Download Chemistry Homework: Kinetics and Thermodynamics of Reactions - Prof. Stefan Franzen and more Assignments Physical Chemistry in PDF only on Docsity! 1 Homework #9 Due: December 2 Name _________________________ Chemistry 331 1. The kinetics of double-stranded formation for a dodecamer containing two G.T base pairs was measured by temperature-jump kinetics. The reaction is: 2 CGTGAATTCGCG DUPLEX The following data were obtained: T oC k1 (105 M-1 s-1) k-1 (s-1) 31.8 0.8 1.00 36.8 2.3 3.20 41.8 3.5 15.4 46.7 6.0 87.0 A. Determine Ea, ∆H‡ and ∆S‡ for the forward and reverse processes; assume that the values of Ea, ∆H‡ and ∆S‡ are independent of temperature. B. Determine the standard enthalpy, ∆Ho and entropy, ∆So changes for the reaction. You may assume that these quantities are independent of temperature. Determine the equilibrium constant for the reaction at 37 oC. 2. What is the maximum age of a sample that can be measured by 14C dating if the error of measurement is 0.5%? 3. Write an expression for the appearance of D by each of the following mechanisms: 1. k 1 k 2 A ⇔ B , B + C → D k –1 B is at steady state 2. k 1 k 2 A + B ⇔ AB , AB + C → D k –1 where AB is formed in a rapid prequilibrium step. 2 4. Gaseous ozone undergoes decomposition according to the stoichiometric equation: 2 O3 (g) 3 O2 (g) Two alternative mechanisms have been proposed for this reaction. I. 2 O3 (g) 3 O2 (g) (bimolecular, k1) II. O3 (g) O2 (g) + O (g) (preequilibrium, k1 and k-1) O3 (g) + O (g) 2 O2 (g) (rapid k2) A. Derive rate laws for the formation of O2 by each of these mechanisms. B. Thermodynamic measurements give the standard enthalpies of formation for O3 as ∆fHo = 142.3 kJ/mol and for O as ∆fHo = 249.4 kJ/mol. The observed activation enthalpy for the overall reaction is ∆H‡ = 125.5 kJ/mol. Sketch a curve of the enthalpy vs. O3 concentration for each of the two proposed mechanisms. Label the curves with the appropriate values of ∆H. C. Which mechanism seems most likely given the available data? 5. Consider the following reactions involved in the formation and disappearance of ozone in the upper atmosphere. III. O2 O + O (hν greater than 41,322 cm-1 or λ below 242 nm) IV. O + O2 + M O3 + M V. O3 O2 + O (λ = 190 - 300 nm) The first and third reactions are photochemical processes that are driven by sunlight. The second reaction is unimolecular. The species M can be N2, O2 etc. Certain molecules (e.g. NO, NO2 etc.) emitted by aircraft in the upper atmosphere can reduce the ozone concentration. VI. NO + O3 NO2 + O2 (k1) VII. O + NO2 NO + O2 (k2) Note that NO is not used up in these reactions, but is catalytic. NO can last for several months in the ozone layer before it diffuses out. A. Calculate the number density of oxygen molecules at 20 km altitude. Use T = 217 K for this calculation and assume that the partial pressure of O2 is 0.2 atm at sea level. B. From the Planck distribution law we calculate that solar insolation below 240 nm is 0.5% of the total, which is approximately 6.5 W/m2 impinging on the upper atmosphere. Assuming that the average energy of UV photons is 240 nm, that the quantum yield for photodissociation of O2 is 0.2 and given the extinction coefficient of diatomic oxygen 2 x 103 M-1 cm-1 calculate the rate constant for photodissociation of diatomic oxygen.
