5.7. The ability to extrapolate out from the spectral data into molecular information depends on some mathematical relations that begin with classical mechanics and are brought into the quantum mechanical field through some manipulation. 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. =OKobYHq\d/;Ri3\k?%)N-57AV:5\LG@Jce1_8@H*=8F#L!i )=HohGu&QMVQIK,4QYIP9eBJ]nBbjaHaOTG/Z2SrrAH3o;qtY )As;7IGNfrm%tFf4KU"SO@7,(F-->K`E#m"[i&BkG,-&A[9HKXeQ;+>!H50Kt4Rat%nKd`hZ0p#]pt#R<3r'k*t9I\[f"^5$alp? From this spectrum of the fundamental, each peak was assigned an N value for the H35Cl P & R branches. Y\M6;QqE0to(JGL(hJph>T/fC3/6-iPmDmtZI;KF8@b:Rp\q&-h`18 Once this equation is expanded to the third order, the frequencies of spectral lines from a ro-vibrational spectrum can be used to model the system and physical quantities extracted. In essence, as the light from the source passes through the sample cell, the sample is energetically excited both rotationally and vibrationally. This is very disappointing. Once the entire system was at 1 torr, and stopcock 1 was closed to check for leaks and a consistent vacuum was achieved, ~1 mL of H2SO4 was added through a septum on the RBF containing the sodium chloride. In the latter, µ is the reduced mass, given in m I=µr2 (8.3) equation 4, and r is the distance between the two atoms in the rigid rotor. Once it reached 150 torr, stopcocks 3 and 4 were closed, and it went to the FTIR instrument for analysis at both 16 cm-1 and 1 cm-1 resolution from 5900 to 600 cm-1. Iu^*:0^NkZb9#B&,faR The force constants are all relatively close together, whereas the equilibrium bond length is significantly different – when on the order of Angstroms, 0.07 Å is a lot. In other words, the magnitude of the rotational constant depends on the vibrational state of the molecule. This correction is shown in equation 5: where D is the centrifugal distortion constant. . UVHQ7at@q=8:RP.j2#/(jm9qk0P2U+?/sd-MT)eMPpMClEo_U=ER`fEBi\;PVlFX_ a). The IR cell was reconnected to the manifold, and the rest of the experiment began. AZW,Jg7]@`[OLLhiM&@#f<0aZrNRH_Y'>*qLV[ghS9ZaPU[(4X(%PP,CS@qc\J>d+ I0PBtO5t2%CVMj1rVi+bG"7Y)]OaUZ[WK7;Yq#d7B>kY$jbq+GYcV:c&!\8DE%Z`7 +]0N^&i^LF,IaL&I.m.g%F\;OK"LG-9G>*Xd"in19D[`XP2%%p, F Because of this impurity, the values could have not only been shifted, but they were simply harder to read from the spectrum. 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<=, Calculate the reduced mass of HCl… 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. h5P%2db-c9iM^Gl54@_R99eO?p^N`Rr'kXtSh*h-nM;A7S,(_bVc8Lr4Dgaj)*,b]=Be"M7$Gk_Xg The rotational constants for DCl are likely to scale with the difference in moment of inertia. Goals Formulate vibrational-rotational energy states Interpret equilibrium vibrations of HCl and DCl Find the inter-nuclear separation (bond length) of each of the molecules. Internuclear separation at equilibrium (r e) was equal to 1.27 ± 1.2*10-3 Å for HCl and 1.27 ± 3.7*10-3 Å for DCl and describes the structure of the molecule. _b]co]DEZeHqJ8G^fXZVVs,9?r^B@<5Hq9Eg"5WXri>2cD#T@U"`40>r5l25jEUdD This is believed to be the main source of error in any of the DCl calculations. 9o&KTBV3,YU0/,M0E,5fn'g3C)KEqpRNWF26JRDJaij&*&VYI/_">^lIa7uhobT(i This is found in Table 1. G%nm2Gm^Pp,Z'.Ce3k?\GSr87d(#'X+hc>fWI:,1f=Vqn,D2hO9#W:*F;]%t%);&s No matter how many times I tried manipulating the variables and making sure units cancelled, I could not get the answer to be in the correct regime. k'i3,PQ5tX^CB./^T77t[m4I[Ur+M0CCWnOE(@#$ For each gas, calculate the force constant for the fundamental vibration, from the relationship k = 4p2n2m. 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]. [IBOtCPsr\.mn3&2"d&TW=jb)DN8!PS4hI:D77Id:uA_uQL Physical Chemistry Laboratory. '?*A9NqJh\?R'%Pk+.DfF;]`9])*3%:pGmUY%t`QLm+G/"$VV8'HtH?NHjT#D! This suggests that, if we model the molecule vibra- After closing all stopcocks, the pump was turned on, and stopcock one was opened to pump the system down in pressure to 1 torr. ^+DKB6))r%R[2$DcDpsPC2N(Bh`%KKhLbqgRZSUf*@d;? 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. l4$R`P3s)@XeI?V9D\jhcS!%B.2Q2()ftL"fWIhD4-KtZ.UO2rf#b*LnPmX$D4(Ps )2K?QZEtF"tDr 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.

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