What is the index of hydrogen deficiencyd in the molecule `C_(12)H_(17)NO`?

Options

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

Answer

To find the index of hydrogen deficiency (IHD) for the molecule \( C_{12}H_{17}NO \), we can use the formula:

\[ IHD = 0.5 \times (2C + 2 - H - X + N) \]

Where:
- \( C \) = number of carbon atoms
- \( H \) = number of hydrogen atoms
- \( N \) = number of nitrogen atoms
- \( X \) = number of halogen atoms (which is 0 in this case)

### Step-by-Step Solution:

1. **Identify the number of each atom in the molecular formula**:
- From \( C_{12}H_{17}NO \):
- \( C = 12 \)
- \( H = 17 \)
- \( N = 1 \)
- \( X = 0 \) (since there are no halogens)

2. **Substitute the values into the IHD formula**:
\[ IHD = 0.5 \times (2 \times 12 + 2 - 17 - 0 + 1) \]

3. **Calculate the expression inside the parentheses**:
- Calculate \( 2 \times 12 = 24 \)
- Now substitute back:
\[ IHD = 0.5 \times (24 + 2 - 17 + 1) \]
- Simplify:
\[ IHD = 0.5 \times (24 + 2 - 17 + 1) = 0.5 \times (10) = 5 \]

4. **Conclusion**:
- The index of hydrogen deficiency (IHD) for the molecule \( C_{12}H_{17}NO \) is **5**.