Question

Let's say you have found a bottle of liquid in your garage. The label on the bottle only tells you that the formula is \(\mathrm{C}_{5} \mathrm{H}_{10}\). You obtain the \({ }^{1} \mathrm{H} \mathrm{NMR}\) spectrum of the unknown from the local university. The spectrum has signals at \(\delta 5.9\) (1 H, multiplet), \(5.1\) (1 H, doublet), \(5.0\) (1 H, doublet), \(2.0\) (2 H, quartet), \(1.4\) (2 H, looks like sextet), and \(0.9\) (3 H, triplet). What is the unknown liquid? Why are there six signals in the \({ }^{1} \mathrm{H}\) NMR spectrum?

Short answer

The unknown liquid is 3-methyl-1-butene. There are six signals because the molecule has six different hydrogen environments.

Step-by-step solution

Analyze Chemical Formula

The formula \(\mathrm{C}_{5} \mathrm{H}_{10}\) tells us that the unknown compound has 5 carbon atoms and 10 hydrogen atoms. This can suggest several possibilities, including branched and unbranched alkenes.

Count Hydrogen Atoms in NMR

Check the integration values from the \(^{1} \mathrm{H} \mathrm{NMR}\) spectrum: The spectrum has six signals with the following hydrogen counts: 1 H, 1 H, 1 H, 2 H, 2 H, and 3 H, which add up to 10 H. These match the formula \(\mathrm{C}_{5} \mathrm{H}_{10}\), confirming that all hydrogen atoms are accounted for.

Evaluate NMR Splitting Patterns

Observe the splitting patterns for the signals: \(\delta 5.9\) (multiplet), \(\delta 5.1\) (doublet), \(\delta 5.0\) (doublet), \(\delta 2.0\) (quartet), \(\delta 1.4\) (sextet), and \(\delta 0.9\) (triplet). These patterns give clues about the neighboring hydrogen atoms and indicate functional groups typical for alkenes and alkyl chains.

Identify Group Environments

Identify likely environments for each signal based on chemical shift and splitting: \(\delta 5.9\) indicates an unsaturated hydrogen (alkene), \(\delta 5.0/5.1\) indicate hydrogens adjacent to an alkene (vinyl hydrogens), \(\delta 2.0\) for hydrogens on carbons \(\alpha\) to a double bond, \(\delta 1.4\) for methylene groups in an alkyl chain, and \(\delta 0.9\) for a methyl group.

Propose Structure

Putting all these pieces together, a possible structure fitting these data points is 3-methyl-1-butene, CH3-CH2-CH=CH2. This structure accommodates all observed chemical shifts and splitting patterns.

Verify the Structure

Ensure that each part of the proposed structure accounts for each signal: 1 H at \(\delta 5.9\) (multiplet) for the hydrogen on the double bond, 1 H each at \(\delta 5.1\) and \(\delta 5.0\) (doublets) for the hydrogens on the alkene carbon, 2 H at \(\delta 2.0\) (quartet) for the \(\mathrm{CH}_2\) group next to the double bond, 2 H at \(\delta 1.4\) (sextet) for the \(\mathrm{CH}_2\) group further down the chain, and 3 H at \(\delta 0.9\) (triplet) for the terminal methyl group.

Key concepts

Understanding the Chemical Formula

The chemical formula \(\text{C}_5\text{H}_{10}\) gives us vital clues about the structure of the unknown liquid.
It indicates that the compound contains 5 carbon atoms and 10 hydrogen atoms.
This formula is characteristic of alkenes, including both branched and unbranched forms.
Alkenes have a double bond between at least two carbon atoms, which can influence the NMR spectrum.
If we consider all possible structures with 5 carbons and make sure they match this pattern, we can narrow down the list of candidate structures.

Identifying Number of Hydrogen Atoms

Analyzing the \({}^{1}\text{H} \text{NMR}\) spectrum involves counting hydrogen atoms.
This spectrum provides signals at \(\text{δ} 5.9, 5.1, 5.0, 2.0, 1.4, \text{ and } 0.9\) ppm.
The area under each NMR signal, known as integration, given in the spectrum corresponds to the number of hydrogen atoms responsible for each signal.
In this case, the integrals are 1H, 1H, 1H, 2H, 2H, and 3H.
Summing these numbers provides a total of 10 hydrogens, perfectly matching our initial formula \(\text{C}_5\text{H}_{10}\).
This reassures us that all hydrogen atoms in the molecule are accounted for in the NMR.

Understanding Splitting Patterns in NMR

Splitting patterns in NMR arise because of the magnetic interaction between nonequivalent hydrogen atoms.
Each hydrogen atom's signal can split into multiple peaks depending on the number of adjacent hydrogen atoms. This is known as coupling.
For example, a hydrogen adjacent to one hydrogen (n + 1 rule) will appear as a doublet, and a hydrogen adjacent to two hydrogens will appear as a triplet.
In this spectrum, we have several types of splitting:

• Multiplet at \(\text{δ} 5.9\),
• Doublets at \(\text{δ} 5.1 \text{ and } 5.0\),
• Quartet at \(\text{δ} 2.0\),
• Sextet at \(\text{δ} 1.4\),
• Triplet at \(\text{δ} 0.9\).

These patterns hint at the neighboring hydrogen atoms' arrangement, helping us build a more precise picture of the molecule.

Interpreting Chemical Shifts

Chemical shifts in NMR provide information on the chemical environment surrounding hydrogen atoms.
Hydrogen atoms in different environments will experience the magnetic field differently, causing them to resonate at different frequencies.
In this case:

• \text{δ} 5.9 signifies an unsaturated hydrogen (alkene),
• \text{δ} 5.0 \text{ and } 5.1 indicate vinyl hydrogens (adjacent to the double bond),
• \text{δ} 2.0 for hydrogens on carbons \(\text{α}\) to a double bond,
• \text{δ} 1.4 for methylene groups (in an alkyl chain),
• \text{δ} 0.9 for methyl groups (terminal position).

Matching these shifts with known values for various chemical environments helps us identify and confirm functional groups and their positions in the molecule.

Proposing the Structure

Bringing together all the information from chemical formula, hydrogen counts, splitting patterns, and chemical shifts allows us to propose a structure.
The signals and their characteristics suggest that the unknown compound is likely a branched alkene.
One plausible structure is 3-methyl-1-butene (CH\(_3\)-CH\(_2\)-CH=CH\(_2\)).
This structure aligns with each observed chemical shift and splitting pattern:

• 1H at \(\text{δ} 5.9\) (multiplet) - hydrogen on the double bond,
• 1H each at \(\text{δ} 5.1 \text{ and } 5.0\) (doublets) - hydrogens on the vinyl group,
• 2H at \(\text{δ} 2.0\) (quartet) - CH\(_2\) group adjacent to the double bond,
• 2H at \(\text{δ} 1.4\) (sextet) - methylene group further down the chain,
• 3H at \(\text{δ} 0.9\) (triplet) - terminal methyl group.

This structure satisfactorily accounts for all given signals in the \({}^{1}\text{H} \text{NMR}\) spectrum.