A Qualitative-Quantitative'H-NMR Experiment for the
Instrumental Analysis Laboratory John S. Phillips' University of Wisconsin-River Falls. River Falls, WI 54022 James J. Leary James Madison University, Harrisonburg. VA 22807
Nuclear magnetic resonance (NMR) spectroscopy, although most widely used for qualitative analysis, may also he used for auantitative analvsis. A recent note in THIS JOURNAL^ oitlined an approach for quantitative mixture analvsis usine 'H-NMR. The basis of the quantitative use of 'H-NMR dehves from the direct proport~onalrelationship between the area of the proton resonance signal and the numher of protons in the observed resonance. This relationship has been proposed as amethod for the determination of the molecular weight of unknown compound^.^^^ The method, however, bas not been widely used. This note describes an undergr~dunteinstrumental analysis experiment for the determination of molerulnr weight and structure of an unknown romoound usine 'H-NMR. M'r have used this exoeriment in our instrumental analysis courses over the past five vears. The novel asoect of the experiment is that it requires the student to combine both q;antitative and qualitative information from 'H-NMR spectra. The experiment is simple and may be easily accom&ished in a ninnal laboratory period, assuming access to an NMR spectrometer. Theory The determination of the molecular weight of anunknown compound by NMR requires the use of an internal standard of known structure and molecular weight. Known masses of the unknown and internal standard are dissolved in an appropriate NMR solvent. The NMR spectrum of this mixture is obtained, and the relative areas of representative peaks from the standard and the unknown are determined by integration. The following brief derivation illustrates how the molecular weight - of the unknown may he determined by this method. From the mixture (weighed unknown and internal standard) NMR spectrum, the area of a peak or cluster of peaks due only to the internal standard (AI) is equal to a constant (k) times the numher of protons on the internal standard contributing to this peak (NI). This relationship is given by eq 1. A, = k(N1)
(1)
The number of protons (Nr) contributing to the NMR signal for the internal standard is given by eq 4, where mr represents the moles of internal standard and PI is the numher of protons per molecule of internal standard contributing to AI. Similarly, the number of protons contrihuting to the selected unknown signal (Nu) is given by Since the compound is unknown, Pu, the number of protons per molecule of unknown compound contributing to Au, is also an unknown. This problem is overcome by the use of the information contained in the 'H-NMR spectrum of the unknown compound, and some basic knowledge of chemical structure. If the unknown compound contains a t least two sets of nonoverlapping NMR peaks, indicating a t least two sets of structurally nonequivalent protons, the relative areas of the peaks in the pure unknown spectrum are used to provide information concerning the relative numher of protons contributing t o each set of peaks in the spectrum of the unknown. In conjunction with the other information from the 'H-NMR spectrum of the unknown (chemical shift, splitting patterns, coupling constants), this approach almost always allows for the selection of a chemically logical multiple for Pu. Equation 6 is obtained by substituting eqs 4 and 5 into eq 3
Finally, the numher of moles of internal standard in the mixture is equal to the mass of the internal standard ( Wr) divided by its molecular weight (MI). This relationship is expressed by eq 7; eq 8 is a similar relationship for the moles of the unknown compound in the mixture.
Assuming a constant amplifier gain, a similar relationship, eq 2, may be written for the area of any distinct cluster of peaks (A") due only to the unknown compound. A, = k ( N u )
(2)
The constant ( k ) is dependent upon many instrumental factors. Since all quantitative information for the molecular weieht determination is obtained from the mixture spect r u k , k is assumed to remain constant during the collection of this snectrum. Eouations 1and 2 mav he combined, therefore, to yield eq 3.
' Author to whom correspondence should be addressed.
Wallace. T. J. Chem. Educ. 1984, 61. 1074. Barcza. S.J. Org. Chem. 1963, 28,1914. 'Rahman, S. R.; Gennaro. A. R.; Zanger. M. Amer. Lab. 1981 (Nov.),42.
Equation 9 is obtained by substituting eqs 7 and 8 into eq 6 and rearranging t o solve for the molecular weight of the unknown (Mu).
where M c and M Iare the molecular weights of the unknown and the internal standards, WI. and WI are the masses of the unknown and the internal standards in mixture, Au and AI are the areas of selected unknown and internal standard Volume 63 Number 6 June 1986
545
Table 1. Tabulated data for 'H-NMR Spectra* P P ~
~uiilpli~lty
Relative Area
1.21 1.93 4.03
hiplet singlet quartet
pdichlorabenreneC
6.90
singlet
-
mixtured
1.21 1.93 4.03 6.90
triplet singlet quartet singlet
2.04 1.98
emyi acetated
Table 2. The Determlnatlon of Molecular Weight of Ethyl Acetate bv 'H-NMW
1.48 1.50
1.00
P P ~
1.21 1.93 4.03 average
5
M,
2.04
3
1.98 1.36
88.7
0.7
3
91.4 ... .
87
2
88.8 89.6
0.8
Au
~
~
.. .
...
% error
1.7
1.36 1.00
'Solvent = CCI,. Relatlvearesa of peaks Ineach indlvidval m u m isdetamlnodby atlolng average (N= 3) integrationsof each psaL In me spectrum. l"Unkn~wn". molw = 68.1. Llnternslstandard, mol wi = 147. '9.649 Q emvl acetate aw 0.395 g pdlchlorobanzane.
tative elemental comoosition of the unknown. the student determines the mo1ec;lar weight using eq 9 and structure of the unknown compound using qualitative information from the unknown NMR spectrum as well as the experimentally determined molecular weight. Results
NMR peaks, and PU and PI are the numbers of contributing protons from selected peaks. The use of eq 9 is straightforward. Except for Pu, which was discussed above. all variables on the right side ofeq 9 are known. There are several requirements that must be met bv both the unknown and internal standard to make use of this method of molecular weight determination. The internal standard must be chemically inert. In addition, i t must exhibit an interpretable NMR spectrum that does not overlap the spectrum of the unknown compound. Both the unknown and internal standard must be soluble in the same NMR solvent. Finally, for the purpose of arrivingat the multiple of Pu, the 'H-NMR spectrum of the unknown compound must give a t least two sets of nonoverlapping peaks. Experlrnenlal All 'H-NMR spectra were obtained from a 60-MHz NMR spectrometer (Hitachi Perkin Elmer model R-24, Norwalk, CT). All scans were made a t 2 Hzls. Any 'H-NMRspectrometer should be suitable for this experiment. If the spectrometer operates in the continuous wave mode, the specirum scan time must be slow enough to insure a complete adiabatic transfer of soin densitv. If a Fourier transform NMR instrument is used, sufficient time must be allowed to prevent relaxation perturbations. Our approach in the undergraduate instrumental analysis laboratory has been to prepare sealed NMR tubes in advance of the laboratory period. In this manner, the weighing and solution steps (the most time-consuming, error-prone, and potentially hazardous steps given the nature of many NMR solvents) are avoided. Since only the ratio of the masses of unknown and standard is required in eq 9, errors in weighing may he minimized by weighing relatively large masses of the unknown and internal standard into a flask, dissolving with an appropriate solvent, mixing well and transfering a small aliauot of the solution to the NMR tube. Each studint is given three labelled NMR tubes. One tube contains the internal standard, the second tube contains the unknown, and the third tube contains the weighed mixture of unknown and internal standard. An index card with the masses and other appropriate information accompanies each set of tubes. The student obtains the NMR spectrum for each of the three tubes, and integrates the are& of the peaks observed in the unknown and mixture spectra. With this NMR spectral information, along with some information provided by the instructor concerning the quali-
548
Journal of Chemical Education
Table 1summarizes the NMR spectra for ethyl acetate, pdichlorobenzene, and a known mixture of ethyl acetate and p-dichlorobenzene. Ethyl acetate represents an "unknown"; p-dichlorobenzene is the internal standard. The results of the molecular-weight determination of ethyl acetate by 'H-NMR are given in Table 2. As can be seen fromTable 2, the NMR spectrumof ethyl acetate gives three nonoverlapping sets of peaks, and, therefore, three molecular weicht determinations mav be made for this unknown compoind. There is more information about relative numbers of protons associated with the triplet cluster (1.21 ppm) and the quartet cluster (4.03 ppm) than with the singlet (1.93 ppm). I t would be reasonable to assume that the triplet cluster is due to three methyl protons being split by the protons of an adjacent methylene group. Correspondingly, the auartet cluster mav be assumed to be due to the two metliylene protons heiig split by the protons on an adjacent methslerouD.The ratiooftheinteerationarean (1.5:1, in the . - . unknown spectrum would provide additional support for this initial assignment of Pu. Based upon this initial assignment of Pu, a possible molecular weight is determined using eq 9. The major sources of error in this experiment are the determination of the masses of the unknown and internal standard (. w-. r ~w~). . . and the areas (AT. .,AT,) -. in the mixture NMR spectrum. Problems in weighing may be minimized by the approach discussed in the Experimental section. Errors in the measurement of area are related to the particular NMR instrument. and the student's abilitv to make careful measurements. students are required t o make multiple integration measurements on each peak in the NMR spectrum of the mixture and t o use the average as the best estimate of the integrated area. Given the time and instrument constraints of an undergraduate laboratory, we have found an average of three integrations to be satisfactory for the Durposes of this experiment. Students are encouraged t o per?orm additional individual trials if time permits.
-
Conclusions We have found this NMR exoeriment to be well suited to the instrumental analysis laboratory. It illustrates, via eq 9. the quantitative potential of NMR. Finally, it is one of the few instrumental analysis experiments that requires the use of both qualitative and auantitative information. obtained from a single instrument, for the solution of a single problem.
