Formulas, isomer counts and spectra

From a formula to a structure

You are handed a liquid. Its molecular formula is $\text{C}_{4}\text{H}_{10}\text{O}$. Is it an alcohol or an ether? The formula alone cannot say. This lesson gives the tools that can.

The degree of unsaturation

For a compound of carbon, hydrogen and oxygen, the degree of unsaturation is $\dfrac{2C + 2 - H}{2}$. Oxygen does not count. It is the number of rings and double bonds. For $\text{C}_{4}\text{H}_{10}\text{O}$ it is $\dfrac{8 + 2 - 10}{2} = 0$. So the molecule is saturated: an alcohol or an ether, with no ring and no C=O.

Counting the isomers

The saturated compounds $\text{CnH}_{2}\text{n}+2\text{O}$ are alcohols and ethers. Their numbers grow quickly. The program below builds every one, and also finds which have a stereocentre (a carbon with four different groups).

• $\text{C}_{3}\text{H}_{8}\text{O}$: 2 alcohols, 1 ether, 3 isomers, none with a stereocentre.
• $\text{C}_{4}\text{H}_{10}\text{O}$: 4 alcohols, 3 ethers, 7 isomers, 1 with a stereocentre.
• $\text{C}_{5}\text{H}_{12}\text{O}$: 8 alcohols, 6 ethers, 14 isomers, 4 with a stereocentre.
• $\text{C}_{6}\text{H}_{14}\text{O}$: 17 alcohols, 15 ethers, 32 isomers, 13 with a stereocentre.

In $\text{C}_{4}\text{H}_{10}\text{O}$ the only isomer with a stereocentre is butan-2-ol. In $\text{C}_{5}\text{H}_{12}\text{O}$ the four are pentan-2-ol, 3-methylbutan-2-ol, 2-methylbutan-1-ol and 2-methoxybutane.

Infrared: is there an O-H bond?

A bond absorbs infrared light at a wavenumber that depends on its type.

• O-H of an alcohol or phenol: a strong, broad band at about $3200$ to $3600\ \text{cm}^{-1}$. The hydrogen bonds spread it.
• C-H: just below $3000\ \text{cm}^{-1}$.
• C-O of an alcohol or ether: a strong band between about $1000$ and $1300\ \text{cm}^{-1}$.
• C=O: about $1680$ to $1750\ \text{cm}^{-1}$. An alcohol or ether does not show it.

An ether shows the C-H and C-O bands and no O-H band. That one difference separates an alcohol from an ether of the same formula.

Proton NMR: how many kinds of hydrogen?

Each set of equivalent hydrogen atoms gives one signal.

• H on a carbon next to oxygen ($\text{H-C-O}$): about $3.3$ to $4.0$ ppm.
• O-H of an alcohol: a broad signal that moves with concentration and solvent, about $1$ to $5$ ppm. Shaking the sample with heavy water, $\text{D}_2\text{O}$, replaces the OH hydrogen with deuterium, and the signal disappears.
• O-H of a phenol: further downfield, about $4$ to $7$ ppm.

Count the signals. In 2-methylpropan-2-ol there are two: the nine equivalent hydrogens of the three methyl groups, and the OH. In ethoxyethane there are two: the six hydrogens of the methyl groups, and the four of the CH$_2$ groups. In butan-2-ol there are five: two methyl groups, the CH$_2$, the CH and the OH.

Mass spectrum: the molar mass and the pieces

The peak at the highest mass, the molecular ion, gives the molar mass. For $\text{C}_{4}\text{H}_{10}\text{O}$ it is $m/z = 74$. An alcohol often loses water, giving a peak at $M - 18$. An alcohol or ether also breaks next to the oxygen, and the charged piece that keeps the oxygen is seen. A primary alcohol gives a peak at $m/z = 31$, from $\text{CH}_2=\text{OH}^+$.

Zeisel's method: counting methoxy groups

Boil a methoxy compound with hydrogen iodide and the methyl group comes off as iodomethane: $\text{ROCH}_{3} + \text{HI} \to \text{ROH} + \text{CH}_{3}\text{I}$. The iodomethane is passed into silver nitrate, which precipitates silver iodide, one for each methoxy group. From the mass of silver iodide you find the percentage of OCH$_3$, and with the molar mass, the number of groups.

Vanillin, $\text{C}_{8}\text{H}_{8}\text{O}_{3}$, has one methoxy group and is about $20.4\ \%$ OCH$_3$ at a molar mass of $152\ \text{g/mol}$. The groups per molecule read as 1.

Practise with new numbers

Try it in Python

The program builds all the isomers of $\text{CnH}_{2}\text{n}+2\text{O}$ for three, four and five carbons, and counts the ones with a stereocentre.

Common mistakes

• Counting the oxygen in the degree of unsaturation. Oxygen does not change it.
• Expecting a sharp O-H band in an alcohol. It is broad.
• Counting the OH signal as fixed. It moves and disappears with $\text{D}_2\text{O}$.
• Counting each hydrogen as a signal. Equivalent hydrogens give one signal.
• Giving one silver iodide for each molecule. It is one for each OCH$_3$ group.

Remember these

• Degree of unsaturation $= (2C + 2 - H)/2$. Zero means no ring and no double bond.
• Broad band near 3350 cm$^{-1}$: O-H. An ether has C-O and no O-H.
• NMR signals count kinds of hydrogen. The OH signal disappears with $\text{D}_2\text{O}$.
• Zeisel: one AgI for each OCH$_3$.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. How many signals does the proton NMR spectrum of 2-methoxy-2-methylpropane show?

2. A compound $\text{C}_{4}\text{H}_{10}\text{O}$ shows a broad infrared band at 3350 cm$^{-1}$ and four NMR signals, one of which vanishes with $\text{D}_2\text{O}$. Which one is it, of butan-1-ol and 2-methylpropan-1-ol?

3. Which isomer of $\text{C}_{4}\text{H}_{10}\text{O}$ has a stereocentre?

4. What is the degree of unsaturation of $\text{C}_{4}\text{H}_{8}\text{O}_{2}$?

References

• A-Level and IB Chemistry data booklets and texts, for infrared absorption ranges and proton NMR shifts (the ranges given here are approximate).
• Morrison and Boyd, Organic Chemistry, the chapters on spectroscopy.
• Clayden, Greeves and Warren, Organic Chemistry, the chapters on spectroscopy.