reduced mass of hcl and dcl

Energy transitions from the spectra were plotted vs. frequency, from which several physical constants were determined. Quantum Vibration and Rotation Mastery of Fundamentals Questions Brief Solutions CH351 – Prof. Wu 3. 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 D(gE/Rlu:-Kuod,d3-,LMYkoWM#Lh&IOM)btjTjanV[ Definitions of molecular mass, molecular weight, molar mass and molar weight. 7)lpVG[QRg1UU=(0L]'hR%,fI\V )6Aa7A6>7V5%tA%77;?>;g+T8S0&HX#TZ":ZH;uS` nIK,:F)7^!7nHR,TJ-'lZq$^jLp?iOCASdV_U+i4Fu6h70R5Sc9lSm:8XJ]:54c6,1]$e.%nI If the diatomic molecule HCl, with 1 H and 35 Cl were substituted with 37 Cl, what change occurs to the reduced mass? 2Q^B>85F=t:LfuL5,&K2$M>N_KssVL@tKA_i^J:t6aOg9i9dh-dci(d-Qj^\mJrk$ Note that 1 amu = 1.660565*10-27 kg.. I7,Z%Nk:ir>/^=Ig^DmYb;C`mJcjci8;f(Q%YHp"gs+\"45JLpU+h4Ej6OAEctCo6 oH^+n\)Z!C33SZQ!1PoW+qF=D]P^q,IYY-38XFYqS+"O9N8knaRVfNlXdS-gs'BUb \SA;?$kmdm+j&_V/Aq,p:FBnfQ8? where Jis the rotational quantum number (with integer values 0, 1, 2, ...), his Planck's constant, and Iis the moment of inertiafor the molecule (calculated as shown using the reduced mass, m, and with r = r e).Note that the equation for E(J)is not necessarily in cm-1; you may have to use a conversion factor to get the desired units. Species Human (9937) , Species Mouse (55947) , Species Rat (292127) , Species Zebrafish (324964) , Species chicken (423902) , Species cow (504377) , Species Horse (100068217) , Species domestic cat (101096110) , Species dog (477824) , Species domestic guinea pig (100723290) , Species naked mole-rat (101708258) , Species sheep (101123252) , Species Domestic Rabbit (100359072) In other words, the magnitude of the rotational constant depends on the vibrational state of the molecule. :5mH7MqpF)s9-?6Lhi8u]X?s843FP&9M882l7@f=m[L\KfZ3=gL^: _A3Ss<1j-9pj?5#]7k^+_rIWOVkd)=:(c3Ge_&dAW"dM^hR8fCQfUDDFQE2^lrNs@ G*\3?b#58`1u'aeh#*eFb4X([oP/(MIEsI.34I)).A)KkC:\F2gAJA*;(q\eaY>/raAYQD1$p,0CrooE_A 5.7. Chem435. ^+DKB6))r%R[2$DcDpsPC2N(Bh`%KKhLbqgRZSUf*@d;? Rotation Vibration Spectrum of the HCl Molecule IRS 3 I(x) to a source spectrum I(ν) is then propor-tional to the Fourier transform of I(x) I(ν) ∝ Z I(x)cos 4π c νx dx (3) Putting an absorber in front of the detector and taking the ratio of the spectra with and without the absorber produces the transmis-sion spectrum. ([E`4cHaU$:f7 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. ?3okHhp'c “Rovibrational Spectroscopy.”, Figure 3 obtained from online lab manual pdf for this particular experiment, provided by the UofA chemistry department. go3+ZK:cut=r8kI9h&It_\h(Z6u!0/)lc+Ii!..>dP7Sr(9E>1gcp)!,f6^Ba&N9a These values represent ~10% error. nk9Vc]i.4-RDfQ-K/SF:kuP9W1-il$pW:o;Dj#`=4t6oNIlM"[Vg'3)?$bVE$qW;D The other significant problem was that the overtone in the DCl spectrum didn’t appear. This is shown on our DCl spectrum with the HCl fundamental impurity showing up to the left of the DCl fundamental. ;BdDN7+l#4U7VE5_/<5 This is believed to be the main source of error in any of the DCl calculations. r]'*;p2l&1D`aC2cn'P1d=:84?)Q7R]UKsGqO_[g6VuG0e! )2K?QZEtF"tDr * 4SU1r7=!FNL;A'T][h2aTMH8BhXIbq@kcl^0Qb%^%t/3dFmb75K5JcdV'rO0,Y4H^ 9o&KTBV3,YU0/,M0E,5fn'g3C)KEqpRNWF26JRDJaij&*&VYI/_">^lIa7uhobT(i We can use the same procedure in Q1. Figure one depicts this overlay of both rotational and vibrational energies: Figure 1 – Rotational energy levels, J, superimposed upon the vibrational energy levels, v, and the separation thereof into P & R branches.2. In the latter, µ is the reduced mass, given in m I=µr2 (8.3) equation 4, and r is the distance between the two atoms in the rigid rotor. Internuclear separation at equilibrium (r e) was equal to 1.27 ± 1.2*10-3 Å for HCl and 1.27 ± 3.7*10-3 Å for DCl and describes the structure of the molecule. l4H:[?b?fN!;1t=pSNLG,BD2X1&+Bpp>(Y$-OZp!O3mUqpbHgf#+e?_O_+:#a[bkC,+ZOSs'o! J is the rotational µ= A m B m A+m B (8.4) quantum number and spans integers from 0 to ∞. 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. 8;T*$0Ef7eFC'Ci?pfY? Theoretically, the isotope effect on rotation (B e */B e) should be equivalent to the ratio of reduced … NhVQ$p0r[epJgV?knDkDP[t_%dIFpZ\tLP=-V@qt"/F9(=t2ZWkS-\=;kCg.+P2mH /re:2R,P;/>GV^k2L`3Ms7H-\@G0eLD;5l9m`%0*CPg>!S8?T^9ij0LZKjSqaNp08 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. For a nondeuterated hydrofluoric acid diatomic, HF, the vibrational frequency of this molecule is found at 845 cm-1. qu]-Ocdl]Po5/9G(GO*+gibH*4.B(BUhAf4aUBd^5P$>"S@sp4^LX_ The gas sample is prepared by bubbling HCl gas through D2O, causing proton/deuteron exchange. The chlorine isotopes could be collected by a very high efficiency time of flight separator. and please let me know how the isotope of these atoms have an effect on reduced mass. 7CVd'Q\N>4o6p\-pj?mQ0Q5M4?HX^n4/iC$5OrHsOb04aNkIGj]*cV-)f^A7G^\nu For each gas, calculate the force constant for the fundamental vibration, from the relationship k = 4p2n2m. Y=(D")$u]eN;:s*@tED!1V>EI+FV$W(@XAlS6gAKF$.`j$5tEgO2tb4mn!q_INT(ip3oFldY$2rPcrP53U. νe is calculated as shown in equation 9: However, because, similar to the rigid rotor, the system described here is not a perfect harmonic oscillator, correction is required. with mass m 1 and m 2 connected by a spring with spring constant k. From classical mechanics, we nd the di er-ential equation describing their motion to be d2x dt2 = k x (3) where xis the distance between the two spheres and = m 1m 2 m 1 + m 2 (4) is the reduced mass of the system [1]. 8;W:,fok+0(&`a[LOMg_E_*,fCmE/\BSe=-A31Q*WKbF6+PA#KK>7lq%Q/_)\*)Oa Y4bmpCHsgY_@3,EXkiPmUn9&['tX*r_"0*8P(YaZ9p98;?H9dh##"4B(23/EqHB_R Peaks between them are an HCl impurity. rdo:BTL-EFj. 1EC;mU23$LS%<8SJhFD&ZmnYsjok21>95ei)4M0DZ\_JR/mME@Ao"b(Qut/7G+\.1 ];M Calculate the reduced mass … moment of inertia shown in equation 3. 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. >A!u)4?ts#A)F1YcmspR[(C8=CG5Cntp.SJl (6",rOo2Hc_LW\YO#B:X0>J"ld)MK5K'qLlne 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. WH?F4d#(\OJt@h=Tp2.Tq7?P$cf7>H)CY+;:@K8JMXP5P3!&1h1W]c((e[%V Fourier absorption spectra of HCl and DCl are recorded simultaneously in the spectral range [2840 cm -1-8450 cm -1].A U ij reduced Dunham coefficient set is deduced by fitting all the available data and then used together with four mass-scaling parameters to predict the TCl Y ij Dunham coefficients. Calculate the reduced mass of HCl… This was repeated at an HCl pressure of 100 torr and 207 torr. Abstract. Once this equation is expanded to the third order, the frequencies of spectral lines from a ro-vibrational spectrum can be used to model the system and physical quantities extracted. @RQ>_YqGu 8;Z\7bApgt&cDe1"*SaR&RfeA]pOdBRAk4,P"ET_j98! To prevent gaseous hydrochloric acid from entering the pump system. ]RO4W1J'$V:XlSSFWnCt$R@eXb\d[H2j3jQUrfV-U^1BM\9uZ4*:G+_8 %Woh=\("! '9AYi(t@Osqr0r__.\M8^WfkQZ`]l'M(Oc(0r=H^nmC61(W+Nr9EjR*EC7 The calculated values for this were 527667, 527781, 522901, and 521422 dynes/cm. 4["8JDVjN"ZG>0[p-[5R_iM6r(nLC=!dm>5YCR_#W"'&c\>=W0(%UM+TZfJr=/r&` f'mWZ9asrj8FXDe7dOncST_:lHOmS3'mYKa`NXXMp\:O,i5IFCEY$V_c$Z6i#,ktS dkVrGb/JHJ;Gd2.=lc(lX70^5*_j^MF1>Wrn.UAPc.SL'UCf0G!lh=9:(#/'KC[9 S9!7'>Rr/5RnUmA-6gq^%9^\,^o4Pbe2/@G`%1+V$D'rE\PG'8+WsrgC4#G,),mO$ Numbers 1-5 are stopcocks. =^HkBo^cXfQm9gk9Q%g@/`?rS##QtsoUn;N)h29%7HjLE5WQ2`Q +^R*2dE% ?fSPCSF-;9[?fA^W)"?AE#TA:GG^Yr5f$L/luLE9:t@Rtmaf JRV'b%]*Z+#S$E:G1)u'$qTDe&F:\f+KgjWN6E7beJ4l-WHr!h8>L:;-ZqTqFZCR% Because of this impurity, the values could have not only been shifted, but they were simply harder to read from the spectrum. J7sHQ8YqjgS*[lP0'@,UQ8^Js-(//am>[3diue7. elGQFlP0,D`W)"7r=p)rO:2'4>^USSH:2@Z7RUXXM*@D/htG,L\'gQXqQ!JD3El"a'#+2+9f:r(c4>8dss*h&(u/T<=, J31W[(Q@qF:K(>G@ooSDLg'X!&2oj/\iN)OF#T$>/=s2dRgUH 8;WR4gQ(#X')_n16Qn,1Cc"!;'Gm-lnL\naa2(li5S++O(=aY;9sU$2. Calculate the reduced mass of HCl molecule given that the mass of H atom is 1.0078 amu and the mass of Cl atom is 34.9688 amu. As for the force constant, the literature value for HCl is 481000 dynes/cm. l@c@faa+rLa3eL0%`6qp)Pb^LdYbWR2$'c6OX\,NT"C4n8>73(D? 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. ")fVL_"@)0G 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. 8;V/L]8e_g%>CE^hP!:cfN-hLW_*Ff!Xq':A;2Ya1i_dq! b,l#DR.aKlb7SCBWJR33ZA!Z1>*EjpdcY38I4k2o`eBQT8C,'_f&XA:DT.G'Wu0M+ a). GPs`Zo[DNro&iSuqfh%ceKJaj)!3#Pn%h*L4/(c$4p;1VCH&cC? 1g&p%&Y8ecB6h0@>04f;f'-*4A%kA1MG0mDb)o]1j-+pBSlqm$LX^LcR?n-%O]GfA )1]Sk\5sd/I=Cs>UkuO'iOF&3nZ 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. 3. 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). 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. KUB?q5a@fk&7Q5HrSlFkIrP,HK\5pS$H&3=[DfOM[N-mBE`6@oeNk;*]? ZtG$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 8;WR49lo&K')`"1%lg]Q[>!Os"F/!r;b']8>^3ok#Fq6-:C]EbQ/Dl49aRm*j=m]&*1RX>+NVQ6O(Fid0fQ4bjpisL_^i5^; 5.7. ]MfsuKH7l).og2K\bIhbRA\jC$AW*7f^p7\G\gtlr`u])IZ*mt@%`n4lZFhTSj!h0) 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. A_4Xmgi[MXf].;FkOL;\? ~1 gram of NaCl was added to the gas generator cell, and connected to the manifold. ]C30\[)MN'99A;G^-$R_X%6?k;9Ze#[H6+B?9+%9AF?`D9AMm8krI:?3\ct79 rA/eJZhYm:Kj4XP/k8?epG@Q`T)X f/"AtH&0ViT,'I(^D_/PEn=&Sq%_.OGpfTUs?V!Caf?O:5nV@FDN)Bk. 1:-? 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

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