Make a drawing corresponding to the range of 4000 to 400 cm-1, indicating the different zones and types of vibrations that you should observe if you analyze a hydrocarbon.
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Make a drawing corresponding to the range of 4000 to 400 cm-1, indicating the different zones and types of vibrations that you should observe if you analyze a hydrocarbon.
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- 1-31. We shall learn when we study molecular spectroscopy that heteronuclear diatomic molecules absorb radiation in the microwave region and that one determines directly the so-called rotational constant of the molecule defined by B = 8721 where I is the moment of inertia of the molecule. Given that B = 3.13 × 105 MHz for H35C1, calculate the internuclear separation for H35C1. The atomic mass of H and 35C1 are 1.008 and 34.97, respectively.Given these two equations, calculate Cv for CO2 and N2 using the velocity of sound. 6. According to statistical mechanics, the contribution to Cy due to the ith vibrational mode of a molecule is c ee;/T Cv,vib,4 = R(7) ³ (e®,/T — 1)² › where Oi = hcv./kB, h is Planck's constant, and c is the speed of light in cm s-¹. v; is the vibrational frequency of the ith vibrational mode in wavenumbers (cm-¹). The quantity O, has dimensions of temperature and is sometimes referred to as the vibrational tem- perature (of the ith vibrational mode). The total vibrational contribution to the molar heat capacity for an N-atom (linear) molecule is then Cy,vib Cv,vib,i Calculate Cy for CO₂ at 300 K, assuming that the translational and rotational con- tributions are (3/2)R and R, respectively, and use the preceding equations to obtain the vibrational contribution. Four vibrational modes for CO₂ are expected (3N- 5). How- ever, three fundamental frequencies are observed at v= 667.3, 1340, and 2349.3 cm-¹.…Carbon dioxide and water are important greenhouse gases. Sketch the fundamental vibrations for both molecules and indicate which you expect to be infrared active.
- The IR spectrum of 2-methyl-1-butanol (H;CCH,CH(CH;) CH,OH) and tert-butyl methyl ether [(CH;);COCH3] are shown below. Assign cach spectrum to the correct com- pound and identify the frequencies and the functional groups used to support your assignment. λ (μm) 6 7 8 9 10 11 12 1314 15 2.5 100 3 5 90 80 70 60 50 40 30 20 10 4000 3600 3200 2800 2400 2000 1800 1600 1400 1200 1000 800 600 400 Frequency (cm-1) A (µm) 7 8 9 10 11 12 13 14 15 2.5 100 3 5 20 4 6 90 80 70 60 50 40 30 20 10 4000 3600 3200 2800 2400 2000 1800 1600 1400 1200 1000 800 600 400 Frequency (cm¬!) (%) Transmission (%) Transmission 20a.) What is the ratio of the number of Cl_2 molecules in the excited vibration to the number in the zero-point level. b.) Calculate the ratio of the number in the v=1 level to the total number. v_0 = 559.7 cm^-Consider the following Greenhouse Gases (GHG's): Sulfur hexafluoride, carbon dioxide, and trifluoromethane (a hydrofluorocarbon). Using the concepts of asymmetrical stretching and infrared absorption, rank the gases from weakest to strongest greenhouse gas, and explain your ranking that CH4 is a stronger GHG than CO2). HINT: Consider ö=c=ö carbon dioxide sulfur hexafluoride trifluoromethane
- The force constant of the hydroxide anion, ¹ H ¹6 O is 2500 N/m. Assume it is a harmonic oscillator. Use the constants in the che302r library: 1 ΝΑ = N.A (number of particles) ħ hb (Js). c = cl (m/s). = a. Compute w for the fundamental vibration. w = 1.26e15 S-1 b. Compute the energy corresponding to the fundamental vibration. E = 4.17e-19 X JWhat IR frequencies would enable a chemist to distinguish between these molecules? CH;CH2OH and CH;CH2OCH;CH3 and CH, HCHCHCCIICH CH, d 3000-3100 cm-1 (=C-H)| 1620-1680 cm-1 (C=C) 3200-3400 cm-1 (OH) || 3000-3100 cm-1 (=C-H)(Slightly modified McQuarrie 5-41) Many quantum vibrational states are available to molecules. This raises the question: In what vibrational states are molecules actually found? Using sta- tistical mechanics, one can show (see McQuarrie 5-40 if you are interested) that the fraction of molecules in the n-th state is given by: fn = (1-e-hv/kBT) e -nhv/kBT where kB is the Boltzmann constant, kg = 1.380658 × 10-23 J/K. Compute the occupancy of the n=0, 1 and 2 states at 300 K and 1500 K for a "typical" harmonic frequency, we = 2650 cm-1. For practical purposes, what vibrational state is a typical molecule found in?
- Predict the number of vibrations for the following con pounds (picture given). Number of vibrations for a nonlinear molecule is given by 3N-6, where N = number of atoms. Number of vibrations for a linear molecule given by 3N-5The space immediately surrounding stars, the circumstellar space, is significantly warmer because stars are very intense black-body emitters with temperatures of several thousand kelvin. Discuss how such factors as cloud temperature, particle density, and particle velocity may affect the rotational spectrum of CO in an interstellar cloud. What new features in the spectrum of CO can be observed in gas ejected from and still near a star with temperatures of about 1000 K, relative to gas in a cloud with temperature of about 10 K? Explain how these features may be used to distinguish between circumstellar and interstellar material on the basis of the rotational spectrum of CO.Be sure to answer all parts. Covalent bonds in a molecule absorb radiation in the IR region and vibrate at characteristic frequencies. (a) A molecular vibration absorbs radiation of wavelength 28.3 um. What frequency (in s) corresponds to that wavelength? Enter your answer in scientific notation. x 10 (b) A molecular vibration has a frequency of vibration of 7.574 x 10" Hz. What wavelength (in um) corresponds to that frequency? um
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