Chemical kinetics
1. Pseudo-first order reactions
Definition of first pseudo-first order reaction.
A pseudo-first order reaction is a chemical reaction that appears to follow first-order kinetics, despite not being truly a
first-order reaction in terms of its stoichiometry. It occurs when one reactant is present in excess or at a constant high
concentration compared to the other reactant(s), allowing the concentration of the excess reactant to remain
approximately constant throughout the reaction. As a result, the rate of the reaction only depends on the
concentration of the other reactant, making it a first-order reaction. One example can be the reaction between and
Enzyme and its Inhibitor where [I]>>[E].
How can you determine the actual rate constant?
The rate constant in a pseudo first-order reaction can be determined starting from K obs and the concentration of the
“excess reactant”. In the initial rate method, you perform a series of experiments with different initial concentrations
of the reactant in excess, measuring the initial reaction rates. By determining the relationship between the initial rate
and the concentration of the excess reactant, the effective rate constant can be obtained.
→ k obs = k [S excess]. The slope of the line is k.
K obs is not a real constant because it changes when the concentration of the second reactant changes.
Example of a pseudo-first order reaction.
Let's consider the reaction between a reactant A and a reactant B to form a product P: A + B → P; Suppose the initial
concentration of reactant A is much higher than the concentration of reactant B. Due to this large excess, the
concentration of A remains approximately constant throughout the reaction. Under these conditions, the rate of the
reaction can be expressed as: Rate = k[A]⁰[B]; Since the concentration of A is effectively constant, we can treat it as a
constant, and the rate equation simplifies to: Rate = kobs * [B]; Here, k obs is the observed rate constant, and the
reaction appears to follow first-order kinetics with respect to B, even if the actual reaction order is different. So, in this
case, the reaction is a pseudo-first order reaction with respect to B, as its concentration appears to be the sole
determining factor in the rate of the reaction, while the concentration of A is effectively held constant due to its large
excess.
i.e. [CH3I] + [H2O] → CH3OH + HI where [H2O] >> [CH3I]
,2. Rate constant (k) of a first-order irreversible reaction; list the different ways to determine it.
- Initial reaction rate
- Slope determination
- Determination of the half-life of a reactant
Choose one and describe the principle and the correlated plot(s).
Slope determination:
The first graph is typically exponential for an irreversible first order
reaction as the concentration decreases over time.
The logarithmic form (2nd graph) results in a linear graph when plotted
over time → slope = -k.
Half-Life Method:
For a first-order reaction, the half-life (t1/2) is constant regardless of the initial concentration. By measuring the time
taken for the concentration of the reactant to decrease by half, multiple experiments can be conducted at different
concentrations to determine the half-life. The rate constant (k) can then be calculated using the equation
→ k = 0.693 / t1/2.
3. Halftime
Definition of halftime for a first order irreversible reaction.
The half-life of a first-order irreversible reaction is the time required for the concentration of the reactant to decrease
to half of its initial value. It is denoted as t1/2.
Mathematic correlation with the rate constant.
t1/2=ln2/k=0.693/k
4. Arrhenius plot
What is the Arrhenius plot?
The Arrhenius plot is a graphical representation of the Arrhenius equation. It is used to analyze the temperature
dependence of the rate constant (k) for a chemical reaction. In the Arrhenius plot, the natural logarithm of the rate
constant ln(k) is plotted against the reciprocal of the absolute temperature (1/T) on a graph. The plot typically shows a
linear relationship, and the slope and intercept of the negatively sloped line can provide valuable information about
the reaction.
Which kind of information can be retrieved from it?
- Activation Energy (Ea): the minimal energy molecules must
possess to react and form a product.
- Pre-exponential Factor (A): the number of times molecules
will have to right orientation to cause the reaction.
Arrhenius equation: having the above values, the Arrhenius
equation can be determined to then obtain the rate constant at
any given T.
5. Derivation of the Arrhenius equation from the
collision theory
The Arrhenius equation explains how T affects k based
on the collision theory. As T increases, k increases
exponentially because higher T provides more kinetic
energy to molecules increasing their speed and
frequency of successful collisions. Only collisions
with enough energy to overcome the activation barrier
will lead to a reaction.
, Transition-state theory
6. Reaction coordinates
Identify in the following plot the chemical species of the enzyme catalyzed
reaction. Point the position of the transition state (X‡) of the step: ES → EP.
Enzymes accelerate both forward and reverse reactions allowing the system to
reach equilibrium quicker. Enzymes do not change the equilibrium; they only reduce
the time needed to reach it.
Is the reaction equilibrium shifted toward the reagents or products? Why?
In this case, the eq. is shifted towards the products due to their lower energy.
7. Plot of the reaction (energy vs reaction coordinates)
Reaction: S→P
a. Plot the graph that relates the variation of system energy during the reaction as a function of the reaction
coordinates (in the ABSENCE of catalysis). Red plots.
b. The same of point a, but in presence of NON enzymatic catalysis. Blue plot graph 1.
c. The same of point a, but in presence of enzymatic catalysis. Blue plot graph 2.
(Draw the correct labels on axes and indicate the chemical species (stable and transient) during the reaction.
Draw all the steps)
Non enzymatic catalysis Enzymatic catalysis
8. Equilibrium constant and transition state free energy.
Why is the equilibrium constant of a reaction not altered if the reaction is catalyzed by an enzyme?
In the presence of an enzyme, the activation energy is lowered. Enzymes accelerate reaction in both directions, but
they do not affect the position of the equilibrium.
Enzymes catalyze reactions by lowering the activation energy, facilitating the attainment of equilibrium more rapidly.
However, the ratio of product to reactant concentrations at equilibrium remains the same, as the equilibrium constant
is determined solely by the thermodynamics of the reaction. Enzymes increase the reaction rate without affecting the
equilibrium position or the equilibrium constant.
9. Which is the mathematical relationship between the rate constant of a
reaction and the deltaG + - ?
k = rate constant
kb = Boltzmann constant
h = Planck constant
10. Transition state in binding.
Is there a transition state also in the binding processes?
Yes, there is a transition state complex (or activated complex) also in the binding process.
1. Pseudo-first order reactions
Definition of first pseudo-first order reaction.
A pseudo-first order reaction is a chemical reaction that appears to follow first-order kinetics, despite not being truly a
first-order reaction in terms of its stoichiometry. It occurs when one reactant is present in excess or at a constant high
concentration compared to the other reactant(s), allowing the concentration of the excess reactant to remain
approximately constant throughout the reaction. As a result, the rate of the reaction only depends on the
concentration of the other reactant, making it a first-order reaction. One example can be the reaction between and
Enzyme and its Inhibitor where [I]>>[E].
How can you determine the actual rate constant?
The rate constant in a pseudo first-order reaction can be determined starting from K obs and the concentration of the
“excess reactant”. In the initial rate method, you perform a series of experiments with different initial concentrations
of the reactant in excess, measuring the initial reaction rates. By determining the relationship between the initial rate
and the concentration of the excess reactant, the effective rate constant can be obtained.
→ k obs = k [S excess]. The slope of the line is k.
K obs is not a real constant because it changes when the concentration of the second reactant changes.
Example of a pseudo-first order reaction.
Let's consider the reaction between a reactant A and a reactant B to form a product P: A + B → P; Suppose the initial
concentration of reactant A is much higher than the concentration of reactant B. Due to this large excess, the
concentration of A remains approximately constant throughout the reaction. Under these conditions, the rate of the
reaction can be expressed as: Rate = k[A]⁰[B]; Since the concentration of A is effectively constant, we can treat it as a
constant, and the rate equation simplifies to: Rate = kobs * [B]; Here, k obs is the observed rate constant, and the
reaction appears to follow first-order kinetics with respect to B, even if the actual reaction order is different. So, in this
case, the reaction is a pseudo-first order reaction with respect to B, as its concentration appears to be the sole
determining factor in the rate of the reaction, while the concentration of A is effectively held constant due to its large
excess.
i.e. [CH3I] + [H2O] → CH3OH + HI where [H2O] >> [CH3I]
,2. Rate constant (k) of a first-order irreversible reaction; list the different ways to determine it.
- Initial reaction rate
- Slope determination
- Determination of the half-life of a reactant
Choose one and describe the principle and the correlated plot(s).
Slope determination:
The first graph is typically exponential for an irreversible first order
reaction as the concentration decreases over time.
The logarithmic form (2nd graph) results in a linear graph when plotted
over time → slope = -k.
Half-Life Method:
For a first-order reaction, the half-life (t1/2) is constant regardless of the initial concentration. By measuring the time
taken for the concentration of the reactant to decrease by half, multiple experiments can be conducted at different
concentrations to determine the half-life. The rate constant (k) can then be calculated using the equation
→ k = 0.693 / t1/2.
3. Halftime
Definition of halftime for a first order irreversible reaction.
The half-life of a first-order irreversible reaction is the time required for the concentration of the reactant to decrease
to half of its initial value. It is denoted as t1/2.
Mathematic correlation with the rate constant.
t1/2=ln2/k=0.693/k
4. Arrhenius plot
What is the Arrhenius plot?
The Arrhenius plot is a graphical representation of the Arrhenius equation. It is used to analyze the temperature
dependence of the rate constant (k) for a chemical reaction. In the Arrhenius plot, the natural logarithm of the rate
constant ln(k) is plotted against the reciprocal of the absolute temperature (1/T) on a graph. The plot typically shows a
linear relationship, and the slope and intercept of the negatively sloped line can provide valuable information about
the reaction.
Which kind of information can be retrieved from it?
- Activation Energy (Ea): the minimal energy molecules must
possess to react and form a product.
- Pre-exponential Factor (A): the number of times molecules
will have to right orientation to cause the reaction.
Arrhenius equation: having the above values, the Arrhenius
equation can be determined to then obtain the rate constant at
any given T.
5. Derivation of the Arrhenius equation from the
collision theory
The Arrhenius equation explains how T affects k based
on the collision theory. As T increases, k increases
exponentially because higher T provides more kinetic
energy to molecules increasing their speed and
frequency of successful collisions. Only collisions
with enough energy to overcome the activation barrier
will lead to a reaction.
, Transition-state theory
6. Reaction coordinates
Identify in the following plot the chemical species of the enzyme catalyzed
reaction. Point the position of the transition state (X‡) of the step: ES → EP.
Enzymes accelerate both forward and reverse reactions allowing the system to
reach equilibrium quicker. Enzymes do not change the equilibrium; they only reduce
the time needed to reach it.
Is the reaction equilibrium shifted toward the reagents or products? Why?
In this case, the eq. is shifted towards the products due to their lower energy.
7. Plot of the reaction (energy vs reaction coordinates)
Reaction: S→P
a. Plot the graph that relates the variation of system energy during the reaction as a function of the reaction
coordinates (in the ABSENCE of catalysis). Red plots.
b. The same of point a, but in presence of NON enzymatic catalysis. Blue plot graph 1.
c. The same of point a, but in presence of enzymatic catalysis. Blue plot graph 2.
(Draw the correct labels on axes and indicate the chemical species (stable and transient) during the reaction.
Draw all the steps)
Non enzymatic catalysis Enzymatic catalysis
8. Equilibrium constant and transition state free energy.
Why is the equilibrium constant of a reaction not altered if the reaction is catalyzed by an enzyme?
In the presence of an enzyme, the activation energy is lowered. Enzymes accelerate reaction in both directions, but
they do not affect the position of the equilibrium.
Enzymes catalyze reactions by lowering the activation energy, facilitating the attainment of equilibrium more rapidly.
However, the ratio of product to reactant concentrations at equilibrium remains the same, as the equilibrium constant
is determined solely by the thermodynamics of the reaction. Enzymes increase the reaction rate without affecting the
equilibrium position or the equilibrium constant.
9. Which is the mathematical relationship between the rate constant of a
reaction and the deltaG + - ?
k = rate constant
kb = Boltzmann constant
h = Planck constant
10. Transition state in binding.
Is there a transition state also in the binding processes?
Yes, there is a transition state complex (or activated complex) also in the binding process.
