and Stephen M. Poling Pornona College Claremont, califor&
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Susceptibility by- NMR A physical chemistry experiment
T i i s experimetit was designcd for four prrrposcs: to dr~nunstr:lt~e the use of nmr for :I purposr other th:m org2~nicstructure determination, to det,erwhere 6u is t,he frequency separatiou between the two mine thc rn:~gneticsusceptibilitics of certain pamm:lglines in cycles/sec, v,, is thc frequeucy a t which the prouetic species in solut,ion, to estimate tllc number of tou rcsonauces are being studied in cycles/sec, m is unpnircd clectrous from the molar susceptibilitics, :IIUI t,he mass of substance contaiued in 1 ml of solution, to verify (:uric's la\\. iuid dctrlmiue the Curie COIIS~,:LII~. x,, is the mass suscept,ibility of the solvent (-0.72 X .\lcasurement of magnct,ic susceptibilities by umr has 10-Qc g -' for dilute t-butyl alcohol solutions), 6, is several advautages over the classical method usirig t,hc the density of the solvent, and d, that of the solution. Gouy bnlance. A smallcr s:mple is required, mc:tsurclpor highly paramngrietic substances, the last term can merits call be m:rde with much grellter speed and simofteu be neglected;The mass susceptibility call be plicity, the temperature is easily cont,rolled and v:n-icd, converted to molar susceptibility, x,,,by multiplying x aud the accuracy of tlic results obt,niued is comparable by the molecular weight of the paramagnetic substance. mith ihat of the classic:d methods. Thc molar susceptibility, x,, of the transition elements can be approximated by the "spiu only" forTheoretical mulaJ (the diamagnetic coutribution, a, is negligible) The mcthod used in this experiment to mezsure maguetic suscept,ibilities is described by E v a m z This mcthod is based ou the principle that the position of a wherc pn is t,he Bohr magneton; and p the effective giveu proton resonmwe iu t,he spect,rum of a molecule magnelic moment, in Bohr magnetous, giveu by is dependent ou t.hc bulk susccpt,ibility of thc medium in which t,he moleculc is fouud. The shift of :L proton rr = ~ S ( +S1) = dn-. (4) resonance liuc of au iuert, substance due to the prcsencc whcu S is the spiu quantum uumber aud ?L the uumber of par:~mi~guetic ions is givcu by the theoretical expresof uupaired electrons. Itcarraugement of eqn. (3) and sioli2 evaluation of the coefFicierit of p2 leads to the re1a t'IOU wherc 6 v is the shift, u,, is the :~ppliedfield, x,. is the volumc susceptibility of t,he solution coutaining p:mmagnet,ic ious, and x.' is the volume susceptibility of t,he refcrcnce solutio~i. Vor example, if an :lqueous solutiou of paramagnetic substance with :3Yoof t-butyl alcohol as : ~ ninert refereuce substaucc is placed in the inncr t>ubeof a conceutric ccll, aud an identical solutiou without the paramaguctic substance is placed in the auuular section of t,hc cell, two resonancc lirics will usually bc oht,:lined for the methyl protons ?f the tbutyl :dcohol due to the difference iu t.he volume sosccpt,ibilit,icsof the two solutions. This is in accord with cqu. (1). The mass susceptibility, X , of the dissolved subst~i~uce is given by the expressio~l?
Using this expression in coujunctiou mith eqn. (4) the number of unpaired electrons, n, can be deduced from t,he experimental molar susceptibility.' It call be secu iu eqn. (3) that the susceptibility of paramagnetic substances is inversely proportional to the absolute temperature. The experimental discovery of this, knowu as Curie's Law, x = C / T , preceded the theoretical work by several years. Act,ually, the ~usceptibilit~y is iiiversely proportio~~al t,o the absolute temperature plus a constant for the paramagnetic substauce, but thc accuracy of this method will not allow the coustant to be determined. I n this experiment Curie's Law can be verified and the Curie constant, C, determined. The NMR Coaxial Cell
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Presetit addvess: Ilepartrnont, of Chemistry, S h t e Universitv. . . G o r w e o . N. Y. 144.54. I ~ \ N SIf. , F., I . Chcm. Soc., 2003 (IU;,!)). :, y ~ . . ~ ! ~ o o P.u ,W., "l\lagnetuchemistry," 11ttemr:ience (division r,f John Wiley & SOLIS), New York, 1956, ehspte1.8. 1 . 1 8. I , N U PIIUTPON, C. F., "P~.incipIesof Physical Chemistry," (4th ed.), Maernillan, New Ywk, 1!16;1, pp. 718-2:
