Physical Chemistry Third Edition

1016 24 Magnetic Resonance Spectroscopy

and the applied magnetic field at which absorption by thejth nucleus occurs is

B 0 j

hν

gNβN

+σjB 0 j (24.4-6)

For proton NMRtetramethyl silane(TMS), Si(CH 3 ) 4 , is chosen as a reference

substance. It has a single sharp spectral line and a rather large shielding constant,

3. 1 × 10 −^5 31 ppm (parts per million). The difference between the applied field

necessary for the reference substance to absorb and that necessary for a given proton

to absorb is called thechemical shiftof that nucleus. One variable used to specify the

chemical shift isδ, which is usually expressed in ppm. For nucleus numberj,

δj

B0ref−B 0 j

B0ref

× 106 ppm (24.4-7)

From Eq. (24.4-6) we can write:

δj

σrefB0ref−σjB 0 j

B0ref

× 106 ppm≈(σref−σj)× 106 ppm (24.4-8)

The approximate equality in Eq. (24.4-8) is valid to four significant digits, becauseB0ref

andB 0 jwill differ only by ten or twenty parts per million. The variableδordinarily lies

between 0 and 15 ppm, but there are a few substances containing protons with negative

values ofδ(larger shielding constants than TMS). A second variable used to specify

the chemical shift isτ:

τ10 ppm−δ (24.4-9)

The values of the shielding constant are related to the structure of the molecule,

because a larger electron density around the proton generally remains in a larger

shielding constant. If a proton is close to another nucleus of high electronegativity,

it will generally have a smaller electron density around it and a smaller shielding

constant. Its peak will appear “downfield” from the TMS peak at a relatively large

value ofδ. Table A.25 of Appendix A provides a list of typical values ofδfor

protons in different chemical environments. The values of δcan be different in

different substances with similar functional groups, but the table is useful as a general

guide.

An NMR spectrum is a graph in which a spectral line is represented by a peak. The

area under the peak is proportional to the number of nuclei producing the spectral line.

A low-resolution spectrum suffices to show the chemical shifts.

6543210

Absorbance

/ ppm

Figure 24.3 The Low-Resolution

Proton NMR Spectrum of 1-Prop-

anol (Simulated).

EXAMPLE24.12

Figure 24.3 shows schematically the low-resolution proton NMR spectrum of 1-propanol.

Interpret this spectrum.

Solution

The molecule contains protons in four kinds of electronic environments. The proton on the

oxygen is bonded to an electronegative atom, and has a smaller shielding constant and a

larger value ofδ. The first peak from the left, withδ 5 .8 and with relative area unity, is due

to this proton. The protons bonded to the carbinol carbon produce the second peak from the