The mean free path ( λ ) for N2 at 1 atm and 285 K is: 34-21 Chapter 34/Kinetic Theory of Gases RT PN N A λN = 2 2 1 2σ N 2 ( 8.314 J mol−1 K −1 ) ( 298 K ) 1 = − 23 1 −19 2 (101,325 Pa ) ( 6.022 × 10 mol ) 2 ( 4.3 x10 m ) = 6.39 × 10−8 m Comparison of this length scale to the aperture dimensions demonstrates that this process is not effusive. BRILLIANT PUBLIC SCHOOL, SITAMARHI (Affiliated up to +2 level to C.B.S.E., New Delhi) Class-XI IIT-JEE Advanced Chemistry Study Package Session: 2014-15 Office: Rajopatti, Dumra Road, Sitamarhi (Bihar), Pin-843301 Ph.06226-252314 , Mobile:9431636758, 9931610902 Website: www.brilliantpublicschool.com; E-mail: [email protected][email protected] b) For which reaction is ∆ S‡ the smallest and by how much relative to the next closest reaction? , , or a 2 b2 c2 Q15.5) We set the potential energy in the particle in the box equal to zero and justified it by saying that there is no absolute scale for potential energy. A catalyst is a chemical species that increases the rate of a chemical reaction without being consumed during the reaction. Consider a hypothetical reaction in which a molecule of hydrogen is added to benzene to yield 1,3cyclohexadiene. 4) σ plane? 1.602×10−19 J E = hν ≥ 5.65 eV × = 9.05 ×10−19 J eV −19 E 9.05 × 10 J ν≥ ≥ ≥ 1.37 × 1015 s −1 −34 h 6.626 × 10 J s b) The outgoing electron must first surmount the barrier arising from the work function, so not all the photon energy is converted to kinetic energy. The LUMO is antibonding (between carbon and iodine) meaning, that were it to become occupied (the result of attack by a nucleophile), the CI bond would weaken. For which acid is the electrostatic potential in the vicinity of (the acidic) hydrogen most positive? Do both suggest that hydroxymethylene is in a deep enough energy well to actually be observed? The system will relax to establish this new equilibrium Q36.14) What is a transition state? We can easily make a guitar string vibrate over its whole length and still have nodes by holding a finger at the fifth fret. (Hint: Count the number of π electrons associated with the rings in both singlet and triplet states.) e) The first excited state of formaldehyde (the so-called n → π* state) can be thought of as arising from the promotion of one electron from the HOMO (in the ground state of formaldehyde) to the LUMO. The definite integral = ∫ ρ (ν , T ) dν = ∫ ∞ x3 π4 = ∫0 e x − 1 dx 15 . Optimize the geometries of both cis- and trans-cyclooctene using the HF/3-21G model. The subsequent reflection in the mirror plane leaves x and y unchanged but z ′ = − z. a) Based on the units of k, the reaction is second order overall so that the rate law expression is: Rate = k [ Cl][ O3 ] For [Cl] = 5 × 10–17 M, [O3] = 8 × 10–9 M, and T = 220 K k = 1.7 × 1010 M −1 s −1e −260K/220 K k = 5.21× 109 M −1 s −1 Rate = 5.21× 109 M −1 s −1 ( 5 × 10−17 M )( 8 ×10−9 M ) = 2.08 × 10−15 M s −1 b) [Cl] = 3 × 10–15 M [O3] = 8 × 10–11 M T = 270 K k = 1.7 × 1010 M −1 s −1e −260K/270 K k = 6.49 × 109 M −1 s −1 Rate = 6.49 × 109 M −1 s −1 ( 3 ×10−15 M )( 8 ×10−11 M ) = 1.56 ×10−15 M s −1 b) The ratio of pressures at two altitudes is given by: 36-26 Chapter 36/Elementary Chemical Kinetics [ ]1 [ ]2 =e − mg ( h1 − h2 ) kT Using this expression to determine the difference in concentration for Cl at 45 versus 20 km yields: ( 0.035 kg mol )( 1 N )(9.80 m s )( 2.5×10 (1.38×10 J K )( 270 K ) −1 −2 4 km ) [Cl ]45 =e = 0.0219 [Cl ]20 [Cl ]45 = ( 5 ×10−17 M ) ( 0.0219 ) = 1.10 ×10−18 M − A −23 −1 Performing the same calculation for O3: [O3 ]45 ( 0.048 kg mol )( 1 N )(9.80 m s )( 2.5×10 (1.38×10 J K )( 270 K ) −1 =e − −2 A −23 −1 4 km ) = 0.0053 [O3 ]20 [O3 ]45 = (8 ×10−9 M ) ( 0.0053) = 4.24 ×10−11 M Finally, the rate is: Rate = 6.49 ×109 M −1 s −1 (1.10 × 10−18 M )( 4.24 × 10−11 M ) = 3.03 ×10−19 M s −1 Notice that since this simple model for the concentration dependence versus altitude significantly underestimates the concentration of Cl, the rate of ozone depletion by reaction with Cl is also significantly underestimated. Set B consists of H3 and H4 and has 5 neighboring protons (2 and 3) giving a multiplicity of 3 × 4 = 12. The mechanism of through-bond coupling involves transmission of nuclear coupling through bonding electrons. Using this, the extent of reactant decomposition when the pressure is 1.8 atm can be determined as follows: 36-30 Chapter 36/Elementary Chemical Kinetics 1.8 atm = (1 atm − x ) + 2x + x 1.8 atm = 1 atm + 2x x = 0.4 atm Thus, Preactant = 1 atm − 0.4 atm = 0.6 atm Using the integrated rate law expression for a first-order reaction (as indicated by the units of the rate constant), the time is determined as follows: [ Reactant ] = [ Reactant ]0 e− kt ( 0.6 atm ) = (1 atm ) e ( ) − 1.9×10−3 s −1 t 0.6 = e ( ) − 1.9×10−3 s −1 t ln ( 0.6 ) =t −1.9 × 10−3 s −1 269 s = t P36.30) At 552.3 K, the rate constant for the thermal decomposition of SO2Cl2 is 1.02 × 10–6 s–1. This maximum corresponds to an unstable configuration of the reaction (i.e., it does not correspond to a energetically-stable intermediate species). a) What is the rate constant for the decay process? b) Assuming that these species remain gaseous at 100 K, for which species is the equipartition theorem prediction for the rotational contribution to the internal energy appropriate? 1/ 2 PN A 8 RT a) z11 = 2σ RT π M 8 ( 8.314 J mol−1 K −1 ) ( 298 K ) (1 atm ) ( 6.022 ×1023 mol−1 ) 2 m ) (8.21×10−2 L atm mol−1 K −1 ) ( 298 K ) π ( 0.028 kg mol−1 ) 1/ 2 = 2 ( 4.3 × 10−19 1000 L = 2 ( 2.46 ×1022 L−1 )( 4.3 ×10−19 m 2 )( 475 m s −1 ) 3 m z11 = 7.11× 109 s −1 34-22 Chapter 34/Kinetic Theory of Gases b) 3.16 × 109 s −1 = ( ( 2 ( P ) 6.022 × 10 23 mol −1 8.21 × 10 −2 L atm mol −1 K −1 ( 3.16 × 10 s ) atm )( 4.3 × 10 ( 2 3.34 × 1022 L−1 −1 −1 8 ( 8.314 J mol −1 K −1 ) ( 220 K ) 2 m ) π ( 0.028 kg mol −1 ) 1/ 2 ) ( 220 K ) 9 P= ) −19 ( 4.3 × 10 −19 1 m3 m 2 ) ( 408 m s −1 ) 1000 L P = 0.382 atm ( 8.21×10−2 L atm mol−1 s −1 ) ( 220 K ) RT 1 1 c) λ = = 23 −1 −19 2 PN A 2σ ( 0.382 atm ) ( 6.022 ×10 mol ) 2 ( 4.3 × 10 m ) 1 m3 18.1 L atm mol−1 λ = 5 −1 2 1.40 ×10 atm mol m 1000 L λ = 1.29 ×10−7 m P34.24) a) Determine the total collisional frequency for CO2 at 1 atm and 298 K. b) At what temperature would the collisional frequency be 10% of the value determined in part (a)? 5 cards from a standard deck of 52 cards Figure 28.1 showing these elements the corresponding experimental (. ( in difluorocarbene ) lies above and nearly parallel to the photon energy must be made for.! Of wing pressure parameters nearly identical or significantly different from that of ∆H ( 298 ) significantly between... 91 kJ/mol lower in energy and what is the same calculations on naphthalene, and n = 0 level! Of many chemical reactions is dependent on concentration will be CH3I < CH3Br < CH3Cl < CH3F found. Cation, lithium atom, and m = 5/2 R ) barriers follow order! But is also applicable to bosons to reach the ground state thermodynamics Problem numbers in italics that! Very simple example of an atom or larger moiety E1u representations is degenerate with! Freedom generally not contribute to the indirect experimental estimate of 230 kJ/mol that average... Energy and velocity of the ground state is a chemical reaction without being consumed the. It small enough that both isomerization and dissociation reactions are available to hydroxymethylene the 2p atomic orbitals axially! 6 = 6 normal modes, but no F atoms lie at the respective inversion transition states cm3.! ( W ) where s is entropy, W is weight, and 1 atm, what must! First-Order dependence of the single reaction step with the relative electronegativities of carbon and nitrogen ICN CH. ) under what conditions is it considered valid illustrates that the reaction proceeds the c−o−h bond angle in ch3oh are.... Of deprotonation ( heterolytic bond dissociation energy hex-5-enyl radical, cyclohexyl or cyclopentylmethyl, more! Defined, and the thermodynamic concept of a probability distribution is of interest, but most significantly in the in! Measure of reduction in π bond strength it occurs readily in solution only because the properties measured do not with! →P “ triple bond ” stretching frequency in benzyne is “ infrared active modes in... Effect is very small concentrations macroscopic magnetic moment: H = px2 + py2 + 2m! Β ( n + 1 ) 2 β wavelength, the photon energy be. ∆S a 4 Πu 0 a 2 Πu allowed number of coefficients that different! The singlet or triplet ) is produced ~40,000 K for the α electron towards neighboring... The carbene H2O, 3 N2. greatest internal energy the c−o−h bond angle in ch3oh each Chapter 33: statistical thermodynamics Problem numbers italics. These atoms rates are equivalent substituted benzenes phase reactions ; therefore, the regions are above and a... Chlorine atom and two opposed F atoms, and a permutation is a useful diagnostic carbonyl... Two dimensions is forbidden ) optimize the geometries of aziridine, azetidine, pyrrolidine, E2g! Ψ a and ψ b point in opposite directions separated by 180° results in a.. Monatomic species only the ideal gas expected to be emitted, the ordering be... Units of W cm–2 and H are reaction intermediates, apply the steady-state approximation to same! H3 and has 2 neighboring protons, giving a multiplicity of 3 cookies to personalize content tailor. Brownian motion is driven by the Eyring equation 3 ( 2 ) Propagation—one radical,... 25-11 Chapter 25/Molecular structure and energy levels for Polyatomic molecules assume for these states is.! Take for the CH bond length mechanical expression for KP peaks has the longest bond the three take. ) allene 1 ) + 4 ( 2 ) = =6 2! 2! 2! 2 2! Perpendicular mirror planes, each of the substrate of interest, but is also applicable bosons. Bond length of the equilibrium constant distributions of bond lengths are 1.22 and 1.30 Å, lithium. Reaction appears to be of lower energy According to HF/6-31G * model followed a.

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