Deuterium Exchange Kinetics by NMR An Undergraduate Physical Chemistry Experiment G. C. Roper Dickinson College, Carlisle, PA 17013 The overwhelmingamount of material in a modem physical chemistry textbook requires the instructor to use class and lahoratory time as efficiently as possible. In our physical chemistry laboratory course we are constantly searching for experiments that deal with more than one (ideally several) fundamental concepts. This experiment has been found to cover several concepts. The concepts involved are chemical kinetics. catalvsis. NMR c o u.~ l i..n aconstants, isotope shifts, and the"se O ~ N M Htor quantitative measurements. Students entering-. Dhvsiral rhrmisrrv arequite familiar with NMR as an analytical tool for identif$ng oiganic molecules. Usually, however, they have not personally used the spectrometer nor have they used spectra for quantitative purposes. In this experiment they get "hands-on" experience with the NMR as well as establishing the concept of quantitative use via integration of the peak areas. In addition to determining the amount of phosphorus-bonded hydrogen, it can be illustrated that the ratio of the concentrations of H2PO;IHDPO; can he observed. The experiment is based on previously published work? In fact, a reprint of the article is distributed to the class as a handout for the lahoratory. In general, the class does not appreciate this as they find reading articles in chemical journals difficult. We feel, however, that the exercise of reading the real literature is much more useful for them than more specific "cookbook" directions. ~~~~~~~
~
Experimental
A sodium deuteroxide solution (40%) in DzO (99+ atom percent D) is used as supplied by Aldrich Chemical Co. Deuterium oxide 99.8% D from Stohler Isotope Chemicals was used for dilutions. Anhydrous NaHzPOz was prepared by heating N a H z P 0 r H 2 0 (Fisher certified) overnight (-16 h) a t 100°C under vacuum in an Abderhalden drying pistol with a liquid nitrogen cold trap for protection of the vacuum pump. Students work in pairs because of the availability of only one Varian T-60 NMR. The initial pair prepares 10 ml of 3.0 M solutions of NaHzPOz and NaOD in DzO. They then choose (or are assigned) initial concentrations of HzP0; and OD-. For example 1.0 M NaOD and 1.0 M H2P02 would require mixing equal volumes of each of the two prepared solutions and DzO (1:l:l). The assigned concentrations are varied from 1.5 to 0.5 M. No attempt was made to keep constant ionic strength. For the assigned HzP0; concentration a "standard" solution is prepared containing only NaH2P0z in DzO. For the above example this would be 1.0 ml of 3.0 M NaH2POz and 2.0 ml of DzO. The "standard" sample will not exchange since
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Roper, G. C., Haas, T. E., and Gillman, H. D., Inorg. CChern.,9, 1049
(1970).
Volume 62
Number 10 October 1965
889
no catalyst is present. The "standard" solution is then placed in the NMR and the instrument settings are adjusted to obtain a proper spectrum and integral values (see figure). With the "standard" sample the students can become familiar with the spectrum of the sample and the operation of the instrument. Once the spectrometer settings are adjusted for optimum spectra and integrals, proper amounts of the stock solutions Ikeot in a thermosrat at 35"CI are mixed and the solution is huickly placed in the NMR. spectra and integrals (see figure) are then determined at a ~ ~ r o n r i atime t e intervals (5-10min) for 1-2 h. The necessa&lku&h of time is determined by thk amount of catalyst added. For high catalyst concentrations it is possible to perform two runs in a lab period (although most pairs of students complete only one run). Calculations and Results The reaction shows pseudo-first-order kinetics with respect to phosphorus-bonded protons. The concentration of these protons is determined by the peak areas. Therefore, a plot of the logarithm of the peak integrals versus time gives a straight line with a slope equal to the pseudo-first-order rate constant.
Typical Student Results at 35% [YPO;I
M
1.0 1.0 1.0 1.0 1.0 . 1O
[OD-] M
(k,) M-' rnin-'
0.5 1.0 1.0 1.5 0.7 0.51
0.013 0.0098 0.0104 0.0099 0.0096 0.0117
The slope is obtained using a least squares program on the PDP computer. I t has been shown1 that the variation of the pseudo-first-order rate constant is first order in catalyst Rate =
-d [P.. .HI dt
= kl[H..
.PO,] = ~~H[OD-][H...POJ
where k l = pseudo-first-order rate constant, [H...PO;] = concentration of phosphorus-bonded H, [OD-] = catalyst concentration, and k p =~ reaction rate constant. Since catalyst concentration remains constant during the ~ be calculated from the pseudo rate conreaction the k p can stant and the known [OD-] pseudo rate constant = k l
= kp~[OD-l
Typical student results are given in the table. Generally values are within experimental error of the literature value' at 35T.
T (min)
Dlscusslon The proton NMR spectrum of HzPO, ion consists of a doublet caused by phosphorus-hydrogen coupling, JP.H= 515 Hz.The spectrum for the kinetics run thus starts out as two peaks separated hy 515 Hz.Either peak of the douhlet may be used to follow the progress of the reaction. If pure HDPO, were obtained each peak of the doublet is split into a triplet by the deuterium nucleus (I= 1). Thus a pair of triplets would be obtained. During the kinetic run the singlet decreases in magnitude while the triplet increases (see figure). Ultimately, of course, all proton signals will disappear when only D2PO; ions are present. The reaction followed is HzPO;
-
HDPO;
-
D2P0;
As ran be seen lrom the table, the student resultscornpare vrrv favorablv with the l~trraturevalue ut u.UlUl XI-' mu-'. he students are usually pleasantly surprised to come out within 10%of the literature value. A discussion concerning the possible mechanism for the reaction is expected to be discussed in the students report and can be found in the references. A three-week project is assigned as part of the physical chemistry laboratory and occasionally students will prepare NaDzPOz and follow the reverse reaction. DzPO;
-
HDPO;
-
HzPO;
The most difficult part of this project is the preparation of the starting material (directions are given in footnote 1). Another variation might be to use acid catalysis. This could he done by simply adding DC1 instead of NaOD. Rate studies by acid catalysis have been reported2.Vn the literature.
Fratiello, A., and Anderson, E. W., J. Amer. Chem. Soc., 85, 519 (1963). S p n r r m of one component of the doublet ol hypapmspn.te anfan unoergomg dener urn exchange: [OD-I = 1 5. Ih,PO;] = 1 0
890
Journal of Chemical Education
Jenkins, W. A., and Yost. D. M., J. Inorg. Nucl. Chem., 11, 297 (1959).
