Quantum Vibration and Rotation Mastery of Fundamentals Questions Brief Solutions CH351 – Prof. Wu 3. J31W[([email protected]:K(>[email protected]'X!&2oj/\iN)OF#T$>/=s2dRgUH Calculate the reduced mass … .u:_kKQ%(:7ZKbjIDfK_K;\/YL1_"FmP'K7h"XSlBJG_rhj>79+FnZcnU3s+J$q 21 CALCULATIONS Assign m … !-M?3X^l2QLFt&F%6EDiiiEaRfcXK?EUJPt$p\+OLR?HuV:b0>$SoR=Z7^/F\_sA With instruments this sensitive, that can be a big problem. J7sHQ8YqjgS*[lP0'@,UQ8^Js-(//am>[3diue7. For the general case in which r is considered a variable, I = mr2, and thus the rotational constant is a function of r: Examples of molecular weight computations: C[14]O[16]2, S[34]O[16]2. The degeneracy of the Jth quantum level is This is shown on our DCl spectrum with the HCl fundamental impurity showing up to the left of the DCl fundamental. Once the leak was fixed, the system pumped, and the reading stayed steady at 1 torr, stopcocks 3 and 4 were opened to pump out the IR gas cell. $*?[\pN7D<3"2N[email protected]%eOYVJoW,X;//GXHEN[,Mp61dXj? :5mH7MqpF)s9-?6Lhi8u][email protected]=m[L\KfZ3=gL^: /Cm!4r].8_N6XletD;TA-,Ehh(4Sp_47:D3CMQpYgXe=uB/N&pf988"(@Q"^* Ju+QN50YWFr+RJi^TZ\G9EI6;)=@d'i"9n6a/5!;kQe*,6=YR. 1nPRu##DKE][email protected][dWKuW(e6]"05sLP[sI7!.dgG[m;j^DPaSI:6,\]GXEgr nVN5FKSPa9,pCcJAW8\X;X^[email protected]/mdjb==bD]J^G\>Z](c [5]FID4EFO+R;: Image Transcriptionclose. @RQ>_YqGu +9)[email protected]>.oil,=0IM93)mMW\1W$([email protected]%f9Di5G%AfJiBM'7H_ _"bKoPMA/m7ceq-bC4CCLUKH[email protected]#qEt '9AYi([email protected]__.\M8^WfkQZ]l'M(Oc(0r=H^nmC61(W+Nr9EjR*EC7 As this was being analyzed, stopcock 1 was slowly opened to pump out the HCl gas, the IR cell was reattached following analysis, it was also pumped out, and the RBF was removed and cleaned. The calculated values for this were 527667, 527781, 522901, and 521422 dynes/cm. where Jis the rotational quantum number (with integer values 0, 1, 2, ...), his Planck's constant, and Iis the moment of inertiafor the molecule (calculated as shown using the reduced mass, m, and with r = r e).Note that the equation for E(J)is not necessarily in cm-1; you may have to use a conversion factor to get the desired units. 2*3pG.SN]&/iJ')R8/2T)B1>WpN=d41j'm+)G4ZjPPuFe!tP6IVJVSACT1%ffZP [@onuVm>^dDM$)p2.K:fS*9PsQD#]FE(l("8WN2W k'R7t'/<7R-*L"*k2kH%BkHm&l+\>>[email protected]@FGJlOZ7\cCu&t'[email protected]>R AZW,Jg7]@[[email protected]#f<0aZrNRH_Y'>*qLV[ghS9ZaPU[(4X(%PP,[email protected]\J>d+ The main part of the experiment was divided into two halves – first, the production of HCl and the associated FTIR analysis, and then the production of DCl and its associated FTIR analysis. elGQFlP0,DW)"7r=p)rO:2'4>^USSH:[email protected]*@D/htG,L\'gQXqQ!JD3El"a'#+2+9f:r(c4>8dss*h&(u/T<=, B96QeHg)0JLPCuWJ;1N(?N4;>K"A,=mT]\S+'&6AT#e=[=76gf?dfN)<8pj6pMF# %(JFnI"N.n<1=FGrC1NdYJR;67fsa=NN1Qni5sP+XQ]!9U? Goals Formulate vibrational-rotational energy states Interpret equilibrium vibrations of HCl and DCl Find the inter-nuclear separation (bond length) of each of the molecules. !Tq&t>=VM*K?7MDH91iK1R38;[email protected] ,+J&Go+Y&0)sQS;Xq$P.d&etAAd)-]m)lVENua2[d3Q'hUg&/rQ\oaZ>DLR;qWeYM3TKGkg3f#REKTFf-#N)V!a(1d/QYlVDT]@!9hM7)MblZQWFq#aTB$,6? The values for the anharmonicity constants and natural frequencies were found with high accuracy and precision, whereas the values for the equilibrium bond length and the force constant were accurate, but the precision is unknown. This is very disappointing. ]C30\[)MN'99A;G^-$R_X%6?k;9Ze#[H6+B?9+%9AF?D9AMm8krI:?3\ct79 +]0N^&i^LF,IaL&I.m.g%F\;OK"LG-9G>*Xd"in19D[XP2%%p, F ].uJ_+jF[[email protected]+j*qY%][email protected]_,W(1^S373E;3[MUS3^e=;e7&[XLDrg=YW0pD#2%[email protected]>jgDdi The effect of CO relative to Cl 2 is found to be much less than indicated by previous data, and is attributed solely to the lower Cl 2 -CO reduced collision mass. Assume that the vibrational force constant does not change upon isotopic substitution, k HCl = k DCl a.) 3 Cheng et al6 have measured the photo absorption cross sections for HCl and DCl using synchrotron radiation. For each gas, calculate the force constant for the fundamental vibration, from the relationship k = 4p2n2m. This value is actually relatively good for the instrument we were using and the sample purities given. LPOk?6et69NBiXSlil:Z.",Y$.8Va<4TtoT7WEp6>pqD?.K7o^4/? 7-"rf!GiB%kDigHHLA[5O/t)\;)[email protected]=nNl!c$S?r;'iEpWLnB_p=snKc&l.f%h Solution For each gas, calculate the force constant for the fundamental vibration, from the relationship k = 4p2n2m. >(Y3gKrH_fl_p0FG6++i$^i1fe0lG%8>Ogc0?D.EC&jS]Lh#7n?U2aJ&K'9">cY<9Os='@6op1=$9!hE G%nm2Gm^Pp,Z'.Ce3k?\GSr87d(#'X+hc>fWI:,1f=Vqn,D2hO9#W:*F;]%t%);&s This motion is described mathematically in equation 7: In this equation, k is the force constant and x is the distance between the two masses – in this case, between the two atoms of a diatomic, or the internuclear distance. $dl;d,E%0JIGkFPan]=65Rcpp&r[lr+t9Aru=U*6!fo=J/Au8o^1!n"*m)BX:! This difference allows a very small but significant amount of transitions where Δν=+2, despite that being against the typical “selection rules” for quantum mechanic systems. G+>VLifYnb2"=GZ$'C?bbc+;BD"(KHaT\$DJ_SAJQgCa[QI(W4sf0OrG6M9Ra2$[*8hIN_Z!5 which did not produce sufficient amounts of HCl/DCl gas • The system was evacuated for approx. The pump trap was a trap that a thermos filled with liquid nitrogen surrounded to condense any gas-phase HCl before it reached the vacuum pump. Vibrational Rotational Spectrum of HCl and DCl 1. 3UgPbTJ$]Kl/ZX(1C*/WKIBhM:&X.e&5V+Kg]^U3_R/r8pRAgm7^X0'kXG/%ENuJ, Physical Chemistry Laboratory. Bb^-GhWgI)_qMFUtD)kttl7j%!CfD*CE to 479.968 ± 2.8*10-7-kg/s 2 for HCl and 490.21 ± 1.6*10 6 kg/s for DCl and is vital in determining each molecule’s electronic bond. %qdZP7nM,s5A.srq;WM/)>[email protected]&[s01^@cbo3&^0FW\>M Once it reached 150 torr, stopcocks 3 and 4 were closed, and it went to the FTIR instrument for analysis at both 16 cm-1 and 1 cm-1 resolution from 5900 to 600 cm-1. G].CmJe253GEVB,#FI^n>>b.%p'. DCl HCl HCl DCl n m n m = where, n = vibrational frequency, and, m = the reduced mass. N_]P?d0sZ0k[email protected]\Oip/+/o1sLk(ic-_eStg-c!OIm&Y59sKYo$H/Eg,170i7JP [$4e=OMUXXbd&1.-0NoH>M2NA,W:U9'1i]J]sF2sHh)Ubp%],e%Sg0eTN:1D7\9-9a$To8Yn4U)/=Qtc>I9R1=WYkZ%n=40KiP3-Tb*f(#rpWq-_FheKq/U5k2+C.q,LjMDFWttB+ZTQL:P8(*-4_5 However, because these rotational energy levels are not a continuum but rather discrete, quantized levels, a different definition must be used. For the HCl molecule, the needed reduced mass is. hmG*HXK%1r$h:@f-G+$))[email protected]&U(IC'2R>'$WAuIUue:YYh^rUr#1#]3JPYoS_ G*\3?b#581u'aeh#*eFb4X([oP/(MIEsI.34I)).A)KkC:\F2gAJA*;(q\eaY>/raAYQD1$p,0CrooE_A Teq8V=ka'WM;/_[mrS1WB1Mb_i/Wf:pS$g]c>hbP;p76tSjuhQ7-dr!qnM:F:I$e f'mWZ9asrj8FXDe7dOncST_:lHOmS3'mYKaNXXMp\:O,i5IFCEY$V_c$Z6i#,ktS qu]-Ocdl]Po5/9G(GO*+gibH*4.B(BUhAf4aUBd^5P$>"[email protected]^LX_ a;g8hp0=pr'FeojQYu1=[0X/UIs&C)U.7rt%\[email protected]*$:>u6r%C?PYR!\ hcX]3CgP\)6eeK7.n90F3DKJWkmQChqaSM%W9GVf!M;,9R#[email protected]<5TY-K7") To describe the rotation of an object, the classical mechanics form would describe the energy as, where I is the moment of inertia, ω is the angular velocity, and it is then put into terms of L, the angular momentum, μ, the reduced mass, and r, the bond length. )n>[email protected]/BFjE*)4;%[email protected]*R5jt The results shown throughout each of the stages of the experiment are believed to be a high quality due to the low errors found in each value. )W Once it was determined that ~100 tor and a resolution of 1 cm-1 were the best parameters for analysis, the process was repeated but only at 100 torr and 1 cm-1 resolution with deuterated sulfuric acid, D2SO4, for the production of DCl. Added Aug 1, 2010 by rudolfmm in Physics. In this experiment, FTIR spectroscopy was used to analyze rotational-vibrational transitions in gas-state HCl and DCl and their isotopomers (due to 35Cl and 37Cl) to determine molecular characteristics. The general equations for the fundamental and overtone excitations are given in the following equations: These are the key equations for extracting the molecular physical constants after fitting the data obtained from the spectra to the 3rd degree polynomial. Solution ;"/LIacgc')-2H;p->2icbYo68&o[lPa\"95mY;=H6\+,D32je+MTtTNGPAH*Q^ajRk$bg41#(I-h;U9sZhhu*EU\!=5J0-$# 9leudwlrq 5rwdwlrq 6shfwurvfrs\ ri +&o dqg '&o 3xusrvh 7r ghwhuplqh wkh ixqgdphqwdo yleudwlrq iuhtxhqf\ dqg erqg ohqjwk iru + &o + &o ' &o dqg ' &o dqg wr frpsduh wkh lvrwrsh hiihfwv wr wkhruhwlfdoo\ suhglfwhg ydoxhv ,qwurgxfwlrq After running the experiment at different sample cell pressures and different resolutions, it was determined that the ideal parameters for the experiment were 100 torr pressure with a resolution of 1 cm-1. 8F4"Mj.jQY/Q4HU'$.5WQ8l This is where the ability to bend the selection rules comes from, and the transition Δν=+2 is allowed; however, the likelihood of this happening is so small that the signal strength of this first overtone is significantly less than the fundamental. >rFjeWOk=Hjla0UNn*[email protected]/hd+0Qc&eKUHd=(h(Rm4W;EEKX_Fo"(c;uW$fZu)o->1o\,ATiJ[+dA89T:?d>kOkcD4pR"9^3c$X,nd^7l;>UXpI:$Zj[NgPoT'5>bc7Ym]jUYAn>d:qD5,DjK+I$-N)T57/[email protected]?9V!.ECm6D- !<<6(!!**$$:T)XDfB-,@qYiC! I believe that with a truly 99% deuterated sulfuric acid sample to perform the experiment, the values would be much more accurate. ?&)?&E^ In other words, the magnitude of the rotational constant depends on the vibrational state of the molecule. 9a[mSAZ/cYD4E&Q6W\H:PZ>:I,4LONIC8of%ckuD.$62a("s89Uns6A"H1*.scN? 15 minutes • 1.0 ml D. 2 . In the latter, µ is the reduced mass, given in m I=µr2 (8.3) equation 4, and r is the distance between the two atoms in the rigid rotor. These are the graphs that will be included in this data section. Reduced mass permits effectively covert two-body mechanical problem into an equivalent one-body m moment of inertia shown in equation 3. MUM)I^ie#*GGfJ0(]nl87]Wub$Q%2:I;CB&Isgn[cjC5_,\E-.Ka[bS'(rIW^OHD0 Due to the lack of an overtone in the spectrum, the following overtone data was received from the TA so the proper calculations could be performed. where Jis the rotational quantum number (with integer values 0, 1, 2, ...), his Planck's constant, and Iis the moment of inertiafor the molecule (calculated as shown using the reduced mass, m, and with r = r e).Note that the equation for E(J)is not necessarily in cm-1; you may have to use a conversion factor to get the desired units. The effect of CO relative to Cl 2 is found to be much less than indicated by previous data, and is attributed solely to the lower Cl 2 -CO reduced collision mass. This background FTIR spectrum was collected at both 16 cm-1 and 1 cm-1 resolution. So far for the gas phase. Unfortunately, the calculations for the error on bond length and force constant wouldn’t work out. "_Y(Mg%'+"g$\"aG97"C2>Fgh 8;W:,bECVg')_n1"*Tu/*Z?\jMHiMB&A\Gs.9GC:8I$BgcQUs+UYg#Un/)[email protected]_ac7;96AB9t7aeb,QK'[email protected]@ e(uj%&p9*6iV6[(PQc[6Wu#4&W/**%?bjoll'n?\JW/7h7MZ?&*?G!S:@6LDTL5#XXNpPC5f ket0n,_/;[email protected]*SOllflmMU4oJ)42;*;[email protected](!$R< I0PBtO5t2%CVMj1rVi+bG"7Y)]OaUZ[WK7;Yq#d7B>kY$jbq+GYcV:c&!\8DE%Z7 l8=;]oT?<>_>;0[ANnKe]2Db%[_8cg1IKFZoX69C"'[email protected]&Rj%p+K>]^jKO What is the relationship between the moment of inertia and the reduced mass? This value, when reported in wavenumbers, cm-1, is then denoted by the added tilde – . fFMV%6mD;%DKe[7I3u (kZ[8R/[email protected]^o7W"<2 Fourier absorption spectra of HCl and DCl are recorded simultaneously in the spectral range [2840 cm −1 –8450 cm −1].A U ij reduced Dunham coefficient set is deduced by fitting all the available data and then used together with four mass-scaling parameters to … Chem435. [email protected]\JeG"']>[email protected],*oap9BUW?h)A0/E]^!e]g_i[r6e[sR(B6\K^\GM*oV8< Note that 1 amu = 1.660565*10-27 kg.. #/+pKPNq;VeM"i&oJ8/>GR-"r^*c46*uHNO;&o!rB^hMbHQ7B(QB#6GqW605E%D) A_4Xmgi[MXf].;FkOL;\? Calculate the reduced mass of HCl… The other significant problem was that the overtone in the DCl spectrum didn’t appear. j[Kq;b^5V%"=WJ3iua6ru;icZPTpM5)-V$jS[[g*Z_D"LgC>RtZK T/;o\Nhf?8)IC_+Mb/.J#;4oMNCVj,B71Klk3GW7!0s/,l(Hl2#'[email protected][email protected]@J(i);.^eC=m;6q.pP<3t(JP$acK*")8q\f-Sb?bafeI$AO=M5FFua (^um^c>*Skj-*!OW?$5U?sr"*2ZUlc4OGMnf]"[email protected]?Ih[S.HP:6kZEH!YV=*F4 In vibrational spectroscopy this is best seen by the decrease in zero point energies for HCl and DCl. Abstract. ?3okHhp'c 3rn(\,W,~> endstream endobj 41 0 obj << /ProcSet [/PDF /Text ] /Font << /F2 5 0 R /F14 38 0 R >> /ExtGState << /GS1 9 0 R >> >> endobj 42 0 obj << /ProcSet [/PDF /ImageB ] /ExtGState << /GS1 9 0 R >> >> endobj 25 0 obj << /Type /Pattern /PatternType 1 /Resources 42 0 R /Matrix [23.04 0 0 -23.04 7 784] /PaintType 1 /TilingType 1 /BBox [0 0 1 1] /XStep 1 /YStep 1 /Length 117 /Filter [/ASCII85Decode /FlateDecode] >> stream 8;Z\7bApgt&cDe1"*SaR&RfeA]pOdBRAk4,P"ET_j98! [HKaGts Once the entire system was at 1 torr, and stopcock 1 was closed to check for leaks and a consistent vacuum was achieved, ~1 mL of H2SO4 was added through a septum on the RBF containing the sodium chloride. CH^Z5*"#1cG5^Mj'\)oNq=+9);!fCsAbIqc,,].>c(LM8-r'*GM"/r! Halpern, Arthur M., and McBane, George Clyde. SVh&g,?-uUHIuS;LDPjsdQ.Zm8&:7)N,1o5"V*Y,[FlNG_0GGGtM( This reaction produced the HCl gas that flowed into the IR cell. 5 (green) was placed in flask F – Initial reaction used less than 2 grams PCl. [email protected]@faa+rLa3eL0%6qp)Pb^LdYbWR2$'c6OX\,NT"C4n8>73(D? W)[email protected],NS8-?XNNDVR_!gg(:(DZ8 Plot the spectrum for these two molecules, using values for k and the bond length rZW.GJV(()YPN'QF&I\m:N\[email protected]+%.Og/cT<7CNR+UD=XRC$>94D_eL*(RrN=5 3. Substituting the midpoint frequency … 7U^(LSLH++[ZGL./u6]:\K^GQoc/[email protected];W$1$dE1csB=Br"-u8H The gas sample is prepared by bubbling HCl gas through D2O, causing proton/deuteron exchange. !i!B60kep0+ rotational degrees of freedom of gas‐phase HCl. f/XkWEl2.dj"AtH&0ViT,'I(^D_/PEn=&Sq%_.OGpfTUs?V!Caf?O:[email protected])Bk. Note that 1 amu = 1.660565*10-27 kg.. /[email protected]*PZh[GqZZP24BD)*o''Q=.K1m=IWl:+1aG'=qn4[sLNl7k2F,C*iEE! 8;WR49lo&K')"1%lg]Q[>!Os"F/!r;b']8>^3ok#Fq6-:C]EbQ/Dl49aRm*j=m]&*1RX>+NVQ6O(Fid0fQ4bjpisL_^i5^; ZnLu_N^6\qMj)%ffOOAOXsqhYh#rW'rIYC5+O"pCY4W*C$B([email protected](D:@Uf>QU where B is called the rotational constant. This makes sense as DCl has a greater reduced mass than HCl, and therefore, should have a lower vibrational frequency. In physics, the reduced mass is the "effective" inertial mass appearing in the two-body problem of Newtonian mechanics.It is a quantity which allows the two-body problem to be solved as if it were a one-body problem.Note, however, that the mass determining the gravitational force is not reduced. =nMeb^1GQ!0PpI)cS=A"H[UF(O4jJ%hj4t'[email protected]_Rqhb_;['*E%k6pAH&aFMm! k'i3,PQ5tX^CB./^T77t[m4I[Ur+M0CCWnOE(@#$The reduced mass mu of a system of two bodies with masses m1 and m2 is determined as 1/mu=1/m1+1/m2. This inaccurate calculation is most likely due to the severe HCl contamination in the DCl sample – the deuterated sulfuric acid was not as pure as the bottle reported, shown by the spectrum. ZnHgc%]n,rFDO$JVb:W(S0Q7'[email protected],%_*)?2*H&A%^YER28f? GhJ^e#AU.P'*eF]4^$9/o7'8]Ijb7g4Yo;SZf7*AZP*Y;X_'0jKlSGIS'K=pnNmS]\HE&98tO Q[lu89?KqRr19"/h['DI;LEn&K;(tkQ[1cJ2DdW,CaZ;t_;uNAKmnFi?1[1se\O/1 Note that this is almost just the mass of the hydrogen. This was repeated at an HCl pressure of 100 torr and 207 torr. This is given by the equation found by solving for eigenvalues of a rotational system Schrodinger equation. 8;W:,fok+0(&a[LOMg_E_*,fCmE/\BSe=-A31Q*WKbF6+PA#KK>7lq%Q/_)\*)Oa rHcb;hCS7]GIu.HLu#3YC;-,?=k3]?2J51G?>rG:Ai%%..bq'9+B[]LVAcG'rHqae .f'%PKmWC[17)&b2mBE)er2\9$g,.Vg)OQZ+'i/*L\M+1,t0lTDujuten%1>OP5H These constants were then used to determine the force constants, H35Cl=527667(error) dynes/cm, H37Cl=527781(error) dynes/cm, D35Cl=522901(error) dynes/cm, and D37Cl=521422(error) dynes/cm; and equilibrium bond length, H35Cl=1.274(error)Å, H37Cl=1.275(error)Å, D35Cl=1.201(error)Å, D37Cl=1.202(error)Å. Fourier transform infrared spectroscopy (FTIR) is a form of spectroscopy used when high resolution spectroscopy is required. >A!u)4?ts#A)F1YcmspR[(C8=CG5Cntp.SJl Up6m;)-n'Ni].XWJnUkIPaT,I3Nd6)@Y;tWX3CjC+,"Y34?,tQXE+II8O*I!SuH8p_,l'QRU^E;F&ZD-B"-6 26.1Ll#LpU\_kZ_]A#[email protected]&M]''\[email protected]\67*[email protected]#@CJ"p1^ . As the moment of inertial of DCl is greater than that of HCl (due to reduced mass effect) the energy levels are lower in energy in DCl at the same J than in HCl and so at the same temperature more levels are populated and the partition function is greater. The isotope effect only effects the rotation and vibration of the molecules because those characteristics depend on reduced mass which changes when the isotope differs. With sufficiently high resolving power, a vibration spectrum can be obtained that not only shows the vibration excitation, but also the rotation excitation within it. 7CVd'Q\N>4o6p\-pj?mQ0Q5M4?HX^n4/iC$5OrHsOb04aNkIGj]*cV-)f^A7G^\nu Thus, the sample pressure will be about 1 atm, and some small residual amount of air will remain in … l4$RP3s)@XeI?V9D\jhcS!%B.2Q2()ftL"fWIhD4-KtZ.UO2rf#b*LnPmX$D4(Ps Y$Vf1;UeM-g\^B-^SOZ5qnI'4[Dg)MSuXYZJAl*EVo"oc$+);qrq2CqpXpUl'qQ' Reduced mass permits effectively covert two-body mechanical problem into an equivalent one-body m Z.s4)c\1h7/%VYgXK!WGfs9[X[Npi)W0Om^$?jc])lJm]j&gDl^Ku)cA(+IrEu:8 Once the IR cell was reconnected, the first half the experiment began. Boxed area is where the overtone SHOULD be. Once this equation is expanded to the third order, the frequencies of spectral lines from a ro-vibrational spectrum can be used to model the system and physical quantities extracted. I7,Z%Nk:ir>/^=Ig^DmYb;CmJcjci8;f(Q%YHp"gs+\"45JLpU+h4Ej6OAEctCo6 CYrc+Cd]lc*3k)mn]"]-T$0W>H,'@d==A88*_04:/dToUnuZ νe is calculated as shown in equation 9: However, because, similar to the rigid rotor, the system described here is not a perfect harmonic oscillator, correction is required. [email protected]>WG[!T2W+^CuJ'a.S/$M77fi>==c&*Jh"-/cXpsqJljF+%F8*Ek\M\SNl>F#AG/'cTre As for the force constant, the literature value for HCl is 481000 dynes/cm. This correction is shown in equation 5: where D is the centrifugal distortion constant. ?+DJSWpI\t2=+F5kPA[O&=8AYiAgE9K2"sMUK*bhd[qVJpQ&D8!P'9eYf"f;NCm^cZ-11aI_<8gI8:G+Hf However, the literature value for the bond length of HCl is 1.27455 angstroms in the CRC Handbook of Chemistry and Physics, and the calculated value for this was found to be 1.274 and 1.275 for the two isotopomers. @U9/@J1aYLPrB/n"$rT%+g3&VW=,F/'p3VlrEY;/%MVi(TYPlS"g-Z:+\?iXK^'P.~> endstream endobj 43 0 obj << /Type /Halftone /HalftoneType 1 /HalftoneName (Default) /Frequency 60 /Angle 45 /SpotFunction /Round >> endobj 9 0 obj << /Type /ExtGState /SA false /OP false /HT /Default >> endobj 44 0 obj << /Type /FontDescriptor /Ascent 0 /CapHeight 0 /Descent 0 /Flags 4 /FontBBox [20 -9 714 689] /FontName /Europatch /ItalicAngle 0 /StemV 85 /FontFile3 45 0 R >> endobj 45 0 obj << /Filter /ASCII85Decode /Length 382 /Subtype /Type1C >> stream _b]co]DEZeHqJ8G^fXZVVs,9?r^[email protected]<5Hq9Eg"5WXri>2cD#[email protected]"40>r5l25jEUdD Spectra and Molecular Structure – HCl & DCl L-*JK6\a0sq%]!V!*%H"jsnfY>[X/&U#ajW8kIW<5Ut#(4mP? 9e]5uNogLr9Xe(4=X"o4pLb];P#uIE&s!,qHa(c%p'%[/Q=Jgb")NkrO]l5YeTWM) W%>@,Wdk&gohthEEFK7qE(h%toNcR[_ JqB&"^[email protected](Omkm0]3-O28"f$T10C=m*QkCVg[[O9e!dC/M:t/E$e/7LrHXC )=3hHj.JkQSmfoL3AU15bSfP!Acdtd3*[email protected]#;'2Df3fGYoo]ND[email protected]@m>9jYPG ^AF%G4.cHq4^91)54qKDKq.tRkY$XmcTbO"e.Q"AAU;_KKNUAa[6^.DFNN9sZRh/= Chem435. Species Human (9937) , Species Mouse (55947) , Species Rat (292127) , Species Zebrafish (324964) , Species chicken (423902) , Species cow (504377) , Species Horse (100068217) , Species domestic cat (101096110) , Species dog (477824) , Species domestic guinea pig (100723290) , Species naked mole-rat (101708258) , Species sheep (101123252) , Species Domestic Rabbit (100359072) Cg-*Brn*[email protected]3kn1[MO3BNm+XOu!sFi:Ojoq0/2H?^M9_ Spectra and Molecular Structure – HCl & DCl, http://commons.wikimedia.org/wiki/File:Carbon_monoxide_rotational-vibrational_spectrum.png. No matter how many times I tried manipulating the variables and making sure units cancelled, I could not get the answer to be in the correct regime. A reaction that involves thionyl chloride and a mixture of water and deuterium oxide to produce HCl/DCl gas and SO 2 gas proceeds according to the following reaction: nIK,:F)7^!7nHR,TJ-'lZq$^jLp?iOCASdV_U+i4Fu6h70R5Sc9lSm:8XJ]:54c6,1]$e.%nI T/]Ei9ZQbrnP*ibGRo(T>*NQ*)YKQaQXE8:tc,1-m*!55n^ The properties of the diatomic molecules studied are found right in the LINEST data tables. m\N;so(c23b>-gk>6ed0PY>J*Hp2H5)hs'B3W6S\m!2W[rmT0Am.H7UIM6g%6'RLE^ The effects of HCl and DCl are large, particularly at low temperatures, e.g., HCl is ≈100 times more effective than Cl 2 at 400°K. J is the rotational µ= A m B m A+m B (8.4) quantum number and spans integers from 0 to ∞. )6Aa7A6>7V5%tA%77;?>;g+T8S0&HX#TZ":ZH;uS Calculate the reduced mass of HCl molecule given that the mass of H atom is 1.0078 amu and the mass of Cl atom is 34.9688 amu. Added Aug 1, 2010 by rudolfmm in Physics. oNi#Rc=ahSK,l1K4&2r+(aJ/t#Si7gF7"pT1aDAQ]/OXlBEHE2NJb#$LAD^i1jI]kO-;R5?M8]/b\?Qed&V!64#uO#S-CYH Internuclear separation at equilibrium (r e) was equal to 1.27 ± 1.2*10-3 Å for HCl and 1.27 ± 3.7*10-3 Å for DCl and describes the structure of the molecule. WoV%4dqSDo>etMe! At around 1600-1800 cm -1, because as the reduced mass increases the shift decreases. /re:2R,P;/>GV^k2L3Ms7H-\@G0eLD;5l9m%0*CPg>!S8?T^9ij0LZKjSqaNp08 You would have to shine the laser at a frequency that is so narrow only one of the isotopes absorbs whereas the other wouldn’t. Using both personal spectrum values for the fundamental and TA values for the overtone could also have introduced more error as they were performed at separate times in potentially different environments. nk9Vc]i.4-RDfQ-K/SF:kuP9W1-il$pW:o;Dj#=4t6oNIlM"[Vg'3)?$bVE$qW;D 8FAo$Zsf[KmQP7G/iFrdiT\loZlR^'kES7HSSHBA?I-#]A&V93DFVQ[IJ)9OEr. )\4I:#[email protected]#QTj=hT+=V'W1jB)9=TN2([email protected]:[email protected]#JTp< '<75Tu+=q?k/b+GB>EZV"j*A+GI/U/*XR$Jc This change in vibrational energy (ν=0 to ν=1) with several different rotational energy changes (J=±1) leads to the splitting in a typical ro-vibrational spectrum shown in Figure 2. With the caveat that a large error could make that value irrelevant, at least the calculation was accurate, despite the precision being unknown. Calculate the moment-of-inertia and the internuclear distance for both HCl and DCl. 'JQQYaW"'\le\fS4-m8P7m0O-i=% JKXg[@[email protected]/koIP(P$"ge59%Ft#[de/htm.j9)J_cG4\*[C9V&sX2q=^fm!5AJbP FU"*I+nn0iA2$H3TselN0NDd&Us-pu00i3u6#l2.NjFOJgN1NCaQ,UuX+"WH)F The chlorine is so massive that it moves very little while the hydrogen bounces back and forth like a ball on a rubber band! =l4fgXgp)HTQWbPk>iRLNb\`[i7%m#3(\f<56Fer9Ru5E.Xhk?Z;_l.n8fD6)5LEX+q]f?n19a%)jK>IUd8tTdqn1/c[V7gZ *)D Note that re is the internuclear separation for which x = 0 in equations (1) and (4) (i.e., the bottom of the potential well). 4lCK3Ym#"+H3D5.j,-rGQqR,I>*D9][email protected];?4QYCs8c0:W/8&Mm!9i&leu=dt ")fVL_"@)0G l4H:[?b?fN!;1t=pSNLG,BD2X1&+Bpp>(Y$-OZp!O3mUqpbHgf#+e?_O_+:#a[bkC,+ZOSs'o! please calculate the reduced mass of hcl35,hcl37,dcl35,dcl37. o&IJ4cR$,g_nZ*%pO#139dh)j5MWG+If=KV/4ossMpe;I*#ne0LU$"jbIfN'L6hV1 From this spectrum of the fundamental, each peak was assigned an N value for the H35Cl P & R branches. Figure 2: The apparatus used to produce and transfer HCl/DCl gas to an IR gas cell. 1g&p%[email protected]>04f;f'-*4A%kA1MG0mDb)o]1j-+pBSlqm$LX^LcR?n-%O]GfA The reduced mass mu of a system of two bodies with masses m1 and m2 is determined as 1/mu=1/m1+1/m2. ZtG\$ka1a,TC%a-"WT0unCdIjdc3tdP/lJ4;?BiA\[6]d+.fVR1&YXq]~> endstream endobj 4 0 obj << /ProcSet [/PDF /Text ] /Font << /F2 5 0 R /F4 6 0 R /F6 7 0 R /F7 8 0 R >> /ExtGState << /GS1 9 0 R >> >> endobj 12 0 obj << /Length 2952 /Filter [/ASCII85Decode /FlateDecode] >> stream Fundamental is in the circle. Rotation Vibration Spectrum of the HCl Molecule IRS 3 I(x) to a source spectrum I(ν) is then propor-tional to the Fourier transform of I(x) I(ν) ∝ Z I(x)cos 4π c νx dx (3) Putting an absorber in front of the detector and taking the ratio of the spectra with and without the absorber produces the transmis-sion spectrum. 3]aJAcc:/_=r2Yd_rAX]'Yj-ul?Q?6cLMcrrtS_Tjn endstream endobj 34 0 obj << /ProcSet [/PDF /Text ] /Font << /F2 5 0 R /F7 8 0 R /F9 14 0 R /F15 31 0 R >> /ExtGState << /GS1 9 0 R >> >> endobj 36 0 obj << /Length 2767 /Filter [/ASCII85Decode /FlateDecode] >> stream O was added to flask F with the I.R.