A solution and solid state study of niobium complexes University of ...

Chapter 3
conditions, one of the concentrations remain constant while the other varies, e.g.
[A]>>>[B]. This simplifies Equation 3.17 to:
Rate = kobs[A] x and then kobs = k[B] y (3.18)
kobs is the observed pseudo-first order rate constant. By varying the concentration of
A, the rate constant of the reaction can be determined. The rate law for a second
order reaction (where x = y = 1) is given by:
a[A] + b[B] c[C] (3.19)
Rate = k1[A][B] + k2[A] (3.20)
kobs under pseudo-first order conditions ([B]>>>[A]) is given by:
kobs = k1[B] + k2 (3.21)
The equilibrium constant for an equilibrium reaction, where k1 represents the forward
reaction and k2 represents the reverse reaction, is given by:
Keq =
Integration of Equation 3.22 from t = 0 to t yields Equation 3.23:
ln
53
(3.22)
= kobs or [C]t = [C]0 e kobst (3.23)
[C]t and [C]0 represent the concentration change of the reactant at time = 0 and t
respectively. Through the basic principles of the Beer-lambert law, expressing
absorbance in terms of concentration, and a bit of mathematical manipulation,
Equation 3.23 can be given as:
At = A∞ - (A∞ - A0)e kobst (3.24)
where At = absorbance after time t and A∞ = absorbance at infinite time (when
reaction is complete). Absorbance versus time data can be used in a least-squares
fit to give kobs for the reaction. The half-life (t1/2) for a first order reaction, meaning
the time needed for the reactant concentration to decay by 50%, will be:
k1
k2