Q20E - Organic Chemistry (Mcmurry)

Question

The hormone cortisone contains C, H, and O, and shows a molecular ion at ${\mathbf{M}}^{\mathbf{+}}\mathbf{=}\mathbf{360}\mathbf{.}\mathbf{1937}$by high-resolution mass spectrometry. What is the molecular formula of cortisone? (The degree of unsaturation for cortisone is 8.)

Step-by-Step Solution

Answer

The molecular formula for cortisone is ${\mathrm{C}}_{21}{\mathrm{H}}_{28}{\mathrm{O}}_5$

Step 1: Step 1: Nitrogen rule

According to nitrogen rule an organic compound having odd molar mass contain odd number of nitrogen atoms and compound having even molar mass contain even number of nitrogen atoms.

Step 2: Calculating Molecular mass of camphor

High resolution mass spectrometry calculate exact mass of the fragments upto 5 ppm level.

We have given M⁺= 360.1937

Consider M⁺= 360

If the isotopic masses of the atom C,H and O had integral valueof 12 amu, 1 amu and 16 amu, many molecular formulas would corresponds to molecular weight of 360 amu. Because isotopic masses are not integral, however, only one molecular formula is associated with a molecular ion at 360.1937 amu.

To reduce the number of possible formulas, assume that the difference in molecular weight between 360 and 360.1937 is mainly due to hydrogen.

Divide 0.1937 by 0.00783, the amount by which the atomic weight of one 1H atom differs from 1.

                                       $\frac{0.1937}{0.00783}=24.7$

The answer 24.75 gives a “ballmark” estimate of the number of hydrogens in cortisone.

Then divide 360 by 12, to determine maximum number of carbons.

Since,$\frac{360}{12}=30$, we know that cortisone can have not more than 21 carbons if it also includes hydrogen and oxygen. Make a list of reasonable molecular formulas containing C, H and O whose mass is 360 and which contain 20 to 30 hydrogens. Tabulate this and calculate their exact atomic mass value in the text. The only possible formula for Cortisone is data-custom-editor="chemistry" ${\mathrm{C}}_{21}{\mathrm{H}}_{28}{\mathrm{O}}_5$ .          

Step 3:Tabulate and calculate the exact atomic mass

Isotopic mass

Molecular       Mass of      Mass of     Mass of      Mass of

formula carbons      hydrogen    oxygen     molecular ion

$$\begin{gathered} {\mathrm{C}}_{27}{\mathrm{H}}_{20}\mathrm{O} 324.0000 20.1565 15.9949 360.1514 \\ {\mathrm{C}}_{25}{\mathrm{H}}_{28}{\mathrm{O}}_2 300.0000 28.2191 31.9898 360.2089 \\ {\mathrm{C}}_{24}{\mathrm{H}}_{24}{\mathrm{O}}_{3 }288.0000 24.1878 47.9847 360.1725 \\ {\mathrm{C}}_{21}{\mathrm{H}}_{28}{\mathrm{O}}_5 252.0000 28.2191 79.9746 360.1937 \end{gathered}$$

The molecular weight of corresponds to the observed molecular weight of Cortisone. (Note that only the last formula has the correct degree of unsaturation, 8.)