1 Kraitchman's Equations In this problem, you will apply the so-called Kraitchman's equations to some rotational spectro

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1 Kraitchman S Equations In This Problem You Will Apply The So Called Kraitchman S Equations To Some Rotational Spectro 1 (176.76 KiB) Viewed 36 times

1 Kraitchman S Equations In This Problem You Will Apply The So Called Kraitchman S Equations To Some Rotational Spectro 2 (133.24 KiB) Viewed 36 times

1 Kraitchman's Equations In this problem, you will apply the so-called Kraitchman's equations to some rotational spectroscopy data. Kraitchman's equations relate changes in moments of inertia by isotopic substitution with the Cartesian coordinates of the substituted atom in a coordinate system, where the center of mass is defined as the origin of this coordinate system. We will use Kraitchman's equations to calculate the structure of carbonyl sulfide, or OCS, a linear molecule. In order to calculate the positions of each atom in OCS, we need to measure the rotational spectrum of OCS with each of its atoms substituted by an isotope. Problem 1.1. The parent isotopomer of OCS, 16012 C32 S, has a measured rotational con- stant of B 6081.492439 MHz. Calculate the moment of inertia, I, in units of amu. Ų. Problem 1.2. Now, calculate the moments of inertia in units of amu. · ÅP for the three most common singly substituted isotopomers of OCS: . 16013(32S, B 6061.92498 MHz = . 16012C34 S, B 5932.8379 MHZ • 18012C132 S, B = 5704.8607 MHz Problem 1.3. Now, define a reduced mass u where: MAm u= M + Am such that M is the total mass of the parent molecule, and Am is the change in mass introduced by isotopic substitution. Calculate u for all three isotopomers in units of amu. Make sure to use as many significant digits on the isotopic masses as possible (NIST WebBook has a great tabulation of isotopic masses online).
Problem 1.4. Let Iparent be the moment of inertia for the parent isotopic species, 16012C32 S, and Ix (X = C, N, 0) be the moment of inertia for one of the singly substituted isotopomers. Kraitchman's equations state that for atom X, its position with respect to the center of mass is: 1/2 |x = = [,«Ix – Iparem) ( where |2| is the absolute value of the displacement of atom X from the center of mass. Calculate (x) for each atom using the moments of inertia you calculated in the previous problem. Problem 1.5. From the positions you calculate above, place OCS on a line where x = O is the center of mass, place each atom based on their calculated |x| position from the previous part, calculate the C=0 and C=S bond lengths. The experimental equilibrium geometry of OCS has r(C = S) = 1.5628 0.0010 Å and r(C = 0) = 1.1543 +0.0010 Å. How close are your values to these experimental values ? = = =