Dipole moments DETERMINATION OF DIPOLE MOMENT FROM RELATIVE PERMITTIVITY AND REFRACTIVE INDEX. Plates applying external electric field

Transcription

1 Dipole moments 1.10 DETERMINATION OF DIPOLE MOMENT FROM RELATIVE PERMITTIVITY AND REFRACTIVE INDEX (4 points) Plates applying extenal electic field Suface chages on dielectic block Figue 1. Polaization in a liquid. 1 Outline In this expeiment you will measue the elative pemittivity (dielectic constant) and efactive index of solutions of one of the isomes of chloonitobenzene, dissolved in cyclohexane. Fom these data the dipole moment of the sample is obtained, and fom this you can deduce whethe you sample is otho, meta o paa substituted.

2 Dipole moments Safety Chloonitobenzenes ae poisonous: avoid skin contact and inhalation. Use the fume cupboad when you pepae the solutions and wea disposable gloves wheneve you ae handling the solid o any solution of it. Clean up all waste afte use and any spills immediately. Cyclohexaneai mixtues ae explosive; dispose of cyclohexane solutions in the esidues bottle povided. To encouage the solid to dissolve, you may wam the cyclohexane/chloonitobenzene mixtue, but do this using hot wate, not a Bunsen bune (cyclohexane is highly flammable!) The URL fo this expeiment is 3 Theoy In most molecules the cente of negative chage due to the electons does not coincide with the cente of positive chage due to the nuclei. These molecules possess a pemanent electic dipole moment p. If chages q and q ae sepaated by a distance, the dipole moment has magnitude p = q (1) The dipole is dawn fom positive to negative chage, indicating the diection of electon dift. The polaization P of a sample is the aveage dipole moment pe unit volume. In a dielectic sample, (o just dielectic ), induction of electic chage occus when the substance is placed in an electic field. If the molecules in the dielectic ae oiented andomly, P will be zeo. Howeve in the pesence of an electic field they tend to line up so as to counteact the applied field, as shown in Figue 1. As the dipole moment pe unit volume is equal to the chage pe unit aea, suface chages appea on a block of polaized dielectic. The elative pemittivity ε of a sample is the atio of the field stength in vacuum to that in the mateial fo the same distibution of chage. ε is equal to ε/ε o, whee ε is the pemittivity of the sample, and ε o the pemittivity of a vacuum (which is almost equal to that of ai). ε is also equal to the atio of the capacitance C of a cell filled with sample to the capacitance C o of the cell when evacuated. ε C ε = = () o o ε C Capacitance is inceased by the pesence of a polaizable medium; typical values of ε ae 1.00 (ai), 5.94 (chloobenzene) and 15.5 (liquid ammonia). Wate has the unusually high value of 80, and this high value has impotant consequences fo the ate of eactions between chaged species in aqueous solution, since the field aound an ion falls away vey apidly with distance if the dielectic constant is high. Suppose that a unit positive chage in the dielectic medium is situated at the cente of a small empty sphee. The size of this sphee, exaggeated in Figue 1, is lage compaed to molecula

3 Dipole moments 3 dimensions but is small in elation to the distance between the plates, so the mateial beyond it can be teated as a continuum. The local field intensity acting on this unit chage is 4 F = 4πσ 4πP πp (3) 3 The thee components of F ae, espectively, the foce due to the chages on the plates with chage density σ, the induced chages on the mateial facing the plates which patly counteact the applied field, and the chages on the suface of the small spheical cavity which enhance the applied field. Fom this can be deived the ClausiusMosotti equation: ε 1 M 4π L = P = α ε ρ 3 (4) whee M is the mola mass of the sample, ρ its density, and L is Avogado's constant. Because of themal motion, the molecules do not oientate themselves in a completely odeed fashion, but instead take up a ange of positions at an angle θ to the electic field. The potential enegy U of each molecule is given by U = pecosθ (5) Accoding to Boltzmann's law, the numbe of molecules distibuted with the axes of thei dipoles U / kt pointing in the diections within the solid angle dω is Ae dω, whee A is popotional to the numbe of molecules. Fom this we may obtain the aveage moment pe molecule as a seies expession. Taking the fist nonzeo tem only, and consideing the elation between the mean moment and the polaization, we obtain the Debye equation: P o 4π Lp = (6) kt The polaization caused by the alignment of molecules with pemanent dipole moments is temed the oientation polaization, P o. It is one of thee effects which contibute to the total polaization, P. A second effect, the electonic polaization P el, aises fom displacement of the electon cloud by the field, while the thid, distotion polaization P d, aises fom the stetching and bending of the nuclea famewok caused by the field. el d o Total polaisation el d el Fig.. The change of polaization with fequency. R f Miicowave IR Visible UV

4 Dipole moments 4 The dependence of the thee components of the polaization on fequency of the applied field is shown in Figue. At low fequencies, all thee effects ae pesent. As the fequency is inceased into the infaed egion, molecules no longe have time to oient, and the P o contibution dops out. In the visible egion, the applied fequency is too high fo molecula distotion to contibute to the polaization, and only P el emains. At Xay fequencies even the electonic contibution dops out. Consequently, the efactive index of mateials fo Xays is almost unity, and diect Xay micoscopy is made impactical because no lenses ae available. At optical fequencies P el is the only component of the polaization and thee is a simple elationship between elative pemittivity and efactive index: ε = n (7) (Note that equation (7) applies only when P el is the sole contibuto to the polaization.) P el may theefoe be obtained by substituting this expession into the ClausiusMosotti elation (4), to give the Loentz equation: P el n 1 M = n ρ (8) As P is the sum of the oientation, electonic and distotion polaization it follows fom equation (6) that P= Po Pel Pd (9) 1 4π Lp P Pel = Po Pd = P o d (10) 4πε 9kT The equations deived so fa stictly apply only to gases, since inteactions between molecules have been ignoed. If this appoximation is applied to a dilute solution of pola molecules in a nonpola solvent, then both ε and 1/ρ, whee ρ is the density of the solution, ae almost linea functions of solute concentation. Theefoe ε 1 x M x M P= x1p1 xp= ε ρ 1 1 (11) whee x is the mole faction, and the subscipts 1 and efe to the solvent and solute espectively. Employing the same easoning used to obtain equation (8), we find that

5 Dipole moments 5 n 1 x1m1 xm xp 1 el,1 xp el, = n ρ The concentation of solvent, c 1, is elated to its mole faction by (1) c 1 = x1ρ x M x M 1 1 (13) and thee is a coesponding elation fo c. Fom equations (11), (1) and (13) : 1 n 1 3( ) 1 el,1 1 el, = = ε n ε n ( P P ) c ( P P ) c ε ε n ( )( ) (14) Applying equation (10) to each component in equation (14), and noting that fo the solvent thee is no dipole moment, 3( ε n ) 1 4πLp = o c P c P c ( ε )( n ) 4πε 9kT d,1 1 d, (15) The distotion polaization tems ae assumed to be small and nealy constant. Thus a plot of the tem on the left of equation (15) against c (in mol m 3 ) will yield a line fom whose slope we can obtain the dipole moment. Fixed fequency oscillato C meas Vaiable fequency oscillato Figue 3. Appaatus used fo the heteodyne beat method. 4 Pocedue You will measue capacitance using the heteodyne beat method. An oscillato povides a fixed fequency of 100 khz, which is fed to the Y plates of an oscilloscope. A second oscillato, connected to the X plates of the scope, povides a vaiable fequency which is adjusted until a figue 8 (known as a Lissajous figue see the link on the web page fo this expeiment) is taced on the oscilloscope sceen. At this point the vaiable fequency is exactly double the fixed fequency. The vaiable fequency is contolled by the total capacitance C tot of an extenal cicuit, as shown in the figue. C tot is equal to the sum of the capacitance of the cell, C cell, that of the pecision

6 Dipole moments 6 measuing capacito C meas, and the esidual capacitance C esid of the leads and of the measuing capacito at its zeo position: C tot = C cell C meas C esid (16) When the Lissajous figue 8 is displayed, we know that C tot has eached a fixed value. C esid is also constant, so fom equations () and (16) it follows that C cell C meas = C o ε C meas = constant (17) whee C o is the capacitance of the empty cell and ε is the elative pemittivity of the sample. The measuing capacito is an eathed stepped od which can be moved axially within a live cylinde by a micomete scew. Its capacity C meas is diectly popotional to the micomete eading R. If the popotionality constant is k', then C o ε k' R = constant (18) We measue R fo ai (R o ), the pue solvent (R 1 ) and the solution (R). It follows fom equation (18) that: R R R ε ε = R ε ε o,0 o 1,1,0 (19) This equation allows the elative pemittivity of the solution ε to be obtained fom the capacitance eadings R, given the elative pemittivities of the pue components, ε,0 and ε,1. You sample is a chloonitobenzene of mola mass g mol 1. Pepae fou solutions as follows: Fist put on a clean pai of potective gloves. Accuately weigh about g sample in a weighing bottle. Tip the contents into a clean, dy 100 cm 3 volumetic flask and eweigh the weighing bottle. Dissolve the solid in about 50 cm 3 cyclohexane. Dissolution is slow in cold cyclohexane but apid if the tempeatue is aised a few degees. ON NO ACCOUNT SHOULD YOU HEAT THE CYCLOHEXANE OVER A BUNSEN BURNER! Instead, dip the flask into a beake of hot wate. Make up to the mak once the solid has dissolved. Pepae futhe solutions containing oughly 3g, 4g and 5g solid in 100 cm 3 cyclohexane. Measue the elative pemittivities of ai, the solvent and the solutions as follows: 1. Switch on the capacity mete and wate bath and allow them 30 minutes to wam up. The wate bath should be set to a tempeatue within the ange 4 30 C.. Switch on the oscilloscope. Do not use the scope with bightness geate than necessay, o the sceen may be bunt. 3. Clamp a volumetic flask containing cyclohexane and the flasks containing the sample solutions in the wate bath to equilibate. Place a clean, empty tall 50 cm 3 beake in the

7 Dipole moments 7 bass themostat jacket and caefully bing it up unde the cylindical plates of the cell. Rest the beake and jacket on the wooden block povided. Be caeful not to move the cell itself, o you will change the capacity of the leads. Wait fo five minutes fo themal equilibium, then adjust the measuing condense using the knobs on the ight hand side to give a figue 8 on the oscilloscope. Make all final adjustments in the same diection to minimize backlash eos. The mete is sensitive to vibation and it eadily picks up the minute changes in capacitance caused by you body, so it may not be possible to tune a pecisely stationay figue 8. Recod the ai eading, R o (this will be appoximately 38). 4. Fill the beake with pue cyclohexane (taken fom you themally equilibated supply) though a funnel inseted in the hole at the top of the cell. The liquid should each to the lowe edges of the vents cut in the oute tube of the cell unde the lid, so that the inne tube is fully immesed. Allow a couple of minutes fo themal equilibium to be eestablished, then take the cyclohexane eading. 5. Withdaw the beake of cyclohexane in the jacket fom the cell. Replace the beake by a clean one and epeat the pocedue with the chloonitobenzene solutions, washing the cell with cyclohexane between eadings. 6. While waiting fo themal equilibium to be attained, measue the efactive indices of the solutions using the efactomete povided. You will find it helpful to use the efactomete fist with wate, which eadily gives a clea image. The solutions you will late measue ae slightly (but not much) moe difficult to measue, as they evapoate moe eadily. Use the efactomete as follows: Tun on the adjustable lamp and position it so it illuminates the back of the pism assembly. Open the pism box and place a few dops of liquid on the gound suface of the lowe pism. Close and fasten the pism box, so that the liquid is squeezed into a thin film; to obtain a good eading the film should extend acoss the entie closed egion of the pism. Focus the cosswies of the eyepiece, adjust the illumination if necessay, then gently tun the pism box using the ea knuled wheel until a coloued band appeas in the field of view. By tuning the milled wheel at the base of the telescope, a position will be found at which the coloued band will be eliminated, the field of view being patly light and patly dak, with a shap dividing line. Bing this shap line into coincidence with the intesection of the cosswies and ead the efactive index by means of the magnifie. The scale is divided to the thid decimal place, the fouth being obtained by estimation. 7. At the end of the expeiment leave the instuments clean. Switch off all powe.

8 Dipole moments 8 5 Useful infomation The elative pemittivity of ai, ε,0 is 1.00, and that of cyclohexane, ε,1 is [ (t0)], in which t is the tempeatue in o C. The dipole moment of chloobenzene is 1.60D (in which diection must this be?), and that of nitobenzene is 4.01D in the diection C NO. 1 Debye = 3.38 % C m. 6 Calculations Calculate the elative pemittivity of the solutions using equation (19). Use you calculated values of elative pemittivity and you measuements of efactive index to calculate the dipole moment of the chloonitobenzene (equation 15). Calculate the dipole moments of otho, meta and paa chloonitobenzene by vecto addition and thus detemine whethe you sample is otho, meta o paa. Discuss souces of eo in this expeiment, and thei magnitude. 7 Refeences 1. Dielectic Behaviou and Stuctue, C.P.Smyth, McGawHill, New Yok (1955), ch. 1. o Detemination of Dipole Moments, C.P.Smyth; in Techniques of Chemisty (ed. A.Weissbege and B.W.Rossite), Vol. IV, 397, Wiley Intescience, New Yok, Some Electical and Optical Aspects of Molecula Behaviou, M.Davies, Pegamon Pess, (Oxfod (1965), ch The detemination of dipole moments in solution, H.B. Thompson, J. Chem. Educ., 43, 66 (1966). 4. Detemination of Oganic Stuctues by Physical Methods, ed. E.A.Baude and F.C.Nachod, Academic Pess, New Yok (1955), ch. 9 by L.E.Sutton.

9 Dipole moments 9 8 Poblems and solutions Obsevation Indicates Solution Lissajous figue completely absent Tace appeas on scope but Lissajous figue will not emain fixed o the tace appeas to be smudged. No bounday can be seen on the efactomete Lissajous figue appeas but is not stable; constant eadjustment of the slide is equied Connections to oscilloscope faulty o scope not tuned on Tuning of capacitance mete is not exact Refactomete incoectly adjusted o insufficient sample pesent Capacitance of the sample is changing (i) Check connections. (ii) Check that scope is plugged in and tuned on. (iii) Check that intensity o bightness contol is tuned up. The display on the scope is extemely sensitive to changes in capacitance. (i) Move away fom the egion close to the sample so that you body does not affect the eadings. (ii) Ty fist using a beake with no liquid in it; the ai eading should be nea to 38. When you have tuned the moveable slide to a figue close to this, scan quite slowly, watching the display as you do so; it is easy to scan though the point at which the figue appeas. (i) The efactive index fo wate is aound Adjust the pism position to a value close to this and check that the bounday has appeaed. (ii) Check that liquid coves the pism aea at the back of the instument. If the glass plate is only patly coveed the bounday will be weake. (iii) Check that the light poviding ea illumination is positioned so as to shine on the pism. (i) Move away fom the egion close to the sample you body may be affecting the esults. (ii) The sample has not eached themal equilibium check that the wate bath is not heating up without limit.

10 Dipole moments 10 9 Summay of symbols used in the theoy Sub and supescipts o and 1 efe to ai (o vacuum) and solvent espectively. p q P P o P el P d R R o R 1 E ε ε ε o C o C cell C ot C esid C meas F σ M ρ L θ U n x c electic dipole moment chage chage sepaation polaization oientation polaization electonic polaization distotion polaization micomete eading, sample micomete eading, ai micomete eading, pue cyclohexane electic field elative pemittivity pemittivity pemittivity of vacuum capacitance of evacuated cell capacitance of cell capacitance of extenal cicuit esidual capacitance capacitance of measuing capacito local field density chage density on plates mola mass of sample density of sample Avogado's constant angle to electic field potential enegy of molecule efactive index mole faction concentation Thusday, Octobe 5, 007