BITS Pilani General Chemistry Lecture Notes PDF

BITS Pilani Pilani Campus CHEM F111 : General Chemistry Lecture 13 [Extra Class] 1 BITS Pilani, Pilani Campus Molecular Spectroscopy 4 BITSPilani, Pilani Campus Molecular Spectroscopy...

BITS Pilani Pilani Campus CHEM F111 : General Chemistry Lecture 13 [Extra Class] 1 BITS Pilani, Pilani Campus Molecular Spectroscopy 4 BITSPilani, Pilani Campus Molecular Spectroscopy 5 BITSPilani, Pilani Campus 6 BITSPilani, Pilani Campus Electromagnetic Spectrum Electronic Rotational NMR Vibrational The range of energies that can be used for spectroscopy is very large and spans a large proportion of the electromagnetic spectrum. 7 BITSPilani, Pilani Campus  Molecular Spectroscopy Inmolecules, transitions between electronic/vibrational/ rotational energy levels is commenced by irradiating different fraction of EMR. After Energy Before Bohr frequency condition h =  Wavelength  = c/, Wavenumber =   c Spectroscopy: Analysis of electromagnetic radiation absorbed, emitted, or scattered by atoms and molecules. Information regarding energy levels, geometry (bond lengths, bond angles), and bond strengths. 6 BITSPilani, Pilani Campus Absorption/Emission Spectroscopy Absorption can only occur when the energy of the radiation (calculated from the frequency or wavelength) matches the energy gap. If there are several different upper levels (and there usually are) then several transitions will be observed. 7 BITSPilani, Pilani Campus  Types of Spectroscopy Rotational Spectroscopy: Microwave (Low energy): Rotational Transitions Vibrational Spectroscopy: Infra red (intermediate energy): Vibrational Transitions Electronic Spectroscopy: UV/Visible (highest energy): Electronic Transitions Application of this will be taught in in Coordinate chemistry. Nuclear Magnetic Resonance: Radio frequency (lowest energy): Nuclear Transitions Raman Spectroscopy 8 BITSPilani, Pilani Campus Rotational Spectroscopy or Microwave Spectroscopy  Rotational spectroscopy Spectroscopy in the microwave region is concerned with the study of rotating molecules. When a particular molecule rotate, the range of rotational frequencies (corresponding to diff. between rotational levels) is of the order of frequencies: 8x1010 - 4x1011 Hz, (λ: 0.75 - 3.75 mm)→ This falls in the microwave region of the electromagnetic spectrum. 10 BITSPilani, Pilani Campus Pure Rotational spectroscopy At least two atoms bonded together and tumbling in space constitute a rotational motion. Rotation of linear molecules is easy to understand, however the rotation of 3D body is quite complex. A rotating molecule could be approximated to a rigid rotor (not elastic), and thus the rotational energy is quantized. 11 BITSPilani, Pilani Campus RIGID ROTOR-Quantized Levels If such a rotating rigid rotor (molecule) possess a permanent dipole moment, then such rotations will provide a oscillating electromagnetic field that will interact will the electromagnetic field of the incident light (microwave light) and microwave light stimulates rotational translations. The rotating molecule will get excited by absorbing energy from incident microwave light, equivalent to the difference between specific rotational energy levels. Analysis of the transmitted light results in a spectra. 12 BITSPilani, Pilani Campus Selection Rules: Pure Rotational Transitions Gross selection rule: Molecule must be polar (possess a permanent dipole moment) Specific selection rule: ∆J =±1 J ; rotational quantum number Practically applicable to samples in Gas phase. In solids or liquids the rotational motion is usually quenched due to collisions. Long Sample path lengths required. Homonuclear diatomic molecules (H2, O2 etc.) do not have a pure rotational spectrum. Polar molecules are rotationally active: HCl, NH3, H2O, CH3Cl Non polar molecules are rotationally inactive: CH4, SF6, CO2, C6H6 13 BITSPilani, Pilani Campus Diatomic molecule as Linear Rigid Rotor A diatomic molecule may be thought of as two atoms held together with a massless, rigid rod (Linear rigid rotator model). The moment of inertia of the molecule about Ia the centre of mass is given by: I = m1r12 +m2r22 = Ia (along an axis of rotation) m1m2 2 Where: r1 + r2 = r I r  μr2 m1  m2 Other Rotations could be thought of considering the rotational components about perpendicular directions through centre of gravity. Ia = Ib & Ic = 0 Ic Ib Energy levels, EJ (in Joules) = hBJ(J+1) ;B (in Hz) = h/82I OR EJ (in cm-1) = BJ(J+1) ;B (in cm-1) = h/82Ic [B or B is the rotational constant expressed in different units] J = 0,1,2,3,……. is the rotational quantum no. 14 BITSPilani, Pilani Campus Diatomic molecule as Linear Rigid Rotor When a rigid unsymmetrical linear molecule changes its quantum number from J to J+1, the change in rotational energy of the molecule is: ∆E = EJ+1 – EJ = [hB(J+1)(J+2)] – [hBJ(J+1)] ∆E = 2hB(J+1) = hJ Rotational Transition frequencies J  2B(J+1) In spectra, series of absorption lines at J =2B(J+1) appears 2B 4B 6B 8B 10B with J = 0,1,2,3…. [2B, 4B, 6B……..] J = 1 →J = 2 J = 0 →J = 1 15 BITSPilani, Pilani Campus  A Typical Rotation Spectrum Why this pattern Separation 2B from which can be obtain from a rotational spectrum from which moment of Inertia (I), and hence bond length (r) can be calculated 18 BITSPilani, Pilani Campus Relative Intensities of rotation spectral lines Maximally Populated Level For example, Linear molecule, O=C=S, Jmax = 22 17 BITSPilani, Pilani Campus Moment of Inertia for complex molecules Moment of Inertia for other molecules can be calculated Moment of Inertia (ref. to Tab.19.1 of TB) 18 BITSPilani, Pilani Campus  Rotational Spectroscopy Centrifugal distortion: (Molecules are not real rigid rotors) As their bond length increases (easily stretchable bond), their energy level becomes slightly closer. EJ = hBJ(J+1) – hDJ2(J+1)2 D is the centrifugal distortion constant, whose magnitude is related to the force constants of the bonds. 19 BITSPilani, Pilani Campus Other types of molecules Symmetric tops (or symmetic rotors) Oblate symmetric tops Prolate symmetric tops Spherical tops (or spherical rotors) Asymmetric tops The energies of rotational levels for these molecules are given by modified equations and there are extra specific selection rules which govern that out of these which of them are rotationally active or not. 22 BITSPilani, Pilani Campus  BITS Pilani Pilani Campus CHEM F111 : General Chemistry Lecture 14 1 BITS Pilani, Pilani Campus Vibrational Spectroscopy (IR Spectroscopy)  Vibrational spectroscopy Atoms within a molecule are never still. All molecules are capable of vibrating. Complicated molecules vibrate in a variety of ways (modes). These ways could be twisting, stretching, buckling, bending in different regions and in different manner. Each vibrational motion (mode) has its own resonant frequency. Such vibrations can be excited by the absorption of correct amount of energy from electromagnetic radiation.  Observing the frequencies at which absorption occurs gives valuable information about the identity of the molecules and information about the flexibility of its atoms. 3 BITSPilani, Pilani Campus  Recall: 1-D harmonic oscillator n 1 k n ν= 2π m  Energy of 1D-harmonic oscillator is  1 E n =  n + hν; n = 0,1,2,3,   2  Equal spacing (hν) between adjacent energy levels.  Zero point energy = ½hν (corresponds to n=0) 4 BITSPilani, BITSPilani, Pilani Campus Pilani Campus Diatomic Molecule: Potential Energy Curve For the vibration of a diatomic molecule, a difference in the potential energy curve is observed as its bond is lengthened by pulling one atom away from each other or pressing it into the other. 1D-harmonic Oscillator (HO) In a HO, molecule move back and forth with no possibility of stretching beyond the turning point: it does not allow the molecules to dissociate. Diatomic Molecule Equilibrium Bond length (minimum in PE) 5 BITSPilani, Pilani Campus Diatomic Molecule  Harmonic oscillator approximation works very well particularly, near the minimum of the PE curve. In low regions of PE V = ½ kx2 V ~ ½ k(R – Re)2 Stiffer Bond Displacement from equilibrium 6 BITSPilani, Pilani Campus Diatomic Molecule We can use the same solution of Schrodinger equation in low regions of PE curve.  1 E n =  n + hν;  2 n (or v) = 0,1,2,3, . Both atoms joined with a bond move. Effective mass of the molecule to be considered. Fundamental frequency 1 k ν= 2π μ Reduced mass n is vibrational quantum no.; Some books use v as the symbol for vibrational quantum number; It is better to use n to make it different from frequency symbol) 7 BITSPilani, Pilani Campus Selection rules: Vibrational transition Vibrational transitions: At frequencies of 1013 to 1014 Hz, Infrared spectroscopy. (wavenumbers: 4000-400 cm-1) Gross selection rule: The electric dipole moment of the molecule must change during the vibration. The molecule need not have a permanent dipole; only change in dipole moment is required during each mode of vibration, which can shake the electromagnetic field into oscillations. Homonuclear diatomics are IR inactive. During stretching, no change in its electric dipole moment from zero is observed; vibration of such molecule neither absorb nor generate radiation. Heteronuclear diatomic molecules are IR active 8 BITSPilani, Pilani Campus Selection rules: Vibrational transition At room temperature, almost all molecules are in their vibrational ground states (n = 0) and thus, n = 0 to n = 1 is the most important spectral transition. Specific selection rule: Δn = ±1 (also referred as Δv in some books, where n or v is vibrational quantum no.; prefer using n to make it different from frequency symbol) Change in energy for the transition from a state with quantum number n to n+1:  3 ~  1 ~ ~ E  En 1  En   n   hc   n   hc  hc  2  2 Absorption occurs when the incident radiation provides photons with this energy. Molecules with stiff bonds (large k) joining atoms with low masses (small μ) have high vibrational wavenumbers. 9 BITSPilani, Pilani Campus Real Molecules: Anharmonicity For real molecules, the potential energy curve deviates from harmonic oscillator approximation. At high excitations, the swing of atoms allows the molecule to explore regions of potential energy curve where parabolic approximations are poor. The motion then becomes anharmonic. The restoring force is no longer proportional to the displacement. At some point, the molecule possess enough that makes the two atoms apart and never move back towards each other. This energy is called BOND DISSOCIATION ENERGY. 10 BITSPilani, Pilani Campus Real Molecules: Anharmonicity The vibrational energy levels becomes less widely spaced at high excitations. (MORSE POTENTIAL) The convergence of levels at high vibrational levels is given by: En = (n + ½)hν-(n + ½)2 hνxe +................... where, xe is the anharmonicity constant As a result, additional weak absorption lines corresponding to Δn =2,3,... (overtones) appear in the IR spectra. 11 BITSPilani, Pilani Campus Vibrational Spectra: Polyatomic molecules How many ways (modes) in which a polyatomic molecules can vibrate ? This could be answered by accounting, how each atom of a molecule may change its location. Each atom move along any of the three perpendicular axes. For a molecule with N atoms, the number of coordinates required to specify the position of all the atoms is 3N. These 3N displacements can be thought of in terms of various degrees of freedom. Translational : 3 (movement of the centre of mass of the molecule) The remaining 3N-3 are internal modes that leave its centre of mass unchanged. 12 BITSPilani, Pilani Campus  Degrees of freedom Two angles (latitude, longitude) for Linear and three angles (latitude, longitude, azimuthal) for non-linear molecule are required to specify their orientation. Rotational : 2 for linear and 3 for nonlinear molecule. Vibrational : 3N – 5 for linear and 3N – 6 for nonlinear molecule. 13 BITSPilani, Pilani Campus  Summary VIBRATIONAL SPECTROSCOPY (IR Spectroscopy) IR Region: 4000-400 cm-1 Gross selection rule: Electric dipole moment of the molecule must change during each vibrational mode (stretching or bending or twisting). 1 k For each vibrational mode; ν = 2π μ Specific selection rule: Δn = ±1: Most molecules are vibrating in their ground state level. But since for real molecules, the motion is anharmonic: Sometimes Δn = 2, 3 are also observed. Vibrational Modes of freedom: 3N – 5 for linear 3N – 6 for nonlinear molecule 14 BITS Pilani, Pilani Campus HCl: Vibrational spectroscopy HCl: No of normal mode: 3N-5 = 3x2-5 = 1 There is only one vibrational motion (one band in spectrum): stretching back and forth about centre of mass. Fundamental frequency (HCl): 8.65x1013 Hz (This corresponds to light in the infra red region of wavelength 2886 cm-1). It only absorbs the light that has same frequency from EMR. Transmission Absorption 15 BITSPilani, Pilani Campus  BITS Pilani Pilani Campus CHEM F111 : General Chemistry Lecture 15 1 BITS Pilani, Pilani Campus  Summary (Lecture 14) VIBRATIONAL SPECTROSCOPY (IR Spectroscopy) IR Region: 4000-400 cm-1 Gross selection rule: Electric dipole moment of the molecule must change during each vibrational mode (stretching or bending or twisting). 1 k For each vibrational mode; ν = 2π μ Specific selection rule: Δn = ±1: Most molecules are vibrating in their ground state level. But since for real molecules, the motion is anharmonic: Sometimes Δn = 2, 3 are also observed. Vibrational Modes of freedom: 3N – 5 for linear 3N – 6 for nonlinear molecule 2 BITS Pilani, Pilani Campus CO2: Vibrational Spectroscopy CO2: No of normal modes: 3N-5 = 3x3-5 = 4 Each normal mode behaves like independent harmonic oscillators and the energies of each oscillator is given by the same energy expression, but the effective mass changes for each mode. Among these motions, only those mode, which result in the changing dipole moment are infrared active modes. Not Observed in spectrum Predicted Parallel bands value(1537 cm-1) (2349 cm-1) perpendicular bands (667 cm-1) 3 BITSPilani, Pilani Campus  IR Spectrum of CO2 overtones 667 cm-1 (2349 cm-1) (In general, Bending modes are less stiffer than stretching modes): bending vibrations occur at low wavenumbers than stretching vibrations. 4 BITSPilani, Pilani Campus HCN: Vibrational Spectroscopy HCN: No of normal modes: 3N-5 = 3x3-5 = 4 All 4 modes are IR active (a) Symmetric stretching [3386 cm-1] (b) Degenerate bending modes (946 cm-1) (c) Asymmetric stretching [2230cm-1] 5 BITSPilani, Pilani Campus H2O: Vibrational Spectroscopy H2O: No of normal modes: 3N-6 = 3x3-6 = 3 6 BITSPilani, Pilani Campus Methane: Normal modes of vibrations CH4: No of normal modes: 3N-6 = 3x5-6 = 9 SYMMETRICAL MOLECULE: Some of the modes are degenerate; Some of the modes are IR inactive; Difficult to explain IR Inactive (Stretching without C movement) IR Inactive (Bending without C movement) 3156 cm-1 1367 cm-1 (Stretching with C movement) (Bending with C movement) 7 BITSPilani, Pilani Campus IR SPECTRUM OF METHANE GAS TWO STRONG BANDS 3156 cm-1 & 1367 cm-1 are observed. 3156 cm-1 1367 cm-1 8 BITSPilani, Pilani Campus  Vibrational spectroscopy Infrared spectroscopy: powerful tool in identifying organic molecules. (All bonds in an organic molecule interact with infrared radiation) Some modes essentially motions of individual functional groups. Some modes are collective motions of the molecule as a whole : below 1500 cm-1 – fingerprint region of spectrum. Fingerprint region is characteristic of a molecule. C12H26 C10H22 Similar But Not Identical 9 BITSPilani, Pilani Campus IR Spectrum: Infrared spectrophotometer Absorption mode. Transmission mode. A 100 per cent transmittance implies no absorption of IR radiation. When a compound absorbs IR radiation, the intensity of transmitted radiation decreases. This results in a decrease of percent transmittance and hence a dip in the spectrum. The dip is often called an absorption peak or absorption band. IR bands can be classified as strong (s), medium (m), or weak (w), depending on their relative intensities in the infrared spectrum 10 BITSPilani, Pilani Campus  Measures of Intensity Transmittance T of a given sample, at a given frequency, T = I/I0, where I and I0 are the transmitted and incident intensities respectively.  Absorbance A = log I0/I =  log T Beer-Lambert law: A =  c l where l is the sample length (path length), [c] is the molar concentration of the absorbing species, and  is called the molar absorption coefficient. Greater the dipole, the more intense the absorption. (i.e., the greater the molar extinction coefficient () in Beer’s law. IR of gases yields line spectra. IR of liquids or solids, yields bands, the lines broaden into a continuum due to molecular collisions and other interactions. 11 BITSPilani, Pilani Campus Absorption bands in IR Spectrum 1. Position of bands (wavenumber) Strength of bond (k) & Reduced mass (m) Stretching bands (wavenumbers)> Bending bands 2. Intensity of bands Change in dipole moment with distance Concentration of sample 12 BITSPilani, Pilani Campus Effect of k & m on Frequency or wavenumber larger k, higher frequency 1 k n = 2 pc m increasing k C=C = > C=C > C-C 2150 1650 1200 larger atom masses, lower frequency increasing k increasing m C-H > C-C > C-O > C-Cl > C-Br 3000 1200 1100 750 650 C-H stretching frequency > C-D stretching frequency 13 BITSPilani, Pilani Campus  BITS Pilani Pilani Campus CHEM F111 : General Chemistry Lecture 16 1 BITS Pilani, Pilani Campus Effect of k & m on Frequency or Wavenumber larger k, higher frequency 1 k n = 2 pc m increasing k C=C = > C=C > C-C 2150 1650 1200 larger atom masses, lower frequency increasing k increasing m C-H > C-C > C-O > C-Cl > C-Br 3000 1200 1100 750 650 C-H stretching frequency > C-D stretching frequency 2 BITSPilani, Pilani Campus Typical Infrared Absorption Regions WAVELENGTH (mm) 2.5 4 5 5.5 6.1 6.5 15.4 O-H C-H C N C=O C=N C-Cl Very C-O N-H C C few C=C C-N bands C-C N=O N=O * 4000 2500 2000 1800 1650 1550 650 FREQUENCY (cm-1) 3 BITSPilani, Pilani Campus C-H Stretching Region Absorption frequency: Increases with increase in % of s character: sp3