can be considered a methanide.

### Step 2: Analyze Option (b) CaC₂
- **Chemical Name**: Calcium carbide
- **Reaction with Water**:
\[ \text{CaC}_2 + 2\text{H}_2\text{O} \rightarrow \text{Ca(OH)}_2 + \text{C}_2\text{H}_2 \]
- **Conclusion**: This reaction produces acetylene (C₂H₂) and calcium hydroxide, not methane. Therefore, CaC₂ is not a methanide.

### Step 3: Analyze Option (c) Mg₂C₃
- **Chemical Name**: Magnesium carbide
- **Reaction with Water**:
\[ \text{Mg}_2\text{C}_3 + 6\text{H}_2\text{O} \rightarrow 2\text{Mg(OH)}_2 + \text{C}_3\text{H}_4 \]
- **Conclusion**: The reaction produces propylene (C₃H₄), which indicates that it does not form the methanide ion. Therefore, Mg₂C₃ is not a methanide.

### Step 4: Analyze Option (d) Al₄C₃
- **Chemical Name**: Aluminum carbide
- **Reaction with Water**:
\[ \text{Al}_4\text{C}_3 + 12\text{H}_2\text{O} \rightarrow 4\text{Al(OH)}_3 + 3\text{CH}_4 \]
- **Conclusion**: This reaction produces methane (CH₄), indicating that it can be associated with the methanide ion (C⁴⁻). Therefore, Al₄C₃ can be considered a methanide.

### Final Conclusion
Based on the analysis:
- **Correct Options**: (a) Be₂C and (d) Al₄C₃ are methanides.
- **Incorrect Options**: (b) CaC₂ and (c) Mg₂C₃ are not methanides.

### Answer
The formulas of methanides are (a) Be₂C and (d) Al₄C₃.

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