Question

Calculate the index of hydrogen deficiency of cyclohexene, \(\mathrm{C}_{6} \mathrm{H}_{10}\) and account for this deficiency by reference to its structural formula.

Short answer

Answer: The index of hydrogen deficiency (IHD) of cyclohexene (C6H10) is 2. This deficiency is explained by the presence of a single double bond in its structural formula, which causes it to be unsaturated and have two fewer hydrogen atoms compared to its saturated counterpart, cyclohexane (C6H12).

Step-by-step solution

Understanding the Index of Hydrogen Deficiency (IHD) formula

The IHD is a calculation used to determine the degree of unsaturation in a molecule. It shows the number of double bonds, rings, or other structures that cause the molecule to be unsaturated. The general formula to calculate IHD is: IHD = \(\frac{2 * C + 2 + N - X - H}{2}\) , where C is the number of carbon atoms, N is the number of nitrogen atoms, X is the number of halogen atoms, and H is the number of hydrogen atoms in the molecule.

Calculation of IHD for Cyclohexene (C6H10)

Using the formula, and given the molecular formula of cyclohexene as C6H10, we can calculate the IHD: IHD = \(\frac{2 * 6 + 2 + 0 - 0 - 10}{2}\) = \(\frac{12 + 2 - 10}{2}\) = \(\frac{4}{2}\) = 2

Analyzing the Structure of Cyclohexene and accounting for the deficiency

Cyclohexene is a cyclic hydrocarbon with the molecular formula C6H10. Its structure contains one double bond which causes it to be unsaturated. This double bond removes two hydrogen atoms from the structure, explaining why the IHD is 2. In conclusion, cyclohexene has an index of hydrogen deficiency (IHD) of 2, which is due to the presence of a single double bond in its structural formula leading to a lower number of hydrogen atoms compared to the saturated hydrocarbon counterpart, cyclohexane (C6H12).