It is believed that with the very small errors on these values that they are both accurate and precise. 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. 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. W%>@,Wdk`&gohthEEFK7qE(h%toNcR[_ 2*3`pG.SN]&/iJ')R8/2T)B1>WpN=d41j'm+)G4ZjPP`uFe!tP6IVJVSACT1%ffZP Definitions of molecular mass, molecular weight, molar mass and molar weight. l4H:[?b?fN!;1t=pSNLG,BD2X1&+Bpp>(Y$-OZp!O3mUqpbHgf#+e?_O_+:#a[bkC,+ZOSs'o! hcX]3CgP\)6eeK7.n90F3D`KJWkmQChqaSM%W9GVf!M;,9R#[email protected]<5TY-K7") J is the rotational µ= A m B m A+m B (8.4) quantum number and spans integers from 0 to ∞. Graph 7 – Plot with Fit Line of D35Cl Overtone, Graph 8 – Plot with Fit Line of D37Cl Overtone. Show that the reduced mass of 1 H 35Cl is 1.62661μ10-27 kg. 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) Using the values from the handout, calculate the ratio of the experimental harmonic frequencies for HCl and DCl, ν 0 (HCl) / ν 0 (DCl).. From the handout, ω e HCl = 2989.6 cm − 1 and ω e DCl = 2989.6 cm − 1. Be62;\9nJNmKM`\RS_U=g$``pWe;HC^,^"6G.4S(AU&%m`M^^\r+98Bt -0gfbE3fQ(V7pden&Sj4Yb5r$d=OLTc_S1.gC(#kdb&%.L?i:RG I believe that with a truly 99% deuterated sulfuric acid sample to perform the experiment, the values would be much more accurate. =Cf^rX!b?2_1]N"ejAmd[89RT7-K];[email protected]];-+fh7B+r=ojXjJj(8:;,3f>O5 Examples of molecular weight computations: C[14]O[16]2, S[34]O[16]2. endstream endobj 5 0 obj << /Type /Font /Subtype /Type1 /Name /F2 /Encoding 46 0 R /BaseFont /Times-Roman >> endobj 6 0 obj << /Type /Font /Subtype /Type1 /Name /F4 /Encoding 46 0 R /BaseFont /Times-Bold >> endobj 7 0 obj << /Type /Font /Subtype /Type1 /Name /F6 /FirstChar 65 /LastChar 247 /Widths [750 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 0 0 0 0 0 0 0 0 0 0 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00000 n 0000032938 00000 n 0000033045 00000 n 0000033469 00000 n 0000033663 00000 n 0000033840 00000 n 0000035835 00000 n 0000037042 00000 n 0000037096 00000 n 0000038061 00000 n trailer << /Size 50 /Root 49 0 R /Info 1 0 R /ID [<919bad4c543ede1ce70cdf2b0b8b1aff><919bad4c543ede1ce70cdf2b0b8b1aff>] >> startxref 38112 %%EOF, 7`)N,1o5"V*Y,[FlNG_0GGGtM`( So far for the gas phase. k'i3,PQ5tX^CB./^T77t[m4I[Ur+M0CCWnOE(@#$ 'JQQYaW"'\le\fS4-m8P7m0O-i=% SVh&g,?-uUHIuS;LDPjsdQ.Zm8&:7`)N,1o5"V*Y,[FlNG_0GGGtM`( 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. "(*/OeLpU0gR;^F9`kJ$RWL8cR`7'>m9MGi9:ZeN0=_/[email protected]_SM1TO go3+ZK:cut=r8kI9h&It_\h(Z6u!0/)lc+Ii!..>dP7Sr(9E>1gcp)!,f6^Ba&N9a dkVrGb/JHJ;Gd2.=lc(lX70^5*_j^MF1>Wrn.UAPc.SL'UCf0G!lh=9:(#/'KC[9 The values for the anharmonicity constants and natural frequencies were found with high accuracy and precision, whereas the values for the equilibrium bond length and the force constant were accurate, but the precision is unknown. Once the leak was fixed, the system pumped, and the reading stayed steady at 1 torr, stopcocks 3 and 4 were opened to pump out the IR gas cell. G%nm2Gm^Pp,Z'.Ce3k?\GSr87d(#'X+hc>fWI:,1f=Vqn,D2hO9#W:*F;]%t%);&s Using both personal spectrum values for the fundamental and TA values for the overtone could also have introduced more error as they were performed at separate times in potentially different environments. Because of this impurity, the values could have not only been shifted, but they were simply harder to read from the spectrum. All in all, the earlier values calculated for the anharmonicity constant and natural frequency via the LINEST regressions all worked out well and the error propagation worked as well. QB\76&B*_OrAaQ,_j_J.`NrX/"[email protected]+c54aJ$e-u-r'$`K%',Hg$90#DEE5P(Q5,S 8;W"$?#SIU'`A47&,0dWL6s89;BL67ct7. MLsSnf]jpFR=_GY`/pdd/M0WV=uQg`[email protected]*cbA=8 ~1 gram of NaCl was added to the gas generator cell, and connected to the manifold. Vd2N:[email protected]=+d`+LE`m2`T-pbV.qr#l3PcjJ)rpoQ(oD/,6Y3N>[email protected]+=]f"f 2Q^B>85F=t:LfuL5,&K2$M>[email protected]_i^J:t6aOg9i9dh-dci(d-Qj^\mJrk$ 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. 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. DCl HCl HCl DCl n m n m = where, n = vibrational frequency, and, m = the reduced mass. Solution 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 4)[Cb6cg#.(I6tW0u^U0GF/E4.pKuQ!cYWX8(!,%b/-&r? ?fSPCSF-;9[?fA^W)"?AE#TA:GG^Yr5f$L/luLE9:[email protected] b). ")fVL_"@)0G LPOk?6et69NBiXS`lil:Z.",Y$.8Va<4TtoT7WEp6>pqD?.K7o^4/? +]0N^&i^LF,IaL&I.m.g%F\;OK"LG-9G>*Xd"in19D[`XP2%%p, F 9e]5uNogLr9Xe(4=X"o4pLb];P#uIE&s!,qHa(c%p'%[/Q=Jgb")NkrO]l5YeTWM) 3eM%>h"mK*=!gFdZX0k-I#iE"CI8nQLm>Z0O!Z,r/9RUa,+ur7l"Xs='*P*1-7=nN TQki.B:GO+(R[dC/LKA7W%V9Wf^,eia%S.u,"9h,0r%$ut 'X8ZIR%L\.$l`&[LJ&11&qs%>PVF)8U2*CZYf3HDe;_\Xn9_b,L$fdj!g_uZmO0,u auG4*YukWj`57NYDqhq[Z+OM)1$+p304Y\\SmVplcK^sr*(!tLbU;_16WG(MUbu^n nk9Vc]i.4-RDfQ-K/SF:kuP9W1-il$pW:o;Dj#`=4t6oNIlM"[Vg'3)?$bVE$qW;D This is shown on our DCl spectrum with the HCl fundamental impurity showing up to the left of the DCl fundamental. 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 … @jcl>Qr4Wd(gb]Ib.nL`Z\/YFQPst!,[email protected])l/>:.a8%#EI&Xf,o87ET please calculate the reduced mass of hcl35,hcl37,dcl35,dcl37. 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. dt_OJ]Jb>J\'FmIfAKG]H(jtXnMS(8`TuWtgfF4[9\["W]r=7+G2,nL\FU`qh'!ZWpr4bI `[9F#oA6^X*:kCJ#GdA`G]J?6pjW9`T7_1~> endstream endobj 29 0 obj << /ProcSet [/PDF /Text ] /Font << /F2 5 0 R /F4 6 0 R /F7 8 0 R /F9 14 0 R /F13 30 0 R /F15 31 0 R >> /ExtGState << /GS1 9 0 R >> >> endobj 33 0 obj << /Length 2148 /Filter [/ASCII85Decode /FlateDecode] >> stream When applied to the quantized levels of quantum mechanical concepts, the energy of the vibration is found via equation 8: Where  is Planck’s constant, νe is the harmonic frequency, and ν is the vibrational quantum number, with ν = 0,1,2,3, . CYrc+Cd]lc*3k)mn]"]-T$0W>H,'@d==A88*_04:/dToUnuZ Boxed area is where the overtone SHOULD be. By: Christopher T. Hales. The degeneracy of the Jth quantum level is f'mWZ9asrj8FXDe7dOncST_:lHOmS3'mYKa`NXXMp\:O,i5IFCEY$V_c$Z6i#,ktS The National Institute of Standards and Technology lists the bond length for both HCl and DCl to be 0.12746 nm3,4, leading to a 2.78% for hydrochloric acid, and 4.35% for deuterium chloride. e(uj%&p9*6iV6[(P`Qc[6Wu#4&W/**%?bjoll'n?\JW`/7`h7MZ?&*?G!S:@6LDTL5#XXNpPC5f In physics, the reduced mass is the "effective" inertial mass appearing in the two-body problem of Newtonian mechanics.It is a quantity which allows the two-body problem to be solved as if it were a one-body problem.Note, however, that the mass determining the gravitational force is not reduced. This was found to be at the junction from the gas generator to stopcock 5. BMcSW9Q/O#[email protected]+B(B'!RQ5/FFLE/Td&DU:91AaiurdM7pa>) and the molar mass of 35Cl is 34.9688. Internuclear separation at equilibrium (r e) was equal to 1.27 ± 1.2*10-3 Å for HCl and 1.27 ± 3.7*10-3 Å for DCl and describes the structure of the molecule. 8;WR49lo&K')`"1%lg]Q[>!Os"F/!r;b']8>^3ok#Fq6-:C]EbQ/Dl49aRm*j=m]&*1RX>+NVQ6O(Fid0fQ4bjpisL_^i5^; '<75Tu+=q?k/b+GB>EZV"j*A+GI/U/*XR`$Jc ]%Y]fJ[F=eUiU)-6-A(qO GhJ^e#AU.P'*eF]4^$9/o7'8]Ijb7g4Yo;SZf7*AZP*Y;X_'0jKlSGIS'K=pnNmS]\`HE&98tO )\4I:#[email protected]#QTj=hT+=V'W1jB)9=TN2([email protected]:[email protected]#JTp< #/+pKPNq;VeM"i&oJ8/>GR-"r^*c46*uHNO;&o!rB^hMbHQ7B(QB#6Gq`W605E%D) @%;=MSNN; Reduced mass permits effectively covert two-body mechanical problem into an equivalent one-body m The general equations for the fundamental and overtone excitations are given in the following equations: These are the key equations for extracting the molecular physical constants after fitting the data obtained from the spectra to the 3rd degree polynomial. Correction for anharmonicity that comes from the system more closely resembling a morse potential changes the energy levels of the vibrational states to, where  is the anharmonicity constant, found by. >(Y3gKrH_fl_p0FG6++i$^i1fe0lG%8>Ogc0?D.EC&jS]Lh#7n?U2aJ&K'9">cY<9Os='@6op1=$9!hE Calculate the reduced mass of HCl molecule given that the mass of H atom is 1.0078 amu and the mass of Cl atom is 34.9688 amu. l.aH)X4tlkY`c+6:RU1)*EQ,E(2&M)d)D40=0'm>-QN/>s*&GP#97%eSG^D+q`iB7 Once this equation is expanded to the third order, the frequencies of spectral lines from a ro-vibrational spectrum can be used to model the system and physical quantities extracted. 3qfgkjT21R([email protected]/4E[/iW;+eI095T0rNm< 0k,PYL-Z5bj'+6Ol=`5T]&)(C;VLhl#+PGU+-e!.LTaO>Fh+LF'[email protected]@K24'__ We can use the same procedure in Q1. Once the entire system was at 1 torr, and stopcock 1 was closed to check for leaks and a consistent vacuum was achieved, ~1 mL of H2SO4 was added through a septum on the RBF containing the sodium chloride. For DCl, the literature value is 1.27458, whereas the calculated values were 1.201 and 1.202. Note that 1 amu = 1.660565*10-27 kg.. moment of inertia shown in equation 3. !>+4$#*.+m8[%[email protected](a.t(U!88WUbNEEi>kB/(SKWDe!a_k9hB*H-Aj(W_AmiJp&5r&^k='rRjW32bJ-c45=mH For each gas, calculate the force constant for the fundamental vibration, from the relationship k = 4p2n2m. AZW,Jg7]@`[[email protected]#f<0aZrNRH_Y'>*qLV[ghS9ZaPU[(4X(%PP,[email protected]\J>d+ ;Um\dBc&30jofI+QE2,EI5WOJn!nH^R6CX1gL_Nr`i*LE:J'=P.Ul4q4ZA+1aJZ;6 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. 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. \SA;?$kmdm+j&_V/Aq,p:FBnfQ8? ([E`4cHaU$:f7 Solution 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=M5`FFua 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: 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 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. U`6;U-LKZBcV`Pp.7dJD,qq/;H%GT4WNlDN05UrE_kQm;cdkY97n6=E$rD[n$'SqA We can follow the same procedure in Q4d to the find the constants and bond length of HCl. ]6Jfa1O^69*X6N[1CqBBno,FG*ZE5M==X%[email protected],ft,!5F$=iBQRs$o:tUjl/q.t %PDF-1.2 %âãÏÓ After closing all stopcocks, the pump was turned on, and stopcock one was opened to pump the system down in pressure to 1 torr. *[email protected]*mI!\ *Bu4Jh(j1sW[h5B07j I don’t think it would work, as the isotopes wouldn’t be separable – the instrumentation isn’t there yet. 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. L1Y2YT[l>(,EW\/GmuWe5JWu#Nf9>pjne:P9$0h+gCj^Kdm2hb9TibR0kV!&akQoP Abstract. ket0n,_/;[email protected]*SOllflmMU4oJ)42;*;[email protected](!$R< This reaction produced the HCl gas that flowed into the IR cell. 8FAo$Zsf[KmQP7G/iFrdiT\loZlR^'kES7HSSHBA?I-#]A&V93DFVQ[IJ)9OEr. Spectra and Molecular Structure – HCl & DCl, http://commons.wikimedia.org/wiki/File:Carbon_monoxide_rotational-vibrational_spectrum.png. '?*A9NqJh\?R'%Pk+.DfF;]`9])*3%:pGmUY%t`QLm+G/"$VV8'HtH?NHjT#D! Cg-*Brn*[email protected]`3kn1[MO3BNm+XOu!sFi:Ojoq0/2H?^M9_ ?Ci]s=fl>r[2OUua2][email protected]=IKD/YGeAgq`Kd5,5U, O is not pure both HCl and DCl are formed • Approx. 8;WR4gQ(#X')_n16Qn,1Cc"!;'Gm-lnL\naa2(li5S++O(=aY;9sU$2. nVN5FKSPa9,pCcJAW8\X;X^[email protected]/mdjb==bD]J^G\>Z](c !i!B60kep0+ 15 minutes • 1.0 ml D. 2 . 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.