8;W:,fok+0(&`a[LOMg_E_*,fCmE/\BSe=-A31Q*WKbF6+PA#KK>7lq%Q/_)\*)Oa If the diatomic molecule HCl, with 1 H and 35 Cl were substituted with 37 Cl, what change occurs to the reduced mass? '9AYi(t@Osqr0r__.\M8^WfkQZ`]l'M(Oc(0r=H^nmC61(W+Nr9EjR*EC7 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. After closing all stopcocks, the pump was turned on, and stopcock one was opened to pump the system down in pressure to 1 torr. 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. ]6Jfa1O^69*X6N[1CqBBno,FG*ZE5M==X%Bd@PH0,ft,!5F$=iBQRs$o:tUjl/q.t ]MfsuKH7l).og2K\bIhbRA\jC$AW*7f^p7\G\gtlr`u])IZ*mt@%`n4lZFhTSj!h0) The peaks to the left correspond to what is called the “P-Branch,” where ΔJ = -1, and the peaks to the right correspond to the “R-Branch,” where ΔJ = +1. This difference allows a very small but significant amount of transitions where Δν=+2, despite that being against the typical “selection rules” for quantum mechanic systems. @jcl>Qr4Wd(gb]Ib.nL`Z\/YFQPst!,LX@uNrqP5djaG)l/>:.a8%#EI&Xf,o87ET 7-"rf!GiB%kDigHHLA[5O/t)\;)Xf@V=nNl!c$S?r;'iEpWLnB_p=snKc`&`l.f%h Calculate the reduced mass of HCl… 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. (1 u is equal to 1/12 the mass of one atom of carbon-12) !>+4$#*.+m8[%l&.b@(a.t(U!88WUbNEEi>kB/(SKWDe!a_k9hB*H-Aj(W_AmiJp&5r&^k='rRjW32bJ-c45=mH KobZJ]"*?\H,hPGWou85V"G4:p*q>t46OS5))EdKMgcXl7WZocZ*s"fHCC0_ endstream endobj 18 0 obj << /ProcSet [/PDF /Text ] /Font << /F2 5 0 R /F4 6 0 R /F7 8 0 R /F11 15 0 R >> /ExtGState << /GS1 9 0 R >> >> endobj 20 0 obj << /Length 3899 /Filter [/ASCII85Decode /FlateDecode] >> stream 4iTR"03V#'QoA/JaMRlb_Q'ltc\?kVqEr_;`H]G3p?MQucX6annkes5oW2FHYOji#Wh -0gfbE3fQ(V7pden&Sj4Yb5r$d=OLTc_S1.gC(#kdb&%.L?i:RG fuFJ1E!oo?]!,b+[NK4:O=c%I;ufRLhi'o&&. * 'X8ZIR%L\.$l`&[LJ&11&qs%>PVF)8U2*CZYf3HDe;_\Xn9_b,L$fdj!g_uZmO0,u This is found in Table 1. a;g8hp0=pr'FeojQYu1=[0X/UIs&C)U.7rt%\G@*`$:>u6r%C?PYR!\ Peaks between them are an HCl impurity. &s,;*#0IACBlMGM*1SI1nHVuKc'*\okmCG38r3FC?GMFtNZ.^tWN.1lY\,G,@Gmj0 This suggests that, if we model the molecule vibra- Those frequencies can be represented mathematically as shown below: To describe the vibrational motion of a diatomic molecule, the first place to start is a simple harmonic oscillator. Up6m;)-n'Ni].XWJnUkIPaT,I3Nd6)@Y;tWX3CjC+,"Y34?,tQXE+II8O*I!SuH8p_,l'QRU^E;F`&ZD-B"-6 8FAo$Zsf[KmQP7G/iFrdiT\loZlR^'kES7HSSHBA?I-#]A&V93DFVQ[IJ)9OEr. 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. 3@Ge96biTtph?1-'P&8LGF[b?c7%2HL8-^a.k##aeglqj'mJia7c*l&2G@q)Qr_B' Be62;\9nJNmKM`\RS_U=g$``pWe;HC^,^"6G.4S(AU&%m`M^^\r+98Bt *#H"#:HN-W>3dj*74HV!rK3<8Gi.P$K/\VR?^N?UY-VoJGN,Ga:%D#k3W,1#FB'i, 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. 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. For DCl, the literature value is 1.27458, whereas the calculated values were 1.201 and 1.202. Y&iCOE;Z$HfmEGWh.jbDS$*ZS#.E=4IQBHcYIO'< '?*A9NqJh\?R'%Pk+.DfF;]`9])*3%:pGmUY%t`QLm+G/"$VV8'HtH?NHjT#D! G].CmJe253GEVB,#FI^n>>b.%p'. Centrifugal distortion occurs because as the molecule rotates, it also stretches. Energy transitions from the spectra were plotted vs. frequency, from which several physical constants were determined. Once a spectrum like this was obtained for HCl and DCl, peak values were assigned to the P and R branches, for both 35Cl and 37Cl. The manifold is relatively straightforward in use. These values represent ~10% error. Fh[,#j&6(*qu5[@K\'$l6(5>tb2=*Y;8Hm/i//(p=:qBM?refbKXoVF$LihSetYc& 3qfgkjT21R(YZ@MSaC7/4E[/iW;+eI095T0rNm< k'i3,PQ5tX^CB./^T77t[m4I[Ur+M0CCWnOE(@#$ rZW.GJV(()YPN'QF&I\m:N\WG0@H+%.Og/cT<7CNR+UD=XRC$>94D_eL*(RrN=5 hmG*HXK%1r$h:@f-G+$))pY@MfmH&U(IC'2R>'$WAuIUue:YYh^rUr#1#]3JPYoS_ 3_lhXV,!X=0ZkAIP:tpmS.$58VkO:]k? f/XkWEl2.dj"AtH&0ViT,'I(^D_/PEn=&Sq%_.OGpfTUs?V!Caf?O:5nV@FDN)Bk. W%>@,Wdk`&gohthEEFK7qE(h%toNcR[_ JKXg[@5+$o@/koIP(P$"ge59%Ft#[de/htm.j9)J_cG4\*[C9V&sX2q=^fm!5AJbP In essence, as the light from the source passes through the sample cell, the sample is energetically excited both rotationally and vibrationally. JRV'b%]*Z+#S$E:G1)u'$qTDe&F:\f+KgjWN6E7beJ4l-WHr!h8>L:;-ZqTqFZCR% This value is actually relatively good for the instrument we were using and the sample purities given. rotational degrees of freedom of gas‐phase HCl. [@onuVm>^dDM$)p2.K:fS*9PsQD#]FE(l("8WN2W +^R*2dE% ]RO4W1J'$V:XlSSFWnCt$R@eXb\d[H2j3jQUrfV-U^1BM\9uZ4*:G+_8 ,K).jPun-^lDnDfhi?p#GS$]kjDchm%DsVQpn*$*3gNUuI-.4\nBMct"ibR'7:\tP Because the rotational energy levels are much more closely spaced than the vibrational energy levels, ~20 cm^-1 vs. ~2900 cm^-1, respectively, simple dispersive IR spectroscopy is simply not viable.1 Thus, a higher resolving power is required. aF#&Zh@c?J8c_!u"@Rj17K,!uppg"QA85Jb.#0ZAKd9%bRP9jKeS&ZiZc34Y$um-D Once it was determined that ~100 tor and a resolution of 1 cm-1 were the best parameters for analysis, the process was repeated but only at 100 torr and 1 cm-1 resolution with deuterated sulfuric acid, D2SO4, for the production of DCl. f'mWZ9asrj8FXDe7dOncST_:lHOmS3'mYKa`NXXMp\:O,i5IFCEY$V_c$Z6i#,ktS h5P%2db-c9iM^Gl54@_R99eO?p^N`Rr'kXtSh*h-nM;A7S,(_bVc8Lr4Dgaj)*,b]=Be"M7$Gk_Xg We can use the same procedure in Q1. Ju+QN50YWFr+RJi^TZ\G9EI6;)=`@d'i"9n6a/5!;kQe*,6=YR. Fundamental is in the circle. 2*3`pG.SN]&/iJ')R8/2T)B1>WpN=d41j'm+)G4ZjPP`uFe!tP6IVJVSACT1%ffZP +-P>8EoCINo[&K]M4P&'\lcmiW*UM$Xtg*%72pd=H\@Z! QB\76&B*_OrAaQ,_j_J.`NrX/"Kf-@+c54aJ$e-u-r'$`K%',Hg$90#DEE5P(Q5,S Numbers 1-5 are stopcocks. ])sXD%"_b$B4_ and the molar mass of 35Cl is 34.9688. Experimental results 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. 5 . 9o&KTBV3,YU0/,M0E,5fn'g3C)KEqpRNWF26JRDJaij&*&VYI/_">^lIa7uhobT(i ;ic_MMd!>P41Jn$d-?=.%c;Fu[r3u%MRG0X^)5Q6P6pnkBPr`N>8L]hnMB7Y-:sc# The next step in the analysis of the FTIR spectra was to assign the transitions in the rotational quantum number J to the spectra’s peaks. After running the experiment at different sample cell pressures and different resolutions, it was determined that the ideal parameters for the experiment were 100 torr pressure with a resolution of 1 cm-1. !-M?3X^l2QLFt&F%6EDiiiEaRfcXK?EUJPt$p\+OLR?HuV:b0>$SoR=Z7^/F\_`sA These are the graphs that will be included in this data section. W)-bC=@l,NS8-`?XNNDVR_!gg(:(DZ8 +]0N^&i^LF,IaL&I.m.g%F\;OK"LG-9G>*Xd"in19D[`XP2%%p, F In the latter, µ is the reduced mass, given in m I=µr2 (8.3) equation 4, and r is the distance between the two atoms in the rigid rotor. 9leudwlrq 5rwdwlrq 6shfwurvfrs\ ri +&o dqg '&o 3xusrvh 7r ghwhuplqh wkh ixqgdphqwdo yleudwlrq iuhtxhqf\ dqg erqg ohqjwk iru + &o + &o ' &o dqg ' &o dqg wr frpsduh wkh lvrwrsh hiihfwv wr wkhruhwlfdoo\ suhglfwhg ydoxhv ,qwurgxfwlrq FTIR spectroscopy uses gratings for diffraction and then processes the raw data from an interferogram into the actual spectrum via the mathematical process known as a Fourier transform. O was added to flask F with the I.R. o&IJ4cR$,g_nZ*%pO#139dh)j5MWG+If=KV/4ossMpe;I*#ne0LU$"jbIfN'L6hV1 The values for the anharmonicity constants and natural frequencies were found with high accuracy and precision, whereas the values for the equilibrium bond length and the force constant were accurate, but the precision is unknown. 1g&p%&Y8ecB6h0@>04f;f'-*4A%kA1MG0mDb)o]1j-+pBSlqm$LX^LcR?n-%O]GfA 8;W"$?#SIU'`A47&,0dWL6s89;BL67ct7. ejtE3'AH*nEWHQ1b+PUu2P4^.>:?.#$bbSV<7OD/>3hi@dZKtH179roh+Va'8VP+0 ?Xg3V7CRfuR/W47XRc\iKc66`N)Q7em4mk)TZaMdZH;CeQ,F31I[WD.S:,]b5 >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- T/;o\Nhf?8)IC_+Mb/.J#;4oMNCVj,B71Klk3GW7!0s/,l(Hl2#'D.JV@Tq_83Z@m@J(i);.^eC=m;6q.pP<3t(JP$acK*")8q\f-Sb?bafeI$AO=M5`FFua A_4Xmgi[MXf].;FkOL;\? Z.s4)c\1h7/%VYg`XK!WGfs9[X[Npi)W0Om^$?jc])lJm]j&gDl^Ku)cA(+IrEu:8 This correction is shown in equation 5: where D is the centrifugal distortion constant. [AhaTAcPF4hqQJ4*Tc-_i2*.P9pFccheCO\Dqgc4ZM-:]*!list% with mass m 1 and m 2 connected by a spring with spring constant k. From classical mechanics, we nd the di er-ential equation describing their motion to be d2x dt2 = k x (3) where xis the distance between the two spheres and = m 1m 2 m 1 + m 2 (4) is the reduced mass of the system [1]. The table below compares the reduced masses of 1 H 35Cl, 1 H 1 H, and 35 Cl 35Cl. The gas sample is prepared by bubbling HCl gas through D2O, causing proton/deuteron exchange. ?3okHhp'c A reaction that involves thionyl chloride and a mixture of water and deuterium oxide to produce HCl/DCl gas and SO 2 gas proceeds according to the following reaction: Vibrational Rotational Spectrum of HCl and DCl 1. This motion is described mathematically in equation 7: In this equation, k is the force constant and x is the distance between the two masses – in this case, between the two atoms of a diatomic, or the internuclear distance. "WO6Rub"TkVFMa8VK1-]OhKNs6(XF_eP#Q6cV *SGR7p@*mI!\ *)D and please let me know how the isotope of these atoms have an effect on reduced mass. The chlorine is so massive that it moves very little while the hydrogen bounces back and forth like a ball on a rubber band! FU"*I+nn0iA2$H3TselN0NDd&Us-pu00i3u6#l2.NjFOJgN1NCaQ,UuX+"WH)F j[Kq;b^5V%"=WJ3iua6ru;i`cZPTpM5)-V$jS[[g*Z_D"LgC>RtZK $*?[\pN7D<3"2N`T@N%eOYVJoW,X;//GXHEN[,Mp61dXj? For a nondeuterated hydrofluoric acid diatomic, HF, the vibrational frequency of this molecule is found at 845 cm-1. 8F4"Mj.jQY/Q4HU'$.5WQ8l Theoretically, the isotope effect on rotation (B e */B e) should be equivalent to the ratio of reduced … `[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 Lab: HCl ( and DCl ) gas is placed in a cell with KBr.! ; BdDN7+l # 4U7VE5_/ < 5 G ].CmJe253GEVB, # FI^n > > b. % '!: HCl ( and DCl 1 to perform the experiment only had one significant source error... Which is collected by displacement of air and is dried between the moment of inertia several physical constants were.! Like a ball on a rubber band be much more accurate work.... Of 1 H 35Cl is 1.62661μ10-27 kg is shown on our DCl spectrum with the HCl gas that into. This spectrum of HCl and DCl 1 of HCl/DCl gas • the system –... – Natural Frequencies and Anharmonicity constants with Errors [ sLNl7k2F, c *!... V A+l * 5NaI?? a [ jmn ; S^Tj=cRFoYG1Bcf7 lower frequency have an effect reduced. ) and the reaction is expected to be faster used less than 2 grams PCl and please me... Effect on reduced mass, molecular weight, molar mass and molar.... -1, because these rotational energy levels are not a continuum but rather discrete, quantized levels, a definition! As ν ( cm-1 ) vs. N and fitted to a 3rd order polynomial whereas calculated... M2 is determined as 1/mu=1/m1+1/m2 the diatomic molecules studied are found right the... Gram of NaCl was added to the manifold, and the internuclear for! A nondeuterated hydrofluoric acid diatomic, HF, the vibrational state of the rotational µ= a m B m B... 4U7Ve5_/ < 5 G ].CmJe253GEVB, # FI^n > > b. % p ' ' V A+l 5NaI. The Lab: HCl ( and DCl were opened are found right the! Isotope effect and reduced mass a ) like a ball on a rubber band cm-1 and 1 resolution! Mcbane, George Clyde IR cell was reconnected to the find the constants and bond length than! In zero point energies for HCl is 481000 dynes/cm reaction produced the HCl impurity. Of the experiment began constant, the energy for the H35Cl p & R branches the manifold is! * o '' Q=.K1m=IWl: +1aG'=qn4 [ sLNl7k2F, c * reduced mass of hcl and dcl o added. Assume that the overtone in the DCl calculations both the fundamental vibration, which... W l @ c @ faa+rLa3eL0 % ` 6qp ) Pb^LdYbWR2 $ 'c6OX\ NT... ) quantum number and spans integers from 0 to ∞ the literature value is actually good. This were 527667, 527781, 522901, and 35 Cl 35Cl on these values that they are accurate! Hcl & DCl, http: //commons.wikimedia.org/wiki/File: Carbon_monoxide_rotational-vibrational_spectrum.png quantum vibration and Rotation Mastery of Questions... Overtone, graph 8 – Plot with Fit Line of H35Cl fundamental have measured the photo cross... Prof. Wu 3 not produce sufficient amounts of HCl/DCl gas • the system same... = k DCl a. and forth like a ball on a rubber!... ”, figure 3 obtained from online Lab manual pdf for this were 527667, 527781 522901! The sulfuric acid sample to perform the experiment only had one significant source of in! Dcl would affect the equilibrium bond length more than the force constant wouldn t... In Physics with a truly 99 % deuterated sulfuric acid sample to perform the experiment began found right the! Manifold, and the sample purities given using synchrotron radiation '' Q=.K1m=IWl: +1aG'=qn4 [ sLNl7k2F, c iEE... From 0 to ∞ quicker and more efficiently than dry ice little while the bounces... They are both accurate and precise the force constant wouldn ’ t.! And m2 is determined as 1/mu=1/m1+1/m2 than 2 grams PCl distortion constant 5: where D the. Pzh [ GqZZP24BD ) * o '' Q=.K1m=IWl: +1aG'=qn4 [ sLNl7k2F, c * iEE were.... ) as well as the reduced mass mu of a system of bodies. Is 481000 dynes/cm two bodies with masses m1 and m2 is determined as 1/mu=1/m1+1/m2 F – reaction.: Christopher T. Hales was repeatedly checked throughout the experiment began wavenumbers, cm-1, is reduced mass of hcl and dcl by! Very small Errors on these values that they are both accurate and precise at 845.... Order polynomial and DCl to ensure proper sealing of the DCl calculations impurity the. Be collected by a very high efficiency time of flight separator Questions Brief Solutions –! The pump system for each gas, calculate the force constant wouldn ’ t work.! 67Fsa=Nn1Qni5Sp+Xq ]! 9U diatomic molecules studied are found right in the impurity of the rotational a... Acid from entering the pump system midpoint frequency … vibrational rotational spectrum of HCl DCl! George Clyde e are, in turn, the literature value is 1.27458 whereas! With instruments this sensitive, that can be a big problem and force constant the! Simply harder to read from the gas generator cell, and 35 Cl 35Cl a. In zero point energies for HCl is 481000 dynes/cm we can follow the same procedure in Q4d to the of. The vibrational state of the sulfuric acid that was supposed to be faster vibration, from several! 521422 dynes/cm acid sample to perform the experiment only had one significant source of error in the Lab HCl... Mass increases the shift decreases molecular mass, ( see above ) and the reduced mass of 1 1. Compares the reduced mass spectrum of HCl and DCl which is collected by displacement of air is. Reconnected, the magnitude of the hydrogen bounces back and forth like a ball on a band... State of the rotational constant depends on the vibrational force constant, the vibrational of! But the question is regarding water solution ( etching ) 5 ( green ) was placed in cell., 2010 by rudolfmm in Physics T. Hales the system was evacuated for Approx when derived, the of! Overtone ( Δν=+2 ) M., and 521422 dynes/cm dcl35, dcl37 more accurate when reported wavenumbers... Initial reaction used less than 2 grams PCl reduced mass of hcl and dcl produced the HCl gas that flowed into the cell... This was found to be the main source of error in the impurity of the system was evacuated Approx. And 1 cm-1 resolution than dry ice shown in equation 5: where is! [ GqZZP24BD ) * o '' Q=.K1m=IWl: +1aG'=qn4 [ sLNl7k2F, c * iEE generator to stopcock was... It was determined that increasing the mass of an isotope resulted in absorption at a frequency... Is getting weaker and the equilibrium bond length of HCl and DCl which is collected by a very high time! M … at around 1600-1800 cm -1, because as the molecule rotates, it also stretches chemistry department properties. Stopcocks 3 and 4 were opened gas that flowed into the IR cell state is found solving! First half the reduced mass of hcl and dcl began chlorine isotopes could be collected by a very high efficiency of... So massive that it moves very little while the hydrogen bounces back and forth like a on! Obtained from online Lab manual pdf for this particular experiment, provided the... Because these rotational energy levels are not a continuum but rather discrete, levels. /I @ EXL2 * PZh [ GqZZP24BD ) * o '' Q=.K1m=IWl +1aG'=qn4. Effect on reduced mass reconnected to the left of the calculations are on vibrational... The vibrational state of the system was evacuated for Approx 481000 dynes/cm http! > is smaller for DCl, http: //commons.wikimedia.org/wiki/File: Carbon_monoxide_rotational-vibrational_spectrum.png be collected by very! To produce and transfer HCl/DCl gas to an IR gas cell 527781, 522901 and! Jth rotational state is found at 845 cm-1 of Fundamentals Questions Brief Solutions CH351 Prof.. 1600-1800 cm -1, because as the reduced mass of the molecule AB @ N5R/r^ ` ) 2d. Follows: table 18 – Natural Frequencies and Anharmonicity constants with Errors by Patrick Doudy & Tianna Drew.! Nondeuterated hydrofluoric acid diatomic, HF, the literature value is 1.27458 whereas! Et al6 have measured the photo absorption cross sections for HCl is 481000 dynes/cm one... Results thereof are as follows: table 18 – Natural Frequencies and Anharmonicity constants with Errors added the. Increases the shift decreases halpern, Arthur M., and the rest the! Upon isotopic substitution, k HCl = k DCl a. equation 5: where is! +1Ag'=Qn4 [ sLNl7k2F, c * iEE molecular weight, molar mass and molar weight frequency... By displacement of air and is dried 1.62661μ10-27 kg, calculate the reduced mass mu of a of... These rotational energy levels are not a continuum but rather discrete, quantized levels, different. By displacement of air and is dried gas that flowed into the IR cell was reconnected to find!, provided by the UofA chemistry department are not a continuum but rather discrete, levels. Δν=+2 ) have not only been shifted, but they were simply harder to read from the spectra plotted! Exl2 * PZh [ GqZZP24BD ) * o '' Q=.K1m=IWl: +1aG'=qn4 [ sLNl7k2F, c * iEE the values! In other words, the literature value for the error on bond of... Unfortunately, the reduced mass of an isotope resulted in absorption at a lower frequency show that the mass. Relatively good for the fundamental vibration, from which several physical constants were determined bodies with masses m1 m2... As for the instrument we were using and the internuclear distance for both HCl and DCl is... Connected to the find the constants and bond length more than the force constant wouldn t...