EEC 503 HW 4 SPRING 2009

Due Thursday February 12

1.  Using simple collision theory estimate the collision number for 1 mol (6.022 x 1023 molecules) of hydrogen iodide (HI) present in a volume of 1 m3 at temperature of 300 K. Take dAA=0.35 nm. If the activation energy for the decomposition of HI is 184 kJ/mol, what rate constant does collision theory predict at 300 0C? To what pre-exponential factor and entropy of activation does this result correspond? [MHI=127.91(g/mol)].

2.  A second order reaction in solution has the rate constants of 5.7 x10-5 (L/mol s) at 25 0C and 1.64 x 10-4 at 40.0 0C. Calculate the activation energy and the pre-exponential factor assuming the Arrhenius equation to apply. Then at 250C calculate the Gibbs energy, entropy and enthalpy of activation (ΔG*, ΔS*, ΔH*).

3a) The pseudo-first order rate constant for hydration of CO2 at circum-neutral pH and 25˚C is reported as = 3.7 x 10-2s-1. Since the reaction is bimolecular,

convert that to a proper second order hydration rate constant kh in (M-1s-1). At 5˚C

kh = 6.60 x 10-5 M-1s-1.

From these values estimate and the pre-exponential factor. Note that concentration of water can be taken as constant [H2O] = 55 M where we will use M to denote (mol/L).

b) At alkaline conditions CO2 + OH- becomes competitive with the

hydration reaction. The rate constant is reported as:

kf = 7.1 x 103 M-1s-1 at 25˚C and

kf = 7.0 x 102 M-1s-1 at 5˚C

Find and the pre-exponential factor.

c) Consider now the following reaction scheme at 25˚C

CO2 + OH- HCO kf = 7.1 x 103 M-1s-1

HCO CO2 + OH- kr = 1.8 x 10-4s-1

CO2 + H2O H+ + HCO = 0.037s-1

Compute the pH at which the two hydration mechanisms for CO2 (i.e. path 1 and 3) are

of equal importance. Will this pH be a function of temperature? (i.e. repeat for 5˚C).

Note: Kw = [H+] [OH-] = 10-14

4. The rate of the acid-catalyzed reaction between vanadium, Vz, and iodide ions follows the rate equation

r = k [Vz][I -][H+]2

and k is found to be independent of ionic strength. Deduce from this information the charge z on the predominant vanadium species involved in this reaction. Hint: Use transition state and debye huckel theory.

5. The diffusion coefficient of an ion is related to its molar ionic conductivity by the Nernst-Einstein equation

kB - Boltzman constant = 1,3806 x 10-23 J/K

T - absolute temperature in K

- absolute value of the charge number

e - elementary charge (of an electron) = 1.602 x 10-9 C

F - Faraday constant = 96,485 (J/V mol)

The molar ionic conductivities of the H+ and OH- ions at 25˚C are

Use these values together with the value of dAB = 850 pm to estimate the rate constant at 25˚C for the reaction

H+ + OH- H2O

6. Given an aqueous phase reaction rate Ra (M sec-1) expressed per unit volume of the liquid phase show that with a liquid water content, L, the comparable gas-phase rate in air in ppb hr-1 is:

Rg (ppb hr-1) = 2.95 x 1011 LTRa/p

and expressed in % hr-1 is

R (% hr-1 ) = 2.95 x 1013 LTRa/pX

Where p is pressure in atm and X is the total (gas + aqueous) equivalent gas-phase molar ratio of the reactant species. [X (ppb) = [(moles of A in gas + liquid)/(moles of gas)] x 109]

a) We would like to know the rate of sulfate formation through an aqueous S (IV) - O3

reaction in a haze aerosol of L = 10-10. Assume T = 298 K, pH = 5.6 and

pO3 = 5 x 10-8 atm (50 ppb). If the total sulfur concentration concentrations (gas + aqueous) is 5 ppb, calculate the rate of sulfate formation in ppb hr-1 and R in % hr-1.

b) If a rate of SO2 to sulfate conversion is observed to be 10% hr-1, then if

= 5 x 10-9 atm (5 ppb), T = 298 K, pH = 5.6 and pO3 = 5 x 10-8 atm and if

L = 10-6, are reactions with O3, H2O2, and gaseous OH* capable of generating this rate?

c) What minimum aqueous H2O2 concentration is needed to account for a 1 % hr-1

conversion of SO2 ( = 5 x 10-9 atm (5 ppb)),to sulfate when pH = 3, L=10-11,T = 298 K?