Question

When measured on a spectrometer operating at \(200 \mathrm{MHz}\), chloroform \(\left(\mathrm{CHCl}_{3}\right)\) shows a single sharp absorption at \(7.3 \delta .\) (a) How many parts per million downfield from TMS does chloroform absorb? (b) How many hertz downfield from TMS would chloroform absorb if the measurement were carried out on a spectrometer operating at \(360 \mathrm{MHz} ?\) (c) What would be the position of the chloroform absorption in \(\delta\) units when measured on a 360 MHz spectrometer?

Short answer

(a) 7.3 ppm; (b) 2628 Hz; (c) 7.3 δ (ppm).

Step-by-step solution

Understanding the Concept

Nuclear Magnetic Resonance (NMR) spectroscopy measures the absorption of radiofrequency radiation by nuclei. The position of the resonance is measured in terms of a shift (difference in absorption frequency) from a standard, usually Tetramethylsilane (TMS). This shift is expressed in parts per million (ppm), denoted as δ, and is calculated with respect to the operating frequency of the spectrometer.

Calculating ppm for Chloroform

Chloroform is measured at 7.3 δ on a 200 MHz spectrometer. Since δ is already in ppm by definition, the absorption of chloroform is 7.3 ppm downfield from TMS for this measurement.

Calculating Hertz Downfield at 360 MHz

The shift in hertz can be calculated using the formula: \[\text{Shift in Hz} = \delta \times \text{Spectrometer Frequency}\]For a 360 MHz spectrometer:\[\text{Shift in Hz} = 7.3 \times 360 = 2628 \text{ Hz}\]

Calculating δ on a 360 MHz Spectrometer

The ppm value of δ generally remains constant regardless of the spectrometer frequency. Therefore, even on a 360 MHz spectrometer, the δ value for chloroform remains 7.3 ppm. This characteristic ensures consistent chemical shift representation across different spectrometers.

Key concepts

Chemical Shift

In NMR spectroscopy, the concept of chemical shift is essential for understanding how different nuclei in a molecule respond to external magnetic fields. Chemical shift indicates the position of an NMR absorption, expressed in parts per million (ppm) on a scale using Tetramethylsilane (TMS) as a reference point. This shift reflects the local magnetic environment around the nucleus.

• Nearby electronegative atoms or groups can induce shifts by deshielding the nucleus.
• The chemical shift helps in determining the structure and environment of molecules.

When you look at the chemical shift, you're seeing how different nuclei are influenced by electron cloud distributions, which in turn affect their resonance frequencies.

Spectrometer Frequency

Spectrometer frequency refers to the operating frequency of the NMR spectrometer, often measured in megahertz (MHz). This frequency is crucial because it determines how much energy is necessary to flip the nuclear spins.

• The frequency of the spectrometer is proportional to the strength of the magnetic field used.
• Higher frequencies allow for more detailed resolution in spectra analysis.

While the chemical shift in ppm remains constant, the actual frequency in hertz varies with different spectrometer frequencies, helping to understand and compare data across diverse instruments.

Parts Per Million

The unit "parts per million" (ppm) in NMR represents the ratio of the frequency shift relative to the total frequency of the spectrometer. This small-scale measurement allows chemists to effectively compare chemical shifts across different NMR machines.

• PPM provides a standardized scale for comparing shifts from the reference TMS.
• It accounts for differences in spectrometer frequencies by offering a relative shift value.

This scale is pivotal when analyzing complex mixtures, as it ensures that chemical shifts are not tied to any particular spectrometer frequency but can be universally understood.

Chloroform Absorption

Chloroform, represented as CHCl₃, is a common reference point in NMR studies due to its sharp and distinct peak. The absorption of chloroform provides important insights into the molecular structure of a sample. When using a spectrometer at 200 MHz, chloroform shows a single peak at 7.3 ppm

• This position is measured as a shift downfield from TMS.
• The peak’s location in hertz changes with spectrometer frequency, indicating flexibility in analysis.

Understanding chloroform absorption helps in identifying and analyzing specific patterns in molecular configurations, thereby aiding the interpretation of NMR spectra.