What is the index of hydrogen deficiency in the molecule C₁₂H₁₇NO?

4
5
6
7

The Index of Hydrogen Deficiency (IHD), also known as the Degree of Unsaturation, is a measure of the number of rings and/or multiple bonds (double or triple bonds) in a molecule. It can be calculated using the formula:

\[
\text{IHD} = C + 1 + \frac{N}{2} - \frac{H}{2} - \frac{X}{2}
\]

Where:
- \(C\) = number of carbon atoms
- \(H\) = number of hydrogen atoms
- \(N\) = number of nitrogen atoms
- \(X\) = number of halogens (F, Cl, Br, I)

### Given Molecule: \({{C}_{12}}{{H}_{17}}{NO}\)

1. **Identify the elements:**
- Carbon (\(C\)): 12
- Hydrogen (\(H\)): 17
- Nitrogen (\(N\)): 1
- Halogens (\(X\)): 0 (none present)

2. **Substitute values into the formula:**
\[
\text{IHD} = 12 + 1 + \frac{1}{2} - \frac{17}{2} - \frac{0}{2}
\]

\[
\text{IHD} = 12 + 1 + 0.5 - 8.5
\]

3. **Calculate:**
\[
\text{IHD} = 12 + 1 + 0.5 - 8.5 = 5
\]

### Conclusion:
The index of hydrogen deficiency (IHD) for the molecule \({{C}_{12}}{{H}_{17}}{NO}\) is **5**.

Therefore, the correct answer is **2) 5**.