Part I: Unidirectional Kinetics
1. NOx and SOx. Two important contributors to air pollution are nitrogen oxides and
sulfur oxides, toxic gases with significant impacts on human health in large urban
areas around the world In the presence of water, these gases also serve as common
precursors to highly caustic acids that constitute acid rain. One such reaction that
contributes significantly to the formation of sulfuric acid rain follows the reaction of
NO2 and SO2 in the presence of wateri
NO2 (aq) + SO2 (aq) - products
The optical transmittance of an aqucous
solution of excess SO2 was measured at a
wavelength of 400 nm corresponding to
NO2) asa function of time during the fast
injection of a small, fixed amount of NO2
as shown in the figure at right.
Optical absorbance, A, and transmittance.
T, are related exponentially, as
A = =
The Beer-Lambert Law relates the optical absorbance, Ai, of some speciesi to its
where U is the molar absorptivity of species i and I is the path length of the
a Determine the order of this "isolated" reaction in terms of NO2.
b. What is the order of the overall reaction, given that it is first order in SO2?
C. Determine the rate constant of the overall reaction, knowing that ENO2 is 17.5
L mol-1 cm³¹, I was 2.00 cm for the spectrometer, and [SO2(aq) was fixed at
0.250 M during the measurements shown above.
d. Determine the half-life of the NO2-limited "isolated" reaction by inspection
and compare this value to its theoretical value. Explain the result.
2. Kinetic Rate Orders. Determine the order and theoretical (fitted) half-life of the
following reactions using the data provided, assuming that all reactions follow the
a Gaudreau Precipitation
b. Lafleur Reduction
C Selänne Combustion
d. Conn Smythe Reaction
Part II: Equilibrium Kinetics
3. Simple Reversible Reaction Consider the following simple reversible reaction
A(g) - B(g)
The individual (irreversible) rate laws for the forward and reverse reactions are
Tforward (t)= ky[A]
a Write the overall, reversible reation rate law (Treversible (t)) in terms of [A]
b. If the initial mixture (at t =0) is comprised of both A and B in the initial
concentrations [A]° and [B]o, express the reaction rate as the derivative of [A]
with respect to tin terms of [A], t, and necessary constants only (i.e, not [B]).
Solve the differential equation derived in part b by separating variables (t
and [A]) and integrating from the initial state (at t = 0) to marbitrary final
state- Simplify and compare your result to Equation 28.40 in the text.
Hints follow the general procedure described in Problem 28.32 in the text,
although note that this problem is slightly different since [B]o= Oin this case.
Simplify until an expression is reached where some function of [A] is linear
with respect to t.
d. Write the moregeneral expression for "Equation 1" in Problem 28.32 in the
text (where [B]0 is a non-zero constant in this case).
c. Determine k, and kr in units of Hz given that the equilibrium constantat this
temperature is Ka = 5.23, and using the provided reaction rate data-
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