Homework Assignment 2 ATM 507 Fall 2014

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1 Due Tuesday, September 30th Homework Assignment ATM 507 Fall Calculate H for the following reactions. Express your answer in kj/mole and kcal/mole: i) NO NO + O( 3 P) ii) NO + O 3 NO + O iii) H + OH H O + H iv) ClO + BrO Br + OClO. The H values for the individual species are given on the attached table.. The collision frequency is the starting point for calculating the A-factor of a temperature dependent rate constant. The frequency (per cubic centimeter) for a pure gas is given by π d = Z < v > where d is the molecular diameter, n is the number density, and v is the average speed given by n < v >= 8 k BT π m (NOTE: m is the mass of a single molecule.) a) Nitrogen, N, has a molecular weight of 8 g/mole and a molecular diameter of 1.1x10-8 cm. What is the collision frequency in pure nitrogen at i) STP? ii) 1000K, 1 atm? iii) 100K, 0.5atm? (NOTE: for units change (molecule) to collisions (no conversion required, just use collisions in place of (molecule) ); then express your answer in collisions cm -3 s -1.) b) The mean free path is defined as λ = 1 π d n Calculate the mean free path of nitrogen for each of the above temperature and pressure conditions. Express your answer in cm. NOTE: k B = Boltzmann's constant = 1.38x10-16 erg K -1 (or g cm s - K -1 )

2 A couple of hints for problems on this page 1. The best units to use for the Gas Constant (or R) in Arrhenius expressions are the ones with Joules or calories, i.e., R = J mole -1 K -1 = calories mole -1 K -1.. Most reactions (esp. bimolecular reactions) are reasonably well described by the Arrhenius expression. Unless you know or are told otherwise, assume it applies. 3. The reaction of hydroxyl radical with methyl chloride, OH + CH 3 Cl CH Cl + H O, has the following rate constants: at 98K, k = 4.4x10-14 cm 3 molecule -1 s -1 ; and at 400K, k = 1.18x10-13 cm 3 molecule -1 s -1. What is the A-factor and activation energy (in kj/mole) for this reaction? (NOTE: the reaction is properly described by an Arrhenius expression.) 4. The rate constant for a reaction at 30 C is exactly twice the value at 0 C. Calculate the activation energy in kj/mole. 5. Two second-order reactions have identical pre-exponential factors ("A" factors), but their activation energies differ by 0 kjoule mole -1. Calculate the ratio of their rate constants at (a) 0 C and (b) 1000 C. Assume that the Arrhenius equation applies; that is, the activation energies are temperature independent. 6. Peroxyacetyl nitrate (commonly called "PAN") decomposes in the following way PAN PA + NO (using chemical formulae this is:) {CH 3 C(O)OONO CH 3 C(O)OO + NO } Write a rate equation for the decomposition process. (Use PAN instead of the chemical formula.) Integrate the rate equation to obtain an expression for [PAN] as a function of the initial concentration of PAN ([PAN] 0 ), the rate constant, and the time t. If the rate constant at 5 C is 3.6x10-4 s -1, what is the chemical lifetime of PAN? How long does it take before an initial concentration of PAN is reduced to one half its starting value? (This is referred to as its "half life".) 7. (Also S&P problem 4.10) What is the longest wavelength of light, absorption of which by NO leads to dissociation at least 50% of the time? At 0 km, what are the lifetimes of NO by photolysis at solar zenith angles of 0º and 85º? (Hint: use tables and figures in section 4.10.)

3 Enthalpies of Formation of Some Gaseous Molecules, Atoms, and Free Radicals at 98 K Note: 1 calorie = Joule Species H ο f (98 K) kcal mole -1 H 5.1 O (or O( 3 P)) 59.6 O( 1 D) O 0.0 O OH 9.3 HO 3.5 H O H 0.0 H O -3.6 NO 1.6 NO 7.9 NO HNO HO NO -13 CH C H 6-0 CO -6.4 CO HCO 9.0 HCHO -6.0 CH CH 3 O 4.1 CH 3 O 5.5 CH 3 OH Cl 9.0 Cl (g) 0.0 ClO 4. Br 6.7 Br (g) 7.4 BrO 30.4 OClO 5 ClONO 6.3 HCl -.1 H S -4.9 HS 34.9 SO H SO These enthalpies of formation are largely taken from Finlayson-Pitts and Pitts (1986), and originally from Baulch, et al., J. Phys. Chem. Ref. Data, 13, 159 (1984).

4 Homework part worth 4 points. The attached tables list F λ (actinic flux) values for solar zenith angles between 0 and 86 ; and the absorption cross sections and quantum yields for the following reactions at a range of temperatures: 1. H CO + hv H + HCO;. NO + hv NO + O. Your assignment is to calculate rate constants for these photolysis reactions. Perform these calculations in 5 or 10 nm bins. That is, first calculate the contribution to the total rate constant for each bin (think about the best way to average the cross sections and quantum yields to match the bins for the actinic flux) and then sum the results to obtain the overall photolysis rate constant. The cross section and quantum yield data for NO is given in Table 4.5 in the textbook. Note that you are calculating the rate constant for only one of the two possible product channels for the H CO photolysis reaction. Show your work and calculate 4 photolysis rate constants: (Express the result in min -1.) I. k 1 (H CO) at 0 SZA and 93 K; II. k 1 (H CO) at 40 SZA and 93 K; III. k (NO ) at 0 SZA and 98 K; IV. k (NO ) at 60 SZA and 98 K.

ATM 507 Lecture 4. Text reading Chapters 3 and 4 Today s topics Chemistry, Radiation and Photochemistry review. Problem Set 1: due Sept.

ATM 507 Lecture 4. Text reading Chapters 3 and 4 Today s topics Chemistry, Radiation and Photochemistry review. Problem Set 1: due Sept. ATM 507 Lecture 4 Text reading Chapters 3 and 4 Today s topics Chemistry, Radiation and Photochemistry review Problem Set 1: due Sept. 11 Temperature Dependence of Rate Constants Reaction rates change