Question

What is the index of hydrogen deficiency in the molecule \[{{{C}}_{{{12}}}}{{{H}}_{{{17}}}}{{NO}}\]?
1) \[{{4}}\]
2) \[{{5}}\]
3) \[{{6}}\]
4) \[{{7}}\]

Answer 1

Hint:Index of hydrogen deficiency provides the number of multiple bonds and rings are present in the structure of the respective compound. In this formula we substituted a number of carbons, hydrogen, nitrogen and oxygen atoms present in the given compound.

Complete step by step answer:
Index of hydrogen deficiency can easily be calculated by drawing the structure of the compound. When we have the structure, we can count the number of multiple bonds and rings and that gives us the IHD count. But in some cases, we may not be aware of the structure of the compound. In these situations, we can use a simple formula for finding the hydrogen deficiency index.
If you are having a molecular formula of a compound like this \[{{{C}}_{{c}}}{{{H}}_{{h}}}{{{N}}_{{n}}}{{{O}}_{{o}}}{{{X}}_{{x}}}\], then we can write the formula as follows;
\[{{IHD = 0}}{{.5 \times [2c + 2 - h - x + n]}}\] ………………. (1)
Here we have the compound as \[{{{C}}_{{{12}}}}{{{H}}_{{{17}}}}{{NO}}\]which is considered to be an aromatic amine.
From the above equation we can have the values of c=12, h=17, n=1, o=1 and x=0
Substituting these values in the equation (1), we have
$ {{IHD = 0}}{{.5 \times [2 \times 12 + 2 - 17 - 0 + 1]}} \\
  {{ = 0}}{{.5 \times [24 - 14]}} \\
  {{ = 0}}{{.5 \times [10]}} \\
  {{ = 5}} $
This is the simplest way of finding out the index of hydrogen deficiency of a compound.
We can also find out it from the structure of the compound

\[{{{C}}_{{{12}}}}{{{H}}_{{{17}}}}{{NO}}\]
Here we can see four multiple bonds and a ring and the total value is five.
Therefore, the index of hydrogen deficiency or IHD of \[{{{C}}_{{{12}}}}{{{H}}_{{{17}}}}{{NO}}\] is five

So, the correct answer is Option 2.

Note: The compound \[{{{C}}_{{{12}}}}{{{H}}_{{{17}}}}{{NO}}\] is iso pentedrone. It is having great uses because of its medicinal value.The IHD value indicates the number of multiple bonds and rings in a compound. It can be easily calculated by using the IHD formula.