` (a) CH_3 CONH_2 +KOH +Br_2 `
`(b ) CH_3 COOH + ` soda lime
` (c ) CH_3 COOAg +Br _2 `
All the three reactions show similarilty in :

Options

A. Descending of carbon atoms
B. Ascending of carbon atoms
C. both of (1) and (2)
D. None of the above

Answer

To analyze the three reactions given in the question and determine their similarity, we will evaluate each reaction step by step.

### Step 1: Analyze the First Reaction
**Reaction:** \( \text{CH}_3 \text{CONH}_2 + \text{KOH} + \text{Br}_2 \)

1. **Identify the Reactants:** The reactants are acetamide (\( \text{CH}_3 \text{CONH}_2 \)), potassium hydroxide (\( \text{KOH} \)), and bromine (\( \text{Br}_2 \)).
2. **Reaction Type:** This reaction is a degradation reaction known as the Hofmann degradation.
3. **Products Formed:** The acetamide reacts with KOH and Br2 to form methylamine (\( \text{CH}_3 \text{NH}_2 \)) and carbon dioxide (\( \text{CO}_2 \)).
4. **Carbon Loss:** The product formed has one less carbon atom than the original acetamide.

### Step 2: Analyze the Second Reaction
**Reaction:** \( \text{CH}_3 \text{COOH} + \text{soda lime} \)

1. **Identify the Reactants:** The reactants are acetic acid (\( \text{CH}_3 \text{COOH} \)) and soda lime (a mixture of sodium hydroxide and calcium oxide).
2. **Reaction Type:** This reaction is a decarboxylation reaction.
3. **Products Formed:** The acetic acid reacts with soda lime to produce methane (\( \text{CH}_4 \)) and carbon monoxide (\( \text{CO} \)).
4. **Carbon Loss:** The product formed has one less carbon atom than the original acetic acid.

### Step 3: Analyze the Third Reaction
**Reaction:** \( \text{CH}_3 \text{COOAg} + \text{Br}_2 \)

1. **Identify the Reactants:** The reactants are silver acetate (\( \text{CH}_3 \text{COOAg} \)) and bromine (\( \text{Br}_2 \)).
2. **Reaction Type:** This reaction is known as the Hund's-Decker reaction.
3. **Products Formed:** The silver acetate reacts with bromine to produce bromoethane (\( \text{CH}_3 \text{Br} \)) and silver bromide (\( \text{AgBr} \)).
4. **Carbon Loss:** The product formed has one less carbon atom than the original silver acetate.

### Conclusion
All three reactions result in the formation of products that have one less carbon atom than the original reactants. Therefore, the similarity in all three reactions is that they involve the loss of one carbon atom.

### Summary of Similarity
- **Similarity:** All three reactions lead to the formation of products that are one carbon atom less than the respective reactants.