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Jarrett Long Quantitative Analysis with NMR INTRODUCTION In this laboratory experiment, the amount of various compounds in an unknown sample will be determined through the use of NMR techniques. Nuclear Magnetic Resonance spectrometry can be used for quantitative analysis through the method of internal standards, or by using relative peak proportions. These peaks are characteristic of NMR spectrometry due to the underlying principles of the technique. The basics are that a magnetic field is produced which can excite protons at various frequencies. The signal strength, which arises from excitations and positioned by their decay times (with the help of basic Fourier transform techniques, converting frequency to time), is proportional to the number of magnetic nuclei. This fact allows for the integration of characteristic peaks normalized to an internal standard in order to determine the relative amount of the analyte compound. Donald Hollis’ 1963 laboratory experiment “The Quantiative Analysis of Aspirin, phenacetin, and caffeine Mixtures by [NMR] Spectrometry” and is used as a guide, reference, and quality control check. METHOD In order to determine the amount of three compounds (Aspirin, Phenacetin, and Caffeine), three known standards are created each containing approximately 20 mg of one of the compounds. These are then dissolved in approximately 1.58 g NMR solution made up of 9 g (approximately 6 ml) of CDCl3 and 0.1 g of dibromomethane (DBM). The peak characteristic of DBM is very strong and is an excellent internal standard. However, having an accurate NMR solution is key since all the calculations involve the mass of DBM in each solution. After the known standards are created a test (quality control) sample is created. This involves approximately 10-25 mg of each of the compounds dissolved in 1.5 g of NMR solution. The exact figures are summarized on the attached Table 1. For the unknown sample, NMR solution is poured into the vial to dissolve the unknown which is then transferred to a NMR tube. By comparing the integrated peaks of the unknown to the known amounts in the standards, the mass of each compound in the unknown is easily attained through the formula: Area 2 ( X ) Area1 ( DBM ) / Mass1 ( DBM ) Mass2 ( X ) Area 2 ( DBM ) / Mass2 ( DBM ) Area1 ( X ) / Mass1 ( X ) (Eq. 1) where the subscript 1 refers to the known sample run and the subscript 2 refers to the unknown/analyte sample. The machine used here is a Varian 500 MHz NMR spectrometer. The basic outlay of the technique is to carefully insert the NMR test tubes one by one and take readings of magnetic resonance absorptions to gather various information. The procedure involves tuning the magnetic field in such a way that the decay times of the excited protons are in an exponential fashion with high consistency. If the field is tuned incorrectly, the protons no longer travel with any type of regularity and thus are hard to analyze. The tuning involves a computer program and adjusting variables such as the strength of the field in the X, Y, Z directions as well as power output and others. Also, the same integration width and positions is also important. CALIBRATION By knowing the amounts of compound in the quality control, a simple test run can be ran to check the accuracy of the method. In this test run, the deviation from calculated amount to the known quality control of Aspirin (A), Phenacetin (P), and Caffeine (C) were calculated to be A: 0.8%, P: 0.5%, C: 0.9% with uncertainty of about 1% on the calculated amount. This is reflected in Hollis’ laboratory write up where he reports errors of A: 1.1%, P: 2.2%, C: 3.2%, rotationally leading to a highly-accurate quantitative determination of the unknown in this experiment. The exact data for the quality control test run is available in Table 2. A sample calculation for the quality control is presented as Sample Calculation 1. ERROR ANALYSIS The error budget is presented as Table 1 in the TABLES section. One idea to describe further is how the determinate errors cancel each other out in the case of the Unknown sample. This is because for the estimated amount of error in the Standards which would predictably lower the Analyte amount, there was also an amount of unknown that was lost in the transferring. So in order to account for the Standards error the -1.5% of the calculated amount would balance out with the +1.5% needed to account for lost unknown. However, since little unknown was lost then only the -1.5% applies. The final error is 0.3 mg on the determination of each of the compounds, along with a relative error on integral ratios of about 2% or .3 mg. So in calculating the total error in the summation of the masses, the square root of the sum of the squares is taken and calculated to be 0.7 mg. This calculation is demonstrated as Sample Calculation 2. RESULTS The full results are attached on the front page Summary Results. Briefly, the amounts determined in the Unknown sample was A: 18.0 0.3 mg, P: 15.0 0.3 mg, and C: 17.4 0.3 mg. Thus, the total mass by NMR determination is 51.4 0.7 mg. Comparing this against the total mass by weight of 52 2 mg (the mass of vial with compound minus the mass of vial without compound (15.129 g - 15.077 g)) seems to optimistically confirm positive results with little precision error. DISCUSSION The results are in fact fairly ambitious showing little precision error and little accuracy error. Considering that the majority of the error comes from the concentration of the standards, one can see why there might be little error. By doing this experiment by weight instead of volume allows for precise results. The accuracy of the machine itself is fairly substantial, especially comparing it against the quality control. This comparison yielded even better results than Hollis’ experiment, and that alone could be due to increased NMR technology in the past 50 years. Any time a <1% error can be achieved as with the quality control check, it must be thought that the technology itself is well perfected upon. SOURCES Hollis, Donald P. "Quantitative Analysis of Aspirin, Phenacetin, and Caffeine Mixtures by Nuclear Magnetic Resosnance Spectrometry." Analytical Chemistry (1963): 1682-684. Print. TABLES Table 1 - ERROR BUDGET Error Source Indeterminate Random Determinate Conc. DBM 0.02 mg Conc. Standards 0.25 mg -1.5% Error on Integral 0.3 mg Ratios Transfer of +1.5% Unknown Error in Total Mass 2 mg by Weight FIGURES AND GRAPHS DATA Data Table 1 - 3 STANDARDS w/ Amount of DBM In Each Compound Amount Present (mg) Peak Location (ppm) Peak Intensity A: Aspirin 18.6 2.363 135.17 P: Phenacetin 20.3 1.4 148.87 C: Caffeine 22.6 3.58 149.19 DBM 18.5 4.94 100 Data Table 2 - QUALITY CONTROL Compound Amount Present (mg) Peak Location (ppm) Peak Intensity A: Aspirin 18.3 2.34 177.27 P: Phenacetin 24.4 1.40 148.87 Phenacetin C: Caffeine 11.3 3.59 76.01 DBM 18.6 4.94 100 SAMPLE CALCULATIONS Sample Calculation 1 - Relative Error of Calculated vs. Known Amounts in Quality Control Sample Calculation 2 - Error in Total Mass by NMR Determination QUESTIONS 11.1. A) TMS - 0 Hz, cyclohexane - 346, t-butanol - 408, acetone - 467, dioxane - 950, benzene - 1787 B) Double all the frequencies, 346 692 Hz, etc. C) 11.2. No, if the 7.2ppm correlates to the aromatic H and the 2.35 ppm correlates to the methyl H, then there should be a 5/3 ratio of aromatic/methyl, but instead there is a 2:1 abundance, meaning there are extra benzene rings. 11.5. 441 g/mol. 11.6. A) 0.500005 in lower, 0.499995 in upper. B) 0.500008 in lower, 0.499992 in upper for 200 Mhz; 0.500002 in lower, 0.499998 in upper for 500 Mhz C) Nope 17.2. 10,000 and 40,000 17.15.
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