Question

The hydrogen deficiency index for a compound with molecular formula \(C_{13}H_9N_2O_4BrS\) is

• A. 9
• B. 10
• C. 13
• D. 8

Answer 1

The Correct Option is B

To determine the hydrogen deficiency index (HDI), also known as the degree of unsaturation, for the compound with a molecular formula of \(C_{13}H_9N_2O_4BrS\), we apply the following formula: 

The general formula for HDI is given by:

\(HDI = \frac{2C + 2 + N - X - H}{2}\)

Where:

• \(C\) is the number of carbon atoms
• \(H\) is the number of hydrogen atoms
• \(N\) is the number of nitrogen atoms
• \(X\) is the number of halogen atoms (Fluorine, Chlorine, Bromine, Iodine)

In this compound:

• \(C = 13\)
• \(H = 9\)
• \(N = 2\)
• \(O\) and \(S\) do not affect unsaturation directly, so they are omitted in the calculation of HDI.
• \(X = 1\) (since we have 1 Bromine atom)

Plugging these values into the formula gives:

\(HDI = \frac{(2 \times 13) + 2 + 2 - 1 - 9}{2} = \frac{26 + 2 + 2 - 1 - 9}{2}\)

Simplifying further:

\(HDI = \frac{20}{2} = 10\)

Thus, the hydrogen deficiency index of the given compound is 10. This means there are 10 degrees of unsaturation, which could be due to double bonds, rings, or a combination thereof.

Therefore, the correct answer is 10.