Question

What is index of hydrogen deficiency? What is its formula?

Answer 1

The index of hydrogen deficiency is the number of rings and π bonds in a compound.

Explanation:

The formula for the index if hydrogen deficiency (IHD) is

`color(blue)(bar(ul(|color(white)(a/a)color(black)"IHD" = color(black)(1/2("2C" +2 + color(blue)("N") - color(red)("H") - color(green)("X"))color(white)(a/a)|)))" "`

where `"C", color(red)("H"), color(blue)("N")` and `color(green)("X")` are the numbers of each atom in the molecular formula.

For example, the formula for agelastatin A is `"C"_12"H"_13"BrN"_4"O"_3`

`"IHD" = 1/2(24 + 2 + 4 - 13 -1) = 16/2 = 8`

The molecule has eight rings and π bonds [8(r+π)].

The structural formula is

The molecule has four rings and four π bonds (IHD = 8).

I recommend that calculating the IHD be the FIRST THING you do when you know the molecular formula and are trying to determine the structure of an unknown compound,

Answer 2

Warning! Long Answer. The index of hydrogen deficiency is the number of rings and π bonds in a compound.

Explanation:

Here's a second method for determining the Index of hydrogen deficiency (IHD).

The method compares the number of hydrogen atoms in an alkane with those in an equivalent formula for the compound.

A. Hydrocarbons

The general formula for an alkane is `"C"_text(n)"H"_text(2n+2)`.

The general formula for an alkene or a cycloalkane is `"C"_text(n)"H"_text(2n)`.

Thus, each ring or π bond reduces the number of `"H"` atoms by two.

An example is butadiene, `"C"_4"H"_6`.

The formula for butane is `"C"_4"H"_10`.

We are missing four `"H"` atoms, so

`"IHD" = (10-6)/2 =4/2 = "2(r+π)"`

The molecule contains either two rings, two π bonds, or (1 ring + 1 π bond).

B. Halogen compounds

The formula for bromobutane is `"C"_4"H"_9"Br"`.

Replace the halogen with `"H"`, and the formula becomes `"C"_4"H"_10`.

`"IHD" = (10-10)/2 =0/2 = "0(r+π)`

The molecule contains no rings or π bonds.

C. Oxygen compounds

The formula for butanal is `"C"_4"H"_8"O"`.

Ignore the `"O"`, and the formula becomes `"C"_4"H"_8`.

`"IHD" = (10-8)/2 =2/2 = "1(r+π)`

The molecule contains either one ring or one π bond.

D. Nitrogen compounds

The formula for butanamine is `"C"_4"H"_11"N"`.

Replace the `"N"` with `"CH"`, and the formula becomes `"C"_4"H"_11"CH" = "C"_5"H"_12`.

The formula for a five-carbon alkane is `"C"_5"H"_12`.

`"IHD" = (12-12)/2 = 0/2 = "0(r+π)`

The molecule contains no rings or π bonds.

Example

For example, the formula for agelastatin A is `"C"_12"H"_13"BrN"_4"O"_3`. What is its IHD?

We do our replacements on the formula for agelastatin A:

`"C"_12"H"_13"BrN"_4"O"_3 = "C"_12"H"_13"H"("CH")_4 = "C"_16"H"_18`

The general formula for a 16-carbon alkane is `"C"_16"H"_34`.

`"IHD" = (34-18)/2 = 16/2 = "8(r+π)`

The structural formula is

The molecule has four rings and four π bonds (IHD = 8).

I recommend that calculating the IHD be the FIRST THING you do when you know the molecular formula and are trying to determine the structure of an unknown compound,