Question

Predict the relative intensities and the coupling patterns of the signals in the \(^{1} \mathrm{H}\) NMR spectrum of 2-methylpropane (14.23).

Short answer

2-methylpropane's NMR shows a intense \( CH_3 \) singlet and a \( CH \) doublet.

Step-by-step solution

Understand the Molecule Structure

2-methylpropane is also known as isobutane with the chemical formula \( C_4H_{10} \). It consists of a central carbon atom bonded to three methyl groups and one hydrogen atom. This can be visualized as three identical \( CH_3 \) groups attached to a single carbon atom (\( CH \)).

Determine Proton Environments

Identify the distinct sets of protons that create different signals in the NMR. In 2-methylpropane, there are two unique proton environments: (1) The nine protons in the three methyl groups denoted as \( CH_3 \). (2) The single proton attached to the central carbon, \( CH \). As all methyl groups are equivalent, the \( CH_3 \) environments are identical.

Analyze the Coupling Patterns

Protons in an NMR spectrum interact with neighboring protons through coupling, which gives rise to distinct peaks. The \( CH \) proton will be coupled with the \( 9 \) equivalent \( CH_3 \) protons, showing a pattern of splitting described by the \( n+1 \) rule, resulting in a doublet (\( n=9 \), splits into 10 very closely spaced peaks appearing almost like a doublet due to small coupling constants). The \( CH_3 \) protons would exhibit a singlet, as they are equivalent and coupled with just one \( CH \) proton.

Predict Relative Intensities

The intensity of NMR signals is proportional to the number of equivalent protons they represent. The \( CH_3 \) signal from the \( 9 \) methyl protons will be much more intense compared to the \( CH \) signal which arises from only \( 1 \) proton. Generally, the \( CH_3 \) singlet will be nine times as intense as the \( CH \) doublet.

Key concepts

Proton Environments

In NMR spectroscopy, identifying different proton environments is crucial to interpreting spectra. Each unique environment represents a set of protons situated in a particular electronic field, often differentiated by their surrounding atoms or groups. In the case of 2-methylpropane, understanding the proton environments is straightforward. There are two distinct environments:

• The three methyl (H_3]) groups are equivalent because they are symmetrically arranged around the central carbon atom. All these protons experience the same electronic surroundings.
• The single proton attached to the central carbon, noted as H], forms a separate environment due to its unique position in the molecule.

This differentiation allows us to predict two sets of NMR signals: one for the nine equivalent methyl protons and another for the single central proton.

Chemical Shift

Chemical shift in NMR spectroscopy describes the variation of the signal position in the spectrum. The shift results from the electronic environment influencing the local magnetic field experienced by the nucleus. In 2-methylpropane, the methyl (H_3]) groups experience a shift likely occurring downfield relative to the central proton (H]). This downfield shift is due to the electron-donating nature of the methyl groups, which slightly shields the central carbon, moving the signal correspondingly. Chemical shifts are key because they hint at the structural surroundings of the protons. Typically, they are reported in parts per million (ppm), providing a standardized measure against a reference signal, usually MS (tetramethylsilane)]. In practice, careful analysis of these shifts helps elucidate molecular geometry and chemical properties.

Splitting Patterns

Splitting patterns arise in NMR due to interactions between nonequivalent neighboring protons, a phenomenon known as spin-spin coupling. The number of splits or peaks in the pattern is predicted by the +1] rule, where ] is the number of adjacent protons. For 2-methylpropane:

• The H] proton experiences splitting due to the nine equivalent methyl (H_3]) protons. Despite these nine protons, practical splitting appears as a doublet due to small coupling constants and the close spacing of peaks.
• Methyl (H_3]) protons do not show additional splitting since they only couple with one H] proton. This results in a simple singlet.

These patterns provide insights into how different proton environments influence each other within a molecule.

Signal Intensity

Signal intensity in NMR relates directly to the number of protons present in each environment, which determines the height of peaks in the spectrum. More protons equate to stronger signals. For 2-methylpropane:

• The methyl (H_3]) protons generate a strong signal because there are nine equivalent protons. This signal will be notably more intense compared to the H] proton's signal.
• By contrast, the single H] proton yields a much weaker signal. In proportional terms, the intensity of the H_3] singlet would be expected to be approximately nine times that of the H] doublet.

Understanding signal intensity is essential to quantify proton populations and gauge their relative environments in a molecule.

Coupling Constants

Coupling constants quantify the splitting pattern in a spectrum and measure the degree of interaction between coupled protons. They provide insights into the distance and spatial orientation between these protons. In 2-methylpropane:

• The coupling constant between the H] proton and the surrounding nine methyl (H_3]) protons is small. Because of this, the resultant doublet pattern appears more closely spaced than it would otherwise be.

These constants are typically expressed in hertz (Hz) and offer a window into the subtle interactions at play within the molecule, revealing how various protons influence each other's magnetic environments.