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Global Least-Squares Analysis of the IR Rotation–Vibration Spectrum of HCl

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Joel Tellinghuisen

Department of Chemistry, Vanderbilt University, Nashville, TN 37235

J. Chem. Educ., 2005, 82 (1), p 150

DOI: 10.1021/ed082p150

Publication Date (Web): January 1, 2005

Section:

Optical, Electron, and Mass Spectroscopy and Other Related Properties

Abstract

The study of the IR rotation–vibration spectrum is a mainstay of the undergraduate laboratory curriculum in spectroscopy. Typical spectra consist of the fundamental and overtone bands for H³⁵Cl and H³⁷Cl (and sometimes D³⁵Cl and D³⁷Cl). These can be analyzed by least-squares fitting (i) one vibrational level at a time (using the method of combination differences), (ii) one band at a time, (iii) one isotopomer at a time, and (iv) both bands of both (or all) isotopomers simultaneously. The last two approaches involve the simultaneous fitting of two or more similar data sets and yield statistically optimal results. Procedures for doing such fits are illustrated for the data presentation and analysis program KaleidaGraph, with emphasis on the use of the program’s Macro Library for defining components of complex-fit models. Such methods greatly enhance operator efficiency and make global analysis truly feasible for students, as the only effort required of the user is (i) importing or entering the data and (ii) entering the fit-definition functions in very nearly their algebraic form. The article includes a comprehensive summary of standard notation for energy levels in diatomic molecules, a critique of methods used to estimate the key molecular parameters, and a discussion of subtle issues involved in rounding least-squares fit parameters for presentation.

Keywords (Audience):

Upper-Division Undergraduate

Keywords (Domain):

Physical Chemistry

Keywords (Pedagogy):

Computer-Based Learning

Keywords (Subject):

Gases

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This article has been cited by 2 ACS Journal articles (2 most recent appear below).

Integrating Statistical Mechanics with Experimental Data from the Rotational–Vibrational Spectrum of HCl into the Physical Chemistry Laboratory
Bret R. Findley , Steven E. Mylon
Journal of Chemical Education2008 85 (12), 1670
- Integrating Statistical Mechanics with Experimental Data from the Rotational–Vibrational Spectrum of HCl into the Physical Chemistry Laboratory
  Bret R. Findley , Steven E. Mylon
  Journal of Chemical Education2008 85 (12), 1670
  We introduce a computer exercise that bridges spectroscopy and thermodynamics using statistical mechanics and the experimental data taken from the commonly used laboratory exercise involving the rotational–vibrational spectrum of HCl. Based on the results ...
  Abstract | Hi-Res PDF | PDF w/ Links
First-Order or Second-Order Kinetics? A Monte Carlo Answer
Joel Tellinghuisen
Journal of Chemical Education2005 82 (11), 1709
- First-Order or Second-Order Kinetics? A Monte Carlo Answer
  Joel Tellinghuisen
  Journal of Chemical Education2005 82 (11), 1709
  In chemical kinetics, data for the concentration [A] as a function of time can be analyzed by least-squares fitting to the appropriate expression for the integrated rate law. The problem of discriminating between first and second order in such analyses is ...
  Abstract | Hi-Res PDF | PDF w/ Links