Concepts from Chemical Reaction Kinetics - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 254

earlier statement that the Monod no-growth kinetics and Michaelis-Menten kinetics
are identical.
To consider the fact that as organisms grow they also decay at a rate k dec (h − 1 ) ,
one rewrites the Monod equation as

ζ max [

[ ]

d t =

]

d X S

[ ]−

k dec [

]

X X . (5.211)

K s +[ S ]

At low values of [S], there is no net increase in organism density since its growth is
balanced by its decay. Thus d[X]/d t = 0, and

K s k dec
ζ max −

[ S ] min = (5.212)

k dec

represents the minimum concentration of substrate that can maintain a given micro-
bial population. However, the organism may find another compound with a different
[S] min that can sustain another level of population. This compound is called a
co-metabolite . In the natural environment this type of biodegradation kinetics is often
observed.

PROBLEMS
5.1 2 If the standard enthalpy and entropy of dissolution of naphthalene in water
are 9.9 kJ/mol and 59 J/mol/K, estimate the equilibrium partial pressure
of naphthalene over an aqueous solution containing 1 × 10 − 4 mol/L of
naphthalene.
5.2 2 The rate of formation of a pollutant NO(g) by the reaction 2NO 2 →
2NO(g) + O 2 (g) is 1 × 10 − 5 mol/L/s. Obtain the rate of the reaction and
the rate of dissipation of NO 2 .If Δ G 0 for the given reaction is 35 kJ/mol,
what is the concentration of NO 2 in ppmv in air that has 21% oxygen at
1 atm. The total concentration of NO 2 is 10 ppmv.
5.3 1 For the reaction A + 2B → 3C, assume that it follows the stoichiomet-
ric relation given. What is the order of the reaction in B? Write down
the expression for the rate of disappearance of B and the rate of appearance
of A.
5.4 1 For the following hypothetical reaction, A 2 + B 2 → 2AB, the reciprocal
of the plot of [A] (in moles per 22.4 L) versus time has a slope of − 5 when
both A 2 and B 2 are at unit concentrations. Determine the rate constant for
the disappearance of B 2 in units of m 3 /mol/s and m 3 /s.
5.5 2 Derive the equation for the half-life of an n th-order reaction, n A → C.
Would you be able to determine the order of a reaction if the only data
available are different initial concentrations of A and the corresponding
t 1 / 2 values? If so, how?
5.6 1 The reaction 2A → C proceeds with a rate constant of 5 × 10 − 4 mol/L/s:
(i) Calculate the half-life of the reaction when C A is 2 mol/L. (ii) How
long will it take for C A to change from 5 to 1 mol/L?