Concepts from Chemical Reaction Kinetics - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 261

methane has an atmospheric residence time of 10 years, obtain the mean
OH • concentration in the atmosphere.
5.30 2 The acid-catalyzed decomposition of urea has a rate constant of 4.3 ×
10 − 4 h − 1 at 334 K and 1.6 × 10 − 3 h − 1 at 344 K. Estimate the activation
energy and pre-exponential factor for the reaction. What is the rate at a
room temperature of 300 K?
5.31 2 A first-order process has the following rate constants at different ionic
strengths of a 1:1 electrolyte:

I (mol/L) 0.007 0.01 0.015 0.020

K (h − 1 )

2.06 3 5.1 7.02

If one of the ions involved in the reaction has a positive charge, what is the
charge on the other ion?
5.32 1 The rate constant for the decay of natural 14 C radio isotope is 1.2 ×
10 − 4 y − 1 . What is the half-life of 14 C?
5.33 3 The hydrolysis of ArOCOCH 3 to ArOH is base catalyzed. At values of
pH > 2 acid catalysis is unimportant. The uncatalyzed reaction rate k 0 is
4 10 − 5 s − 1 at20 ◦ C.AtpH 8,whatistherateconstantofthereaction?

How much time will it take to reduce the concentration of the compound
to 95% of the original value in a lake of pH 8 at 20 ◦ C?
5.34 3 Pentachloroethane (PCA) is spilled into the Mississippi river at a mean
pH of 7.2 and a temperature of 20 ◦ C. Haag and Mill (1988) report the
following parameters for the uncatalyzed and base-catalyzed reactions of
PCA:

× =

k 0 ( h − 1 ) = 4.9 × 10 − 8 , E a = 95 kJ/mol,
k b ( h − 1 ) = 1320, E a = 81 kJ/mol.

How long will it take to reduce the concentration of PCA in the river to
95% of its original concentration?
5.35 3 Loftabad et al. (1996) proposed that polyaromatic hydrocarbons ( A) in

contact with dry clay surfaces underwent oligomerization. This was inhib-
ited by moisture present in the soil. The reaction scheme proposed was as
follows:

≡

S + A S − A,

S + W S − W,

S − A −→ S + products.

W represents water and S represents a surface site for compoundA. Based
on the above, derive the following rate expression for the reaction of A:
− r A = k 0 C A /( 1 + K θ ) , where K is the equilibrium constant for water
adsorption and θ is the water content (g/kg of soil). k 0 is the apparent rate
constant in dry soil ( θ = 0 ) . State the assumptions made in deriving the
rate expression.