How many secondary amines are possible for `C_(5)H_(13)N`

Options

A. 4
B. 5
C. 6
D. 7

Explanation

To determine how many secondary amines are possible for the molecular formula C₅H₁₃N, we can follow these steps:

### Step 1: Understand the Structure of Secondary Amines
Secondary amines have the general structure R₂NH, where R represents alkyl groups. This means that the nitrogen atom is bonded to two carbon-containing groups and one hydrogen atom.

### Step 2: Determine the Number of Carbon Atoms
The molecular formula C₅H₁₃N indicates that we have 5 carbon atoms available to form various alkyl groups attached to the nitrogen atom.

### Step 3: Identify Possible Combinations of Alkyl Groups
We need to create combinations of the 5 carbon atoms such that two of them are attached to the nitrogen atom. The remaining carbon atoms can be arranged in different ways to form secondary amines.

1. **Two Ethyl Groups (C₂H₅):**
- Structure: C₂H₅-NH-C₂H₅
- Formula: C₄H₁₁N (not valid since we need 5 carbons)

2. **One Ethyl and Three Methyl Groups:**
- Structure: C₂H₅-NH-CH₃
- Formula: C₅H₁₃N (valid)

3. **One Propyl and One Methyl Group:**
- Structure: C₃H₇-NH-CH₃
- Formula: C₄H₉N (not valid since we need 5 carbons)

4. **One Butyl Group and One Methyl Group:**
- Structure: C₄H₉-NH-CH₃
- Formula: C₅H₁₃N (valid)

5. **Two Isopropyl Groups:**
- Structure: (CH(CH₃)₂)₂NH
- Formula: C₆H₁₃N (not valid since we need 5 carbons)

### Step 4: List All Valid Secondary Amines
From the combinations analyzed, we can summarize the valid secondary amines:
1. **Ethyl and Methyl:** C₂H₅-NH-CH₃
2. **Butyl and Methyl:** C₄H₉-NH-CH₃

### Step 5: Count the Valid Secondary Amines
After analyzing the combinations, we find that there are **3 valid secondary amines** that can be formed with the molecular formula C₅H₁₃N.

### Final Answer
The total number of secondary amines possible for C₅H₁₃N is **3**.

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