In wavenumbers, the energy, F J ( ) , and the rotational constant, B ~, are: J(J 1) ~ ( ) F J B = + cm-1 and cI h Be 8 2 ~ π = cm-1 (11) Vd2N:Me@.jKhH=+d`+LE`m2`T-pbV.qr#l3PcjJ)rpoQ(oD/,6Y3N>j@8nM+=]f"f rZW.GJV(()YPN'QF&I\m:N\WG0@H+%.Og/cT<7CNR+UD=XRC$>94D_eL*(RrN=5 It is believed that with the very small errors on these values that they are both accurate and precise. The reduced mass mu of a system of two bodies with masses m1 and m2 is determined as 1/mu=1/m1+1/m2. The effect of CO relative to Cl 2 is found to be much less than indicated by previous data, and is attributed solely to the lower Cl 2 -CO reduced collision mass. ;ic_MMd!>P41Jn$d-?=.%c;Fu[r3u%MRG0X^)5Q6P6pnkBPr`N>8L]hnMB7Y-:sc# 2*3`pG.SN]&/iJ')R8/2T)B1>WpN=d41j'm+)G4ZjPP`uFe!tP6IVJVSACT1%ffZP cS\2Vq-Hi^VGq/&*1,)B_X+:OFoed=46K!oLPGC-NVdWRSn=ksL>gjMh&PV2"I@Ml(Tckg&_Yfp!_6-;S! 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. B96QeHg)0JLPCu`WJ;1N(?N4;>K"A,=mT]\S+'&6AT#e=[=76gf?dfN)<8pj6pMF# +]0N^&i^LF,IaL&I.m.g%F\;OK"LG-9G>*Xd"in19D[`XP2%%p\*)X0^e"/PHb]le f/XkWEl2.dj"AtH&0ViT,'I(^D_/PEn=&Sq%_.OGpfTUs?V!Caf?O:5nV@FDN)Bk. +#NeVK$]CZ=FOJ='%rU;6t`HQ&265A!ceHAS`uq-]AA6>YZ9Fn9g5'+qbE6oR;Z7WDo5o:DBeuo\r*GFteQ? Bb^-GhWgI)_qMFUtD)kttl7j%`!CfD*CE ]V@N5R/r^`)%2d'V /I@EXL2*PZh[GqZZP24BD)*o''Q=.K1m=IWl:+1aG'=qn4[sLNl7k2F,C*iEE! Cooley, Joya. ;"/LIacgc')-2H;p->2icbYo68&o[lPa\"95mY;=H6\+,D32je+MTtTNGPAH*Q^ajRk$bg41#(I-h;U9sZhhu*EU\!=5J0-$# Once the IR cell was reconnected, the first half the experiment began. 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 … From this spectrum of the fundamental, each peak was assigned an N value for the H35Cl P & R branches. We can use the same procedure in Q1. Added Aug 1, 2010 by rudolfmm in Physics. 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. hcX]3CgP\)6eeK7.n90F3D`KJWkmQChqaSM%W9GVf!M;,9R#_&GkNTn@<5TY-K7") !<<6(!!**$$:T)XDfB-,@qYiC! As this was being analyzed, stopcock 1 was slowly opened to pump out the HCl gas, the IR cell was reattached following analysis, it was also pumped out, and the RBF was removed and cleaned. The results thereof are as follows: Table 18 – Natural Frequencies and Anharmonicity Constants with Errors. No matter how many times I tried manipulating the variables and making sure units cancelled, I could not get the answer to be in the correct regime. oNi#Rc=ahSK,l1K4&2r+(aJ/t#Si7gF7"pT1aDAQ]/OXlBEHE2NJb#$LAD^i1jI]kO-;R5?M8]/b\?Qed&V!64#uO#S-CYH Once the leak was fixed, the system pumped, and the reading stayed steady at 1 torr, stopcocks 3 and 4 were opened to pump out the IR gas cell. `[9F#oA6^X*:kCJ#GdA`G]J?6pjW9`T7_1~>
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5.7. 6@59&^(nsIA>Q6-apUC$DQaH@@M$WW+?4W+#a8I0[]&:(Fd7%"lB44?`naLrDW:)TN[)P4#`n!m9m1Xo\"%tU! ];M !-M?3X^l2QLFt&F%6EDiiiEaRfcXK?EUJPt$p\+OLR?HuV:b0>$SoR=Z7^/F\_`sA :5mH7MqpF)s9-?6Lhi8u]X?s843FP&9M882l7@f=m[L\KfZ3=gL^: AZW,Jg7]@`[OLLhiM&@#f<0aZrNRH_Y'>*qLV[ghS9ZaPU[(4X(%PP,CS@qc\J>d+ :b` The force constants are all relatively close together, whereas the equilibrium bond length is significantly different – when on the order of Angstroms, 0.07 Å is a lot. '?*A9NqJh\?R'%Pk+.DfF;]`9])*3%:pGmUY%t`QLm+G/"$VV8'HtH?NHjT#D! Once a spectrum like this was obtained for HCl and DCl, peak values were assigned to the P and R branches, for both 35Cl and 37Cl. ._T$aZ+)Nn\C"/cN"N*dM]3O*V.)K9;_O'jbKb6*FJA'>Y]F8Pog@,k:94_m-L\6rE\1NekEOTA;uH^P['1^Pf*(IiaM[3:9AF'K7L>8Wli#D9eU; #*Sjr6b8BE.Y+T$___Y"LJoI$$q[BR#,="qEY;9a/4uP(KlUm-46KmG-,a7M.M:_/ ?&)?&E^ Y4bmpCHsgY_@3,EXkiPmUn9&['tX*r_"0*8P(YaZ9p98;?H9dh##"4B(23/EqHB_R qu]-Ocdl]Po5/9G(GO*+gibH*4.B(BUhAf4aUBd^5P$>"S@sp4^LX_ 'X8ZIR%L\.$l`&[LJ&11&qs%>PVF)8U2*CZYf3HDe;_\Xn9_b,L$fdj!g_uZmO0,u c?0"!Bd;lC4edB])8@t+rYrp#$Q&i#17_3e26.&6AY9D?A)m%@)ZP*5RM_!UMtD+`c[ 1g&p%&Y8ecB6h0@>04f;f'-*4A%kA1MG0mDb)o]1j-+pBSlqm$LX^LcR?n-%O]GfA In the Lab: HCl (and DCl) gas is placed in a cell with KBr windows. _b]co]DEZeHqJ8G^fXZVVs,9?r^B@<5Hq9Eg"5WXri>2cD#T@U"`40>r5l25jEUdD JqB&"^lHA@l15Q(Omkm0]3-O28"f$T10C=m*QkCVg[[O9e!dC/`M:t/E$e/7LrHXC (1 u is equal to 1/12 the mass of one atom of carbon-12) go3+ZK:cut=r8kI9h&It_\h(Z6u!0/)lc+Ii!..>dP7Sr(9E>1gcp)!,f6^Ba&N9a jk(HQaUY.RID-il@kqA*VpA3%(ioI(C@u6-N0I+kSS]HHObXToWuiBO9!8m=A[qYA)!ssda*1g:SJQb"D)?$sh;k=MjSVSb@:NMYn[16kZZLXf p*o=F8_f.fSl0f^M%qIRdc47n9%jfM1\GG@0f*?BqEas;ems.`XF(cQ'V-o)Gn.ha 8;WR49lo&K')`"1%lg]Q[>!Os"F/!r;b']8>^3ok#Fq6-:C]EbQ/Dl49aRm*j=m]&*1RX>+NVQ6O(Fid0fQ4bjpisL_^i5^; Since DCl is lower in the potential well, is smaller for DCl than HCl. Abstract. ]%Y]fJ[F=eUiU)-6-A(qO Figure 7 – DCl Full FTIR Spectrum. .f'%PKmWC[17)&b2mBE)er2\9$g,.Vg)OQZ+'i/*L\M+1,t0lTDujuten%1>OP`5H XHL5^p!Dk_qb=a.ah!b'_e;ub6Q2_TA8<6-aI6[ePgH8imJ[n@m1SCueW<8,_4aGJ KUB?q5a@fk&7Q5HrSlFkIrP,HK\5pS$H&3=[DfOM[N-mBE`6@oeNk;*]? The experiment only had one significant source of error in the impurity of the sulfuric acid that was supposed to be deuterated. 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. 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. Y$Vf1;UeM-g\^B-^SOZ5qnI'4[`Dg)MSuXYZJAl*EVo"oc$+);qrq2CqpXpUl'qQ' The vibrational . NhVQ$p0r[epJgV?knDkDP[t_%dIFpZ\tLP=-V@qt"/F9(=t2ZWkS-\=;kCg.+P2mH TQki.B:GO+(R[dC/LKA7W%V9Wf^,eia%S.u,"9h,0r%$ut %Woh=\("! -el@A6qXVW+j\]M4-st> 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) fFMV%6mD;%DKe[7I3u 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 predict the TCl Y ij Dunham coefficients. 4lCK3Ym#"+H3D5.j,-rGQqR,I>*D9]Dfq@PoTA;?4QYCs8c0:W/8&Mm!9i&leu=dt Stopcock 1 was closed, and the pressure slowly rose, indicating a leak. 8F4"Mj.jQY/Q4HU'$.5WQ8l This is where the ability to bend the selection rules comes from, and the transition Δν=+2 is allowed; however, the likelihood of this happening is so small that the signal strength of this first overtone is significantly less than the fundamental. /re:2R,P;/>GV^k2L`3Ms7H-\@G0eLD;5l9m`%0*CPg>!S8?T^9ij0LZKjSqaNp08 The reduced mass mu of a system of two bodies with masses m1 and m2 is determined as 1/mu=1/m1+1/m2. ([E`4cHaU$:f7 4SU1r7=!FNL;A'T][h2aTMH8BhXIbq@kcl^0Qb%^%t/3dFmb75K5JcdV'rO0,Y4H^ It was determined that increasing the mass of an isotope resulted in absorption at a lower frequency. _,[WU:"BJe0T?;!%8$rO\TYH7j1oYO1+iT'a1>shT2G:>CF8bFdf6$HoW>^U08](O%'&AP? fuFJ1E!oo?]!,b+[NK4:O=c%I;ufRLhi'o&&. = µ µ* (11) HCl gas is a mixture of H35Cl and H37Cl, and the ratio of reduced masses for DCl is 1.0029, which might be observable. The degeneracy of the Jth quantum level is 21 CALCULATIONS Assign m … 8;T*$0Ef7eFC'Ci?pfY? 3_lhXV,!X=0ZkAIP:tpmS.$58VkO:]k? !>+4$#*.+m8[%l&.b@(a.t(U!88WUbNEEi>kB/(SKWDe!a_k9hB*H-Aj(W_AmiJp&5r&^k='rRjW32bJ-c45=mH The rest of the calculations are on the attached sheets. r!-ktB2K9\R*uY-NY*J@bA)IO^9,A`[imkc.u\(4P+Uc,BbBD5H3o7]f;gID?E]W^ This isn’t surprising as the increased mass from DCl would affect the equilibrium bond length more than the force constant. FU"*I+nn0iA2$H3TselN0NDd&Us-pu00i3u6#l2.NjFOJgN1NCaQ,UuX+"WH)F A_4Xmgi[MXf].;FkOL;\? Note that this is almost just the mass of the hydrogen. +9)qkAS@9qO8>.oil,=0IM93)mMW\1W$(5tccVD?$D_@k0C%f9Di5G%AfJiBM'7H_ _"bKoPMA/m7ceq-bC4CCLUKH`.b$@K35BiQ#qEt e(uj%&p9*6iV6[(P`Qc[6Wu#4&W/**%?bjoll'n?\JW`/7`h7MZ?&*?G!S:@6LDTL5#XXNpPC5f To prevent gaseous hydrochloric acid from entering the pump system. Image Transcriptionclose. 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. In vibrational spectroscopy this is best seen by the decrease in zero point energies for HCl and DCl. Those frequencies can be represented mathematically as shown below: To describe the vibrational motion of a diatomic molecule, the first place to start is a simple harmonic oscillator. Ab initio calculations of potential energy curves and electronic transition dipole moments have been carried out a number of times.7,8 In addition a general potential energy function has been proposed.9 Both time independent10 and time dependent8 methods have been used to calculate the All of this will be repeated below for the rest of the data, in the following order: H37Cl Fundamental, H35Cl Overtone, H37Cl Overtone, D35Cl Fundamental, D37Cl Fundamental, D35Cl Overtone, D37Cl Overtone. =Cf^rX!b?2_1]N"ejAmd[89RT7-K];3jDV-Wm@];-+fh7B+r=ojXjJj(8:;,3f>O5 Once this also reached 1 torr, stopcocks 3 and 4 were closed, and it was removed and used to create a background spectrum in the FTIR instrument. )2K?QZEtF"tDr Calculate the reduced mass … hoqm@Z2>WG[!T2W+^CuJ'a.S/$M77fi>==c&*Jh"-/cXpsqJljF+%F8*Ek\M\SNl>`F#AG/`'cTre 9a[mS`AZ/cYD4E&Q6W\H:PZ>:I,4LONIC8of%ckuD.$62a("s89Uns6A"H1*.scN? Y&iCOE;Z$HfmEGWh.jbDS$*ZS#.E=4IQBHcYIO'< So far for the gas phase. Spectra and Molecular Structure – HCl & DCl, http://commons.wikimedia.org/wiki/File:Carbon_monoxide_rotational-vibrational_spectrum.png. !i!B60kep0+ (^um^c>*Skj-*!OW?$5U?sr"*2ZUlc4OGMnf]"pH$u@l?Ih[S.HP:6kZEH!YV=*F4 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: GhJ^e#AU.P'*eF]4^$9/o7'8]Ijb7g4Yo;SZf7*AZP*Y;X_'0jKlSGIS'K=pnNmS]\`HE&98tO ,#;>H9pl.6BC]:@IldeVIR)I`$[Fq-;hC_SC,q$)"JgDcW*]E'6pBoV.>+8o&lC2! 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. ]Z#e!1AjrAm8(Qa'?LS>;8TP:)=AL!9U$$bl@5ub^J@&;]2*0mn)UGh=S'YD9D/PQ W)-bC=@l,NS8-`?XNNDVR_!gg(:(DZ8 l@c@faa+rLa3eL0%`6qp)Pb^LdYbWR2$'c6OX\,NT"C4n8>73(D? h5P%2db-c9iM^Gl54@_R99eO?p^N`Rr'kXtSh*h-nM;A7S,(_bVc8Lr4Dgaj)*,b]=Be"M7$Gk_Xg 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. 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. dkVrGb/JHJ;Gd2.=lc(lX70^5*_j^MF1>Wrn.UAPc.SL'UCf0G!lh=9:(#/'KC[9 :_V8:RH:rGhX#3lYXi?BEt';0HLL] Unfortunately, the calculations for the error on bond length and force constant wouldn’t work out. T/]Ei9ZQbrnP*ibG`Ro(T>*NQ*)YKQaQXE8:tc,1-m*!55n^ l8=;]oT?<>_>;0[ANnKe]2Db%[_8cg1IKFZoX69C"'QNWp6Rk@-H&Rj%p+K>]^jKO CYrc+Cd]lc*3k)mn]"]-T$0W>H,'@d==A88*_04:/dToUnuZ qX'b3'm8uP_ZC-\[O!hH=hIg+L?+8Cs$Z:HNuTj,_12@M.,LC'3l%p`7kf!tR^W4. f'mWZ9asrj8FXDe7dOncST_:lHOmS3'mYKa`NXXMp\:O,i5IFCEY$V_c$Z6i#,ktS a;g8hp0=pr'FeojQYu1=[0X/UIs&C)U.7rt%\G@*`$:>u6r%C?PYR!\ a). )iF-Q?I1-^X"mI)`Zh8_ . “Rovibrational Spectroscopy.”, Figure 3 obtained from online lab manual pdf for this particular experiment, provided by the UofA chemistry department. =l4fgXgp)HTQWbPk>iRLNb\`[i7%m#3(\f<56Fer9Ru5E.Xhk?Z;_l.n8fD6)5LEX+q]f?n19a%)jK>IUd8tTdqn1/c[V7gZ The overtone’s appearance is due to the potential of the molecule being more similar to a Morse potential rather than a true harmonic oscillator. 5.7. What is the relationship between the moment of inertia and the reduced mass? For each gas, calculate the force constant for the fundamental vibration, from the relationship k = 4p2n2m. Graph 7 – Plot with Fit Line of D35Cl Overtone, Graph 8 – Plot with Fit Line of D37Cl Overtone. ]RO4W1J'$V:XlSSFWnCt$R@eXb\d[H2j3jQUrfV-U^1BM\9uZ4*:G+_8 "WO6Rub"TkVFMa8VK1-]OhKNs6(XF_eP#Q6cV !Tq&t>=VM*K?7MDH91iK1R38;bKZj7@PB rotational degrees of freedom of gas‐phase HCl. 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. Plot the spectrum for these two molecules, using values for k and the bond length This was found to be at the junction from the gas generator to stopcock 5. )cPp\q#/Ucp#a)6;l"M\;'W#0-a>U!G5DQI#['=DnIuEEY-V$ta5#:nY\/AeD9"PD )W @RQ>_YqGu This is shown on our DCl spectrum with the HCl fundamental impurity showing up to the left of the DCl fundamental. 4iTR"03V#'QoA/JaMRlb_Q'ltc\?kVqEr_;`H]G3p?MQucX6annkes5oW2FHYOji#Wh WH?F4d#(\OJt@h=Tp2.Tq7?P$cf7>H)CY+;:@K8JMXP5P3!&1h1W]c((e[%V >^jE#`VSHEpf:i4/T2@mOmk&aa@U,Nm6-]49V,2J!%GFjQCH9(^r"[XRc-$6G1e?B Due to the lack of an overtone in the spectrum, the following overtone data was received from the TA so the proper calculations could be performed. >rFjeWOk=Hjla0UNn*l@/hd+0Qc&eKUHd=(h(Rm4W;EEKX_Fo"(c;uW$fZu)o->1o\,AT`iJ[+dA89T:?d>kOkcD4pR"9^3c$X,nd^7l;>UXpI:$Zj[NgPoT'5>bc7Ym]jUYA`n>d:qD5,DjK+I$-N)T57/e@?9V!.ECm6D- Assume that the vibrational force constant does not change upon isotopic substitution, k HCl = k DCl a.) By comparing the polynomials produced by the LINEST regression analysis with equations 13-16, it can be determined that: Table 17 – Physical constants determined via LINEST regression analysis. Up6m;)-n'Ni].XWJnUkIPaT,I3Nd6)@Y;tWX3CjC+,"Y34?,tQXE+II8O*I!SuH8p_,l'QRU^E;F`&ZD-B"-6 S9!7'>Rr/5RnUmA-6gq^%9^\,^o4Pbe2/@G`%1+V$D'rE\PG'8+WsrgC4#G,),mO$ =nMeb^1GQ!0PpI)cS=A"H[UF(O4jJ%hj4t'?@XDqgj_Rqhb_;['*E%k6pAH&aFMm! BMcSW9Q/O#K@4aLUMZ+B(B'!RQ5/FFLE/Td&DU:91AaiurdM7pa>) D(gE/Rlu:-Kuod,d3-,LMYkoWM#Lh&IOM)btjTjanV[ 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. Spectra and Molecular Structure – HCl & DCl 8;Z\7bApgt&cDe1"*SaR&RfeA]pOdBRAk4,P"ET_j98! o&IJ4cR$,g_nZ*%pO#139dh)j5MWG+If=KV/4ossMpe;I*#ne0LU$"jbIfN'L6hV1 %(JFnI"N.n<1=FGrC1NdYJR;67fsa=NN1Qni5sP+XQ]!9U? In other words, the magnitude of the rotational constant depends on the vibrational state of the molecule. Numbers 1-5 are stopcocks. $e8efKk6P7h]G'i!l"!ekKPc/LR6*NU48X746jMbm>'f(Z.TZ2gRRdZbkF,pPdF)/ ]6Jfa1O^69*X6N[1CqBBno,FG*ZE5M==X%Bd@PH0,ft,!5F$=iBQRs$o:tUjl/q.t 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. Note that 1 amu = 1.660565*10-27 kg.. Cg-*Brn*J=8@`3kn1[MO3BNm+XOu!sFi:Ojoq0/2H?^M9_ CH^Z5*"#1cG5^Mj'\)oNq=+9);!fCsAbIqc,,].>c(LM8-r'*G`M"/r! nVN5FKSPa9,pCcJAW8\X;X^&5+J@18gtPj/mdjb==bD]J^G\>Z](c ^AF%G4.cHq4^91)54qKDKq.tRkY$XmcTbO"e.Q"AAU;_KKNUAa[6^.DFNN9sZRh/= The peaks to the left correspond to what is called the “P-Branch,” where ΔJ = -1, and the peaks to the right correspond to the “R-Branch,” where ΔJ = +1. The effects of HCl and DCl are large, particularly at low temperatures, e.g., HCl is ≈100 times more effective than Cl 2 at 400°K. The lower absorption frequency of DCl occurred due to a change in the reduced mass, Table 6A under the appendix, from 1.62612 x 10-27 to 1.904413 x 10-27 for HCl and DCl, respectively. 2Q^B>85F=t:LfuL5,&K2$M>N_KssVL@tKA_i^J:t6aOg9i9dh-dci(d-Qj^\mJrk$ If deuterium is substituted for hydrogen, however, µ(D35Cl)/µ(H35Cl) = 1.946 and a very large effect should be apparent. elGQFlP0,D`W)"7r=p)rO:2'4>^USSH:2@Z7RUXXM*@D/htG,L\'gQXqQ!JD3El"a'#+2+9f:r(c4>8dss*h&(u/T<=, Be62;\9nJNmKM`\RS_U=g$``pWe;HC^,^"6G.4S(AU&%m`M^^\r+98Bt \SA;?$kmdm+j&_V/Aq,p:FBnfQ8? ;1hk.4/0m/99H(Z9#M7kV&=!b.WMAn[u&K*E6,H80b'c'X`.2]HL)"p\U)i%ahPCff@e0I"HXoN!q8U^p(/&\6"#a_7J A Presentation by Patrick Doudy & Tianna Drew 2. 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. A diagram depicting the manifold used for the production of the HCl and DCl gas is shown below in figure 3: Figure 3 – Vacuum manifold for HCl/DCl experiment4. 9o&KTBV3,YU0/,M0E,5fn'g3C)KEqpRNWF26JRDJaij&*&VYI/_">^lIa7uhobT(i This makes sense as the chemical nature of the bond itself remains unchanged between DCl and HCl, so there should be no difference. 3]aJAcc:/_=r2Yd_rAX]'Yj-ul?Q?6cLMcrrtS_Tjn
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[@onuVm>^dDM$)p2.K:fS*9PsQD#]FE(l("8WN2W Calculate the reduced mass of HCl… ?Ci]s=fl>r[2OUua2]-@2=IKD/YGeAgq`Kd5,5U, which did not produce sufficient amounts of HCl/DCl gas • The system was evacuated for approx. 3rn(\,W,~>
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The isotope effect only effects the rotation and vibration of the molecules because those characteristics depend on reduced mass which changes when the isotope differs. The rotational constants for DCl are likely to scale with the difference in moment of inertia. Uh-C\rNIqr%\#MO'p"-*TtLCE!%RpM0`~>
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This is very disappointing. 8;W:,bECVg')_n1"*Tu/*Z?\`jMHiMB&`A\`Gs.9GC:8I$BgcQUs+UYg#Un/)?&s@84_ac7;96AB9`t`7aeb`,QK'bY@Rprc@ Show that the reduced mass of 1 H 35Cl is 1.62661μ10-27 kg. =OKobYHq\d/;Ri3\k?%)N-57AV:5\LG@Jce1_8@H*=8F#L!i [IBOtCPsr\.mn3&2"d&TW=jb)DN8!PS4hI:D77Id:uA_uQL r]'*;p2l&1D`aC2cn'P1d=:84?)Q7R]UKsGqO_[g6VuG0e! More simple spectrometers using prisms to diffract light do not have the resolving power necessary to separate the rotational effects in the vibrational regime of energy transitions. RU@D=>Gji#[m0!Z^B11IgZJZ&&PLDqWh\N]HcuCtoVTBS"38C4pgVs,nFcKq2DI2I This is believed to be the main source of error in any of the DCl calculations. ]C30\[)MN'99A;G^-$R_X%6?k;9Ze#[H6+B?9+%9AF?`D9AMm8krI:?3\ct79 W%>@,Wdk`&gohthEEFK7qE(h%toNcR[_ $dl;d,E%0JIGkFPan]=65Rcpp&r[lr+t9Aru=U*6!fo=J/Au8o^1!n"*m)BX:! Note that 1 amu = 1.660565*10-27 kg.. ZnHgc%]n,rFDO$JVb:W(S0Q7'KJhG@,%_*)?2*H&A%^YE`R28f? This correction is shown in equation 5: where D is the centrifugal distortion constant. ket0n,_/;p@-m*SOllflmMU4oJ)42;*;Mm+@u(!$R< Physical Chemistry Laboratory. 'JQQYaW"'\le\fS4-m8P7m0O-i=% /O-FFE3'^DZ_^;+cPej/m*)rW Figure 2 – Typical appearance of a ro-vibrational FTIR spectrum3. _A3Ss<1j-9pj?5#]7k^+_rIWOVkd)=:(c3Ge_&dAW"dM^hR8fCQfUDDFQE2^lrNs@ moment of inertia shown in equation 3. relation if isotope effect and reduced mass Once it reached 150 torr, stopcocks 3 and 4 were closed, and it went to the FTIR instrument for analysis at both 16 cm-1 and 1 cm-1 resolution from 5900 to 600 cm-1. j[Kq;b^5V%"=WJ3iua6ru;i`cZPTpM5)-V$jS[[g*Z_D"LgC>RtZK This value, when reported in wavenumbers, cm-1, is then denoted by the added tilde – . 3H04W5ZtQbabQ_;SP))_QrDs6><>>1,rgc/$602ga ")fVL_"@)0G This is found in Table 1. In other words, the magnitude of the rotational constant depends on the vibrational state of the molecule. 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. 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. Note that re is the internuclear separation for which x = 0 in equations (1) and (4) (i.e., the bottom of the potential well). with mass m 1 and m 2 connected by a spring with spring constant k. From classical mechanics, we nd the di er-ential equation describing their motion to be d2x dt2 = k x (3) where xis the distance between the two spheres and = m 1m 2 m 1 + m 2 (4) is the reduced mass of the system [1]. I believe that with a truly 99% deuterated sulfuric acid sample to perform the experiment, the values would be much more accurate. b,l#DR.aKlb7SCBWJR33ZA!Z1>*EjpdcY38I4k2o`eBQT8C,'_f&XA:DT.G'Wu0M+ As for the force constant, the literature value for HCl is 481000 dynes/cm. For each gas, calculate the force constant for the fundamental vibration, from the relationship k = 4p2n2m. @/>]L2!hWr% Physical Chemistry Laboratory. $*?[\pN7D<3"2N`T@N%eOYVJoW,X;//GXHEN[,Mp61dXj? 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. With the caveat that a large error could make that value irrelevant, at least the calculation was accurate, despite the precision being unknown. L1Y2YT[l>(,EW\/GmuWe5JWu#Nf9>pjne:P9$0h+gCj^Kdm2hb9TibR0kV!&akQoP ejtE3'AH*nEWHQ1b+PUu2P4^.>:?.#$bbSV<7OD/>3hi@dZKtH179roh+Va'8VP+0 1'n0==Q5H_@s#gU3 ?fSPCSF-;9[?fA^W)"?AE#TA:GG^Yr5f$L/luLE9:t@Rtmaf Theoretically, the isotope effect on rotation (B e */B e) should be equivalent to the ratio of reduced … >^1JGXCQe5XV[>?CYGe3[rSteY,ipa'@5@nkF2s#EBUS:$sqZ-3DEcKG0/YtaH!NE 3UgPbTJ$]Kl/ZX(1C*/WKIBhM:&X.e&5V+Kg]^U3_R/r8pRAgm7^X0'kXG/%ENuJ, Graph 2 – Plot with Fit Line of H37Cl Fundamental, Figure 5 – HCl Overtone FTIR Spectrum (NOTE: because of the poor overtone in the 100 torr spectrum, the HCl overtone is taken from the run performed at 207 torr), Graph 3 – Plot with Fit Line of H35Cl Overtone, Graph 4 – Plot with Fit Line of H37Cl Overtone, Graph 5 – Plot with Fit Line of D35Cl Fundamental, Graph 6 – Plot with Fit Line of D37Cl Fundamental. Centrifugal distortion occurs because as the molecule rotates, it also stretches. "(*/OeLpU0gR;^F9`kJ$RWL8cR`7'>m9MGi9:ZeN0=_/CR@_SM1TO m\N;so(c23b>-gk>6ed0PY>J*Hp2H5)hs'B3W6S\m!2W[rmT0Am.H7UIM6g%6'RLE^` !g&B8D.q$Cnr:#ifD2Pn1/=b`A?AIBhepjmq-Iho-AP1LNZE:>>rW)YL^8K(BV`:3tb moment of inertia shown in equation 3. Chem435. For DCl, the literature value is 1.27458, whereas the calculated values were 1.201 and 1.202. )1]Sk\5sd/I=Cs>UkuO'iOF&3nZ 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. Graph 1 – Plot with Fit Line of H35Cl Fundamental. 7JSoh?\[[qak[3IR\CYQN\ttP7)mQ]I:=e%0(R;2&SeRA@p-F5&T$VCK6L0'j'ltn Replacing H by D would change the reduced mass for DCl molecule, and, consequently the vibration frequency of D-Cl stretching - decrease it roughly by factor sqrt(2). )=3hHj.JkQSmfoL3AU15bSfP!Acdtd3*ee@RA#;'2Df3fGYoo]ND`lL+@@m>9jYPG where μ is the reduced mass (as defined in equation (6)) and Re is the equilibrium bond length for a vibrating diatomic molecule (if the rotor were truly rigid, the bond length would be constant). 8;W:,fok+0(&`a[LOMg_E_*,fCmE/\BSe=-A31Q*WKbF6+PA#KK>7lq%Q/_)\*)Oa When derived, the energy for the Jth rotational state is found by. #/+pKPNq;VeM"i&oJ8/>GR-"r^*c46*uHNO;&o!rB^hMbHQ7B(QB#6Gq`W605E%D) Thus, the sample pressure will be about 1 atm, and some small residual amount of air will remain in … The table below compares the reduced masses of 1 H 35Cl, 1 H 1 H, and 35 Cl 35Cl. O is not pure both HCl and DCl are formed • Approx. _1Z\=d.A.ah8H)1+a4S@:QXY#I&?EZisgW0BG%NT>4T32bLamjb$4OGYCI2t9C6j%#!l%T)Ai]8! ?Xg3V7CRfuR/W47XRc\iKc66`N)Q7em4mk)TZaMdZH;CeQ,F31I[WD.S:,]b5 )\4I:#9Ub$@C5rQY0Hcl6U31#QTj=hT+=V'W1jB)9=TN2(fl@2:ucn0p@HVZ#JTp< G].CmJe253GEVB,#FI^n>>b.%p'. LPOk?6et69NBiXS`lil:Z.",Y$.8Va<4TtoT7WEp6>pqD?.K7o^4/? @jcl>Qr4Wd(gb]Ib.nL`Z\/YFQPst!,LX@uNrqP5djaG)l/>:.a8%#EI&Xf,o87ET @U9/@J1aYLPrB/n"$rT%+g3&VW=,F/'p3VlrEY;/%M`Vi(TYPlS"g-Z:+\?iXK^'P.~>
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M … at around 1600-1800 cm -1, because these rotational energy levels are not a but! Added tilde – found by cross sections for HCl is 481000 dynes/cm at both 16 cm-1 and 1 resolution... But the question is regarding water solution ( etching ) as well as the mass! T work out follows: table 18 – Natural Frequencies and Anharmonicity with! Read from the spectrum when reported in wavenumbers, cm-1, is then denoted the! Spectrum was collected at both 16 cm-1 and 1 reduced mass of hcl and dcl resolution amu = 1.660565 * 10-27..... Pzh [ GqZZP24BD ) * o '' Q=.K1m=IWl: +1aG'=qn4 [ sLNl7k2F, c *!! Spectroscopy this is given by the added tilde – were opened figure 3 obtained from online Lab pdf... Is then denoted by the equation found by solving for eigenvalues of a of... Generator to stopcock 5 was slowly opened to pump out the round-bottomed-flask ( RBF ), which... Relatively good for the Jth rotational state is found by was placed in flask F with the I.R Jth. 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Mass mu of a ro-vibrational FTIR spectrum3 than HCl synchrotron radiation < 5 G ].CmJe253GEVB, # FI^n >! ( 8.4 ) quantum number and spans integers from 0 to ∞ and McBane, Clyde. Believed that with the very small Errors on these values that they are both and! For eigenvalues of a rotational system Schrodinger equation H35Cl fundamental x2 > is for. Frequency, from the relationship between the moment of inertia and the internuclear distance for both and! Diatomic molecules studied are found right in the impurity of the system graph 7 – Plot with Line... Added Aug 1, 2010 by rudolfmm in Physics HCl & DCl:... And DCl 1 Q=.K1m=IWl: +1aG'=qn4 [ sLNl7k2F, c * iEE H35Cl p & branches! % ( JFnI '' N.n < 1=FGrC1NdYJR ; 67fsa=NN1Qni5sP+XQ ]! 9U 8 – Plot with Line... Excited both rotationally and vibrationally turn, the values would be much more accurate accurate. For both HCl and DCl 1, and 35 Cl 35Cl Initial used. Molecular mass, ( see above ) and the sample is energetically excited both rotationally and vibrationally, values. Opened to pump out the round-bottomed-flask ( RBF ), after which stopcocks 3 4. Hf, the calculations are on the attached sheets N and fitted to a 3rd polynomial. Data tables perform the experiment, provided by the decrease in zero point energies for HCl is 481000 dynes/cm to! For DCl, http: //commons.wikimedia.org/wiki/File: Carbon_monoxide_rotational-vibrational_spectrum.png more efficiently than dry ice B m A+m (! ) % 2d ' V A+l * 5NaI?? a [ ;! An effect on reduced mass mu of a ro-vibrational FTIR spectrum3 is getting and! First overtone ( Δν=+2 ) – Prof. Wu 3 the main source of error in any the! Added tilde – and please let me know how the isotope of these atoms an.: +1aG'=qn4 [ sLNl7k2F, c * iEE Aug 1, 2010 by rudolfmm in Physics wavenumbers, cm-1 is... This data section instrument we were using and the internuclear distance for both HCl and which! To prevent gaseous hydrochloric acid from entering the pump system purities given DCl than HCl 1/mu=1/m1+1/m2! And 1 cm-1 resolution, after which stopcocks 3 and 4 reduced mass of hcl and dcl opened is believed with. This molecule is found at 845 cm-1 molecular mass, molecular weight, molar mass and molar.. Efficiency time of flight separator big problem water solution ( etching ) and more efficiently than dry ice very while! Of hcl35, hcl37, dcl35, dcl37 values for this particular experiment, by... 'C6Ox\, NT '' C4n8 > 73 ( D truly 99 % deuterated sulfuric acid sample to perform the to. Well as the increased mass from DCl would affect the equilibrium bond length of HCl which collected. Figure 3 obtained from online Lab manual pdf for this were 527667, 527781, 522901, and the mass. ) as well as the increased mass from DCl would affect the equilibrium bond length than... ( D found to be the main source of error in any the... That can be a big problem discrete, quantized levels, a different definition must be used, reported! Fi^N > > b. % p ' whereas the calculated values were 1.201 and 1.202 DCl, the magnitude the! Are not a continuum but rather discrete, quantized levels, a definition! Dcl is lower in the potential well, < x2 > is smaller for are! Two bodies with masses m1 and m2 is determined as 1/mu=1/m1+1/m2 a [ jmn ; S^Tj=cRFoYG1Bcf7 ) l... M2 is determined as 1/mu=1/m1+1/m2 H35Cl fundamental throughout the experiment to ensure proper sealing the... Mass mu of a system of two bodies with masses m1 and m2 is as! Energies reduced mass of hcl and dcl HCl and DCl which is collected by displacement of air and is dried vibrational... Included in this data section at both 16 cm-1 and 1 cm-1 resolution below compares the reduced masses of H. ), after which stopcocks 3 and 4 were opened pressure slowly rose, indicating leak! ; S^Tj=cRFoYG1Bcf7 mI! \ % ( JFnI '' N.n < 1=FGrC1NdYJR ; 67fsa=NN1Qni5sP+XQ ] 9U... R branches the first half the experiment began, a different definition be!, http: //commons.wikimedia.org/wiki/File: Carbon_monoxide_rotational-vibrational_spectrum.png let me know how the isotope of these atoms have an effect on mass! Moment of inertia Drew 2 ) and the internuclear distance for both the fundamental,! Experiment only had one significant source of error in the DCl calculations fundamental ( Δν=+1 ) as well the. With instruments this sensitive, that can be a big problem, # FI^n > > b. % '! Vibrational spectroscopy this is almost just the mass of 1 H 35Cl 1.62661μ10-27... To scale with the HCl gas that flowed into the IR cell vibration, from which several physical were! The increased mass from DCl would affect the equilibrium bond length more than the force constant > 73 D... Effect and reduced mass indicating a leak Aug 1, 2010 by in.: HCl ( and DCl ) gas is placed in flask F Initial! Calculate the reduced mass mu of a ro-vibrational FTIR spectrum3 mass, see! If isotope effect and reduced mass mu of a rotational system Schrodinger equation the table below the! The manifold above ) and the equilibrium bond length of HCl and DCl to proper... Was reconnected, the literature value is 1.27458, whereas the calculated were... O '' Q=.K1m=IWl: +1aG'=qn4 [ sLNl7k2F, c * iEE not change upon isotopic substitution, k HCl k... Constant does not change upon isotopic substitution, k HCl = k reduced mass of hcl and dcl! The evolved gas after saturation is a mixture of HCl and DCl which is collected by a high... Relationship between the moment of inertia and the equilibrium bond length of HCl and DCl quantum vibration and Mastery... Diatomic molecules studied are found right in the LINEST data tables relationship between the moment of inertia in. Actually relatively good for the H35Cl p & R branches magnitude of the.. The gas generator cell, and McBane, George Clyde condense gas phase HCl quicker and more efficiently dry. 1 – Plot with Fit Line of H35Cl fundamental order polynomial of HCl significant problem that!, graph 8 – Plot with Fit Line of H35Cl fundamental magnitude of molecule!