D S C Differential scanning calorimetry
EXAFS
H E E D High-energy electron diffraction H P L C High-pressure liquid chromatography
ICPES Inductively coupled plasma-atomic emission spectroscopy I C R Ion cyclotron resonance
INS Ion neutralization spectroscopy I R Infrared
LASER Light amplification by stimulated emission of radiation L E E D Low-energy electron diffraction
L I F Laser-induced fluorescence
M A S E R Microwave amplification by stimulated emission of radiation M C D Magnetic circular dichroism
M O D O R
( M O D R ) Microwave optical double resonance MS Mass spectrometry
N A A Neutron activation analysis
N M D R Nuclear magnetic double resonance N M R Nuclear magnetic resonance N Q R Nuclear quadrupole resonance
O D M C D Optically detected magnetic circular dichroism O D M R Optically detected magnetic resonance
O O D R Optical-optical double resonance O R D Optical rotatory dispersion PA Proton affinity
PES Photoelectron spectroscopy
P M D R Phosphorescence microwave double resonance P M R Proton magnetic resonance (old usage) R I K E S Raman-induced Kerr-effect scattering SAXS Small-angle x-ray scattering
SIMS Secondary ion mass spectrometry SXAS Soft x-ray absorption spectroscopy SXES Soft x-ray emission spectroscopy SXS Soft x-ray spectroscopy
UPS Ultraviolet photoelectron spectroscopy V C D Vibrational circular dichroism
VPC Vapor phase chromatography VLPP Very low-pressure pyrolysis XPS X-ray photoelectron spectroscopy Z A A Zeeman-effect atomic spectroscopy
G E N E R A L R E F E R E N C E S
ADAMSON, A . W . , AND FLEISCHAUER, P. F . , Eds. (1975). " C o n c e p t s o f Inorganic Photochemistry."
Wiley, N e w Y o r k .
EXERCISES 843 BECKER, R. S. (1969). "Theory and Interpretation of Fluorescence and Phosphorescence." Wiley
(Interscience), N e w York.
CALVERT, J. G., AND PITTS, J. N . , JR. (1966). "Photochemistry." Wiley, N e w York.
COTTON, F. A . (1963). "Chemical Applications of G r o u p Theory." Wiley (Interscience), N e w York.
DAUDEL, R., LEFEBVRE, R., AND MOSER, C. (1959). "Quantum Chemistry, Methods and Applica
tions." Wiley (Interscience), N e w York.
EYRING, H . (1944). "Quantum Chemistry." Wiley, N e w York.
HERZBERG, G. (1967). "Molecular Spectra and Molecular Structure. III. Electronic Spectra and Electronic Structure of Polyatomic Molecules." Van Nostrand-Reinhold, Princeton, N e w Jersey.
PITZER, K. S. (1953). "Quantum Chemistry." Prentice-Hall, Englewood Cliffs, N e w Jersey.
POPLE, J. Α., SCHNEIDER, W . G., AND BERNSTEIN, H . J . (1959). "High Resolution Nuclear Magnetic Resonance." McGraw-Hill, N e w York.
POTTS, W. J., JR. (1963). "Chemical Infrared Spectroscopy." Wiley, N e w York.
STREITWEISER, Α., JR. (1964). "Molecular Orbital Theory for Organic Chemists." Wiley, N e w York.
SZYMANSKI, H . A . (1964). "Theory and Practice of Infrared Spectroscopy." Plenum, N e w York.
TOWNES, C. H., AND SCHAWLOW, A . L . (1955). "Microwave Spectroscopy." McGraw-Hill, N e w York.
19-1 Estimate, with explanation, the energy difference between the *Ό and 8P states o f atomic sulfur.
19-5 In a photochemical experiment a n intensity o f 5 χ 10 "9 Ε sec ~1 is incident o n a cell c o n taining 20 c m8 of 0.01 Μ solution o f C r ( N H8)5( N C S )2 +. It is estimated that 90% o f the incident light is absorbed and after 10 m i n of irradiation analysis s h o w s that 0.6% o f the complex has photoaquated to give Cr(NH8)4(H20)(NCS)2+. Calculate the quantum yield.
Ans. 0.44.
19-6 Benzene vapor absorbs at 2 5 4 n m t o give the first excited singlet state 5X, w h o s e radia
tive lifetime is 6.2 χ 1 0 "7 sec. Si disappears by intersystem crossing t o the first triplet excited state 7 \ with a rate constant o f &4 = 4.7 χ 1 0β s e c "1, and 5Ί is quenched by collisions with ground-state benzene with a rate constant of 1.00 χ 1 09 liter m o l e "1 sec" \ b o t h rate constants being for 25°C. Calculate (a) the fluorescence q u a n t u m yield at l o w pressures and (b) the yield at a 0.1 atm pressure (25°C).
Ans. (a) φ<° = 0.26; (b) φ, = 0.16.
19-7 Sketch, with explanation, a n approximate visible-uv absorption spectrum for phenyl acetaldehyde, CeHe— C H2— C H O .
Ans. A b s o r p t i o n s expected at 295, 255, 2 0 0 , 185, and 180 n m (rest o f answer t o be supplied by the student).
19-8 R u ( b i p y r i d i n e ) i+ (A) exhibits a strong room-temperature emission. T h e lifetime in water solution is 1.6 ^sec; the emission yield m a y be taken t o be 1.00. T h e emission is quenched by various species. In particular, if the solution is m a d e 0.01 M i n P t C l i " (B), the emission yield is reduced t o half of that in water alone. Calculate the bimolecular quenching rate constant, that is, k9 for the reaction * A + Β ->• A + *B.
Ans. k = 6.25 χ 1 07 M "1 s e c "1. 19-9 A c o m m o n l y used chemical actinometer is the ferrioxalate o n e , for which the p h o t o
chemical reaction is
F e ( C204) i " Fe(II) + oxalate + oxidized oxalate;
after the irradiation the Fe(II) is c o m p l e x e d with 1, 10-phenanthroline (neglect dilution at this point) and its concentration determined from the optical density at 510 n m , at which wavelength the extinction coefficient o f the c o m p l e x is 1.10 χ 10*. In a particular experiment 2 0 c m8 o f ferrioxalate solution w a s irradiated with light at 4 8 0 n m for 10 min and an optical density of 0.35 was subsequently found at 510 n m . T h e q u a n t u m yield at the irradiating wavelength is k n o w n t o be 0.93. Calculate the light intensity in einsteins absorbed per second. A 1 c m cell is used.
Ans. 1.14 χ 1 0 "9 Ε s e c "1. 19-10 T h e normal vibrational m o d e s for C2H2 are as s h o w n in the a c c o m p a n y i n g diagram.
Explain which are infrared-active and -inactive and which are Raman-active and -inactive.
Η C C Η
V, Ο > * - ^ 5 O - *
-V4
i
v2 — o *o o .
v5
i ^ ^ £
v3 o - _ o * - 0
Ans. Only v3 and v5 are infrared-active;
vx, v2, and v4 are Raman-active. (The student should explain these answers in reasonable detail.)
PROBLEMS 845 19-11 O n e o f the normal m o d e s for /ra/i.y-C2H2Cl2 is s h o w n . T o which I R in C2 h d o e s this
m o d e b e l o n g ? Explain.
Η
+Ans. Au. 19-12 Identify s o m e o f the characteristic b o n d or group frequencies in the infrared spectrum
for methyl ethyl ketone [Fig. 19-13(c)].
P R O B L E M S
19-1 Suppose that the equilibrium internuclear distance is essentially the same for the ground state and a certain excited state of a diatomic molecule (as for the 1 Ag««- zEg- transition of 02) . Explain what the qualitative appearance o f the absorption spectrum o f the dilute gas should be like. Pay particular attention to the relative intensities of transitions in
volving different vibrational states, that is, the general intensity contour of the absorp
tion band, as well as h o w it is centered with respect to the energy for the pure electronic transition.
19-2 The strong S c h u m m a n - R u n g e absorption band of 02 starts at about 200 n m and gradually increases in intensity to a continuum which begins at about 176 n m . Sketch the probable appearance of the ground- and excited-state potential energy curves (that is, produce a pair of plots similar to those o f Fig. 19-6 but consistent with the data for 02) . Explain what happens when absorption is in the region of the continuum—is the excited state produced stable against dissociation, and if not, what might the products b e ? [Note:
the energy to dissociate 02 into t w o ground-state atoms is about 40,000 c m- 1. ] 19-3 H2 excited to the 1IJU state may under s o m e conditions cross to the 827g+ state. Light
emission then occurs. Explain what h a p p e n s in terms o f Fig. 19-2 and estimate the range of wavelengths of the emitted light.
19-4 Sketch a guessed appearance of the absorption spectrum of (a) methyl ethyl ketone, (b) azobenzene, φ—N=N—φ, and
S
II
(c) CeH6- C HaC - C Hs. Explain the basis for your spectra.
19-5 T h e following data were obtained for the benzophenone-sensitized d e c o m p o s i t i o n o f C o ( N H3) J+. A s s u m e that absorption of light by the benzophenone leads to its first triplet excited state in quantum yield φ° and that each encounter with a complex ion which transfers energy produces photochemical decomposition of the complex and deexcitation of the benzophenone with 1 0 0 % efficiency. Derive the kinetics for this situation and plot the data s o as to obtain a straight line graph. If the lifetime o f the benzophenone triplet state is 1.0 χ 1 0- 8 sec, calculate kq, the bimolecular quenching rate constant; compare the result with an estimate of the encounter rate constant.
Complex (M) 0.01 0.005 0.002 0.001 φ for sensitized 0.46 0.25 0.10 0.064
decomposition
19-6 A n alternative actinometer to the ferrioxalate one is that which makes use of the reaction
The photoproduced N C S- is determined spectrophotometrically by forming a complex with Fe(III) of extinction coefficient 4.3 χ 1 0s liter m o l e- 1 c m- 1 at 4 5 0 n m . T h e quantum yield for the photochemical reaction is 0.29 at 520 n m . What is the absorbed light intensity in einsteins per second if irradiation o f 25 c m8 of a 0.02 Μ solution of the complex for 15 min produces a solution which when treated with the Fe(III) reagent has an optical density of 0.25 at 450 n m in a 1-cm cell? (Neglect any dilution due to the reagent.) A companion dark (nonirradiated) aliquot gives an optical density of 0.05 when treated with the Fe(III) reagent.
19-7 The quantum yield for the photoisomerization of trans-Α, 4/-dinitrostilbene is 0.27 at 366 n m , at which wavelength the extinction coefficient is 3.0 χ 104 liter m o l e- 1 c m- 1. What absorbed light intensity in einsteins per liter per second is required to cause a Ι Ο- 8 Μ solution to isomerize at the rate of 1 % m i n- 1? With continued irradiation the cis form builds up; this photoisomerizes back to the trans with a quantum yield of 0.34 at 366 n m . Assuming the extinction coefficient to be half that of the trans form, what stationary state ratio of trans I cis should result (what is the limiting value of this ratio o n sufficiently prolonged irradiation)?
19-8 Biacetyl exhibits a phosphorescence in room-temperature aqueous 0.1 i V H2S 04 solution, the quantum yield in this medium being 2.7 χ 1 0- 8 and the phosphorescence lifetime 6.2 χ 1 0- 5 sec. Addition of the complex ion C r ( N H8)6( N C S )2 + progressively quenches this phosphorescence; thus 5 χ 10~4 Μ complex reduces the phosphorescence yield tenfold and 1 χ Ι Ο- 8 Μ complex reduces it 18-fold. Set up the kinetic scheme for this situation.
Calculate kv, the rate constant for phosphorescent decay t o the ground state, and kq, the bimolecular quenching rate constant; compare the value o f the latter t o that estimated for diffusional encounters (at 25°C).The biacetyl emitting state is produced in 1 0 % yield.
19-9 In the experiments described in Problem 19-8 the quenching o f the biacetyl phosphores
cence was accompanied by a sensitized aquation of the c o m p l e x to yield C r ( N H8)4( H20 ) -( N C S )2 +. A s s u m i n g that each quenching act by a c o m p l e x i o n led to aquation, s h o w that the aquation quantum yield o b e y s an equation o f the form 1/^NH, = α + W C ) , where C is the c o m p l e x concentration. R e m e m b e r that in this situation the incident light is absorbed by the sensitizer biacetyl, and ψΝ Η 8 is the number of m o l e s o f aquated a m m o n i a divided by the number of einsteins of light absorbed by the sensitizer.
19-10 Absorption of light by an organic molecule A leads t o phosphorescence with a quantum yield φν of 0.30 in a particular solvent. S h o w that the relation ^ρ/ τρ = kv holds, where τρ is the experimentally observed lifetime of the phosphorescence and kv is the rate constant for phosphorescent emission. The value of φν is for a deaerated solution; a solution in equilibrium with air has 3.0 χ 1 0- 4 m o l e l i t e r- 1 dissolved oxygen. Encounters between dissolved oxygen and A occur with a rate constant of 5 χ 1 0β liter m o l e- 1 s e c- 1. Calculate φρ in this aerated solution; Λρ = 1.0 χ 1 05 s e c- 1.
19-11 Explain what wavelength of light should be effective in the photoproduction of atoms o n irradiation o f (a) S2, (b) H I , (c) the molecule o f Fig. 19-6 assuming that Dl is 55 kcal m o l e- 1, and (d) I2.
19-12 The normal m o d e s for the H20 molecule are as s h o w n in the accompanying diagram.
Explain which should be infrared-active and -inactive and Raman-active and -inactive.
C r ( N H3)2( N C S )4" ^ C r ( N H8)2( H20 ) ( N C S )3 + N C S-.
SPECIAL TOPICS PROBLEMS 847
Carry the set o f m o t i o n vectors through the symmetry operations o f the HaO point group and determine t o what irreducible representation each m o d e belongs. (The answer m a y be arrived at by considering what vectors are left unchanged or are put into their opposites and comparing with the traces of the various irreducible representations.)
19-13 The normal m o d e s for formaldehyde are as follows: (a) vx = 2766 c m- 1, C H2( s y m ) stretch; (b) v2 = 1 7 4 6 c m- 1, C = 0 stretch; (c) vs = 1 5 0 1 c m "1, C H2 deformation; (d) v4 = 2843 c m -1, C H2( a s y m ) stretch; (e) v6 = 1247 c m "1, C H2 rock, (f) ve = 1164 c m "1, C H2 wag. O n e corresponds to the B% irreducible representation, t w o to the Bx, and three t o the Ax. Explain which is which. In the actual infrared spectrum of formaldehyde, absorptions are observed at 3930 c m- 1, 2910 c m- 1, 2665 c m- 1, and 4013 c m- 1 (among others). Explain h o w these frequencies arise.
t
ι
v, = 2 7 6 6 c m -1 v2 = 1746 c m - ' v3= 1 5 0 1 c m -1 C H2 ( s y m ) stretch C = 0 stretch C H2 d e f o r m a t i o n
v4 = 2 8 4 3 v5 = 1247 v6= 1 1 6 4
C H2 ( a s y m ) stretch C H2 rock C H2 w a g
19-14 Assign, with explanation, the origin o f the various major absorptions in the infrared spectrum o f C H2C 12 [Fig. 19-13(b)].
19-15 Explain what difference y o u might expect to see in the intensities of the C = C stretching vibration in an infrared absorption spectrum as compared to a R a m a n spectrum of (a) H C = C H and (b) H C ^ C C l .
19-16 O n e of the fundamental vibration m o d e s of C O gives rise t o an infrared absorption at 2144 c m- 1. Calculate the vibration frequency (in hertz), the force constant, and the zero-point energy of C O in kilocalories per m o l e (for this vibrational mode).
19-17 T h e infrared absorption spectrum o f C O s h o w s a n intense band at 2144 c m "1, assigned t o the v- = 0 t o i> = 1 transition. Calculate (a) the force constant for C O , and (b) its zero-point energy in calories per m o l e .
SPECIAL TOPICS P R O B L E M S
19-1 Estimate by a calculation the oscillator strength of the absorption bands o f benzophenone in cyclohexane at (a) about 2 5 0 n m and (b) 350 n m (Fig. 19-10). A l s o calculate the emission rate constant Amn for these excited states.
19-2 A s s u m i n g that the ordinate scale of Fig. 19-13 is for 0.1 m m path length, estimate the oscillator strength of the absorption feature for acetone at 900 c m- 1.
19-3 Estimate the oscillator strength of the absorption band of Cr(urea)J+ centered at (a) about 16,250 c m -1 and (b) 14,400 c m -1. A l s o calculate the emission rate constant Amn for these excited states and the corresponding lifetimes for emission.
19-4 Referring t o Fig. 17-15, for a n octahedral c o m p l e x having just o n e d electron t h e first ligand field transition is from a state of symmetry T2g to a state of symmetry Eg (in Oh) . Explain whether or not this transition is allowed by (a) parity and (b) orbital symmetry, that is, by whether the appropriate direct product contains the totally symmetric irre-ducible representation.
19-5 T h e specific rotation [ a ]D of a c o m p o u n d in aqueous solution is 33° at 25°C. Calculate the concentration of this c o m p o u n d in grams per liter in a solution which has a rotation of 3.05° when measured in a polarimeter in which the tube of solution of 20 c m long.
19-6 The specific rotation of saccharose in water at 20°C is 66.42°. Calculate the observed rotation using a polarimeter tube of 20 c m length filled with a 23.5 % by weight solution of this sugar. The density of the solution is 1.108 g c m- 3.
19-7 A solution of 30 g of a substance of molecular weight 350 in 1 liter of water rotates the plane of polarized light by 10.5° (sodium D line, 25°C) with a 30 c m polarimeter tube.
Calculate the specific and the molar rotation of the substance.
19-8 Calculate nx — nr for the solution o f Special Topics Problem 19-5. T h e s o d i u m D line is at 589 n m .
19-9 R e a d data off Fig. 19-29 to m a k e a semiquantitative plot o f g versus wavenumber for Ru(phen)>+.
19-10 Estimate the m o m e n t of inertia o f H C N from the spectrum s h o w n in Fig. 19-30.