Question

The IR spectrum of a \(0.01 \mathrm{mol} \mathrm{dm}^{-3}\) solution of tertbutanol in \(\mathrm{CCl}_{4}\) shows a sharp peak at \(3610 \mathrm{cm}^{-1} ;\) in the IR spectrum of a similar \(1.0 \mathrm{mol} \mathrm{dm}^{-3}\) solution, this absorption is much diminished in intensity, but a very strong, broad peak at \(3330 \mathrm{cm}^{-1}\) is observed. Rationalize these observations.

Short answer

The shift and broadening from 3610 cm⁻¹ to 3330 cm⁻¹ in the IR spectrum are due to increased hydrogen bonding at higher concentrations of tertbutanol.

Step-by-step solution

Understanding IR Absorption

In infrared (IR) spectroscopy, the absorption of IR radiation by molecules causes them to vibrate at specific frequencies. The peaks at specific wave numbers in the IR spectrum are indicative of certain types of molecular vibrations, often corresponding to functional groups within a molecule. A peak at 3610 cm⁻¹ typically corresponds to a free O-H stretch, which is not involved in hydrogen bonding.

Analyze Observation in Dilute Solution

For the 0.01 mol dm⁻³ solution of tertbutanol in CCl₄, a sharp peak is observed at 3610 cm⁻¹. This indicates the presence of free O-H groups that are not hydrogen bonded, as this dilute concentration doesn't favor extensive hydrogen bonding between the alcohol molecules.

Analyze Observation in Concentrated Solution

In the 1.0 mol dm⁻³ solution, the sharp peak at 3610 cm⁻¹ diminishes, and a broad, strong peak at 3330 cm⁻¹ appears. The broad peak is characteristic of O-H groups involved in hydrogen bonding. As the concentration increases, the tendency for tertbutanol molecules to form hydrogen bonds also increases, leading to a shift and broadening of the peak.

Rationalize the Changes in IR Peaks

The disappearance of the sharp peak at 3610 cm⁻¹ and the appearance of the broad peak at 3330 cm⁻¹ in the concentrated solution is due to the hydrogen bonding. Hydrogen bonds cause a decrease in the vibrational frequency (shifts it to lower wave numbers) and broaden the peak because of the variation in hydrogen bond strengths.

Key concepts

Tertbutanol

Tertbutanol, also known as 2-methyl-2-propanol, is a type of alcohol with the molecular formula C₄H₁₀O. It is unique due to its tertiary carbon structure, where the hydroxyl group (-OH) is attached to a carbon atom bonded to three other carbon atoms. This structure influences how it interacts in chemical reactions and with other molecules. It is a colorless solid at room temperature but tends to exist as a liquid when slightly warm due to its low melting point (< 26 °C).
Tertbutanol is notable for its ability to both form and engage in hydrogen bonding due to the presence of the -OH group. This property substantially affects its behavior in solutions and its spectral characteristics when analyzed via infrared spectroscopy. By studying the IR spectrum of tertbutanol at different concentrations, we can learn more about how molecular interactions, specifically hydrogen bonding, manifest in various environmental conditions.

Hydrogen bonding

Hydrogen bonding is a special type of attractive interaction that occurs between a hydrogen atom which is covalently bonded to a more electronegative atom or group, such as oxygen or nitrogen, and another electronegative atom bearing a lone pair of electrons. In organic compounds like tertbutanol, hydrogen bonds are key in determining physical properties such as boiling point and solubility.
The ability of tertbutanol to form hydrogen bonds is noteworthy. At lower concentrations, the influence of hydrogen bonding is minimal, allowing many O-H groups to remain free (not hydrogen bonded). However, at higher concentrations, the proximity of molecules increases and so does the opportunity for O-H groups to establish hydrogen bonds with neighboring molecules. This results in significant changes in their infrared spectroscopy profile, as bonding affects vibrational frequencies and peak shapes.

O-H vibrational frequency

The O-H group in alcoholoic compounds like tertbutanol is key when investigating IR spectra, as it vibrates at more specific frequencies which can be analyzed. Free or unbonded O-H groups typically exhibit a vibrational frequency around 3610 cm⁻¹. This frequency corresponds to a sharp peak because there is a lack of complexity in the interactions involving these groups.
When hydrogen bonding occurs, the vibrational frequency shifts to lower wave numbers due to energy involvement in the bond formation process. For tertbutanol, we see this shift from 3610 cm⁻¹ to about 3330 cm⁻¹ in more concentrated solutions. This shift is a direct reflection of the intermolecular hydrogen bonds formed, which influence the vibrational energy and thus the frequency at which these groups absorb infrared light.

Peak broadening in IR spectroscopy

In IR spectroscopy, peak broadening is a phenomenon where a spectral line or peak appears wider than expected. This broadening often occurs because of the various strengths and environments of hydrogen bonds. In solutions where many interactions occur, such as with concentrated tertbutanol, the IR spectrum will show a broad peak for the O-H stretch.
This broadening is characteristic of hydrogen bonding, as molecules form bonds of varying strengths and lengths. Each slightly different bond interacts with infrared light differently, creating a variety of vibrational frequencies that collectively appear as a single broader peak. The more extensive and varied the hydrogen bonding, the broader the observed spectral peak. Thus, observing a broad peak at 3330 cm⁻¹ for a concentrated tertbutanol solution reflects a diverse range of hydrogen bonding interactions within the solution.