1. Kinetics of chemical reactions: overview
Kinetic experiments study the rate at which reactions occur, that is how the concentration of some molecular species changes as a function of time. In a plot of concentration vs. time, the rate of the reaction at a certain time t is simply the slope of the curve at that time. In the kinetic experiment shown below, the rate of the reaction decreases as the reaction proceeds.
A kinetic plot involves two variables: one independent (time in this case) and one dependent (on the independent variable, concentration in this case). Thus, our graph contains (i) a plot describing graphically the dependence of product concentration on time, and (ii) a plot for the instantaneous rate as a function of time, given by the derivative of the mathematical function describing the dependence in (i).
rate
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2. First order (unimolecular) reactionk
+ :  by convention
Empirical rate law or phenomenological equation: at any time t, the rate of disappearance of the substrate A (= - d[A]/dt) is
equal to that of the appearance of the product B (= + d[B]/dt) and
proportional to [A].
The factor of proportion k is referred to as the rate constant. Here, the first order rate constant has units of s-1.
We need to solve a differential equation (the phenomenological equation) to yield a value for the independent variable [A] at any time t.
This can be done by applying a set of laws (chemical, translated to mathematics), and assuming some conditions related to the system investigated.
[A] + [B] = Constant = [A0]
d[A] + d[B] = 0 Mass conservation
t = 0: [A] = [A0]; [B] = 0 Initial conditions
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3. Integrated solution (pseudo) first orderk
Variables separation
Integration/initial conditions
A0/2
[A] = [A0] e-kt
[B] = [A0] - [A]
= [A0] - [A0] e-kt
[B] = [A0] (1 - e-kt)
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4. First order reversible (uni-uni) reactionk1
k-1
A B
Phenomenological equation
[A] + [B] = Constant = [A0] Mass conservation
d[A] + d[B] = 0
t = 0: [A] = [A0]; [B] = 0 Initial conditions
Substituting B
Variables separation
Variable change
Substituting A
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5. Integrated solution (uni-uni) first orderk1
k-1
A B
Rearrangement
Integration
Substituting a
Rearrangement
Limits
Molar fraction at equilibrium = relative rate of formation
and
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6. Integrated solution (uni-uni) first orderk1
k-1
A B
k1=0.1 s-1; k-1=0.03 s-1
k1=0.03 s-1; k-1=0.1 s-1
5.33 s
5.33 s
0.023 M
0.077 M
0.077 M
0.023 M
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