BIOC2000 Lecture Notes - Lecture 22: Boltzmann Distribution, Activation Energy, Kinetic Energy
Lecture 22: Enzymology Lecture 2
In a state function, the final state is independent of the path taken from the
start – e.g. in ΔH, ΔS, & ΔG
Activation energy:
- The transition between two states requires a molecule to be converted to
a higher energy conformation to overcome an activation energy barrier;
the ‘transition state’
- Reactions are reversible: at the top of the barrier things can go either
way, in the forward or reverse direction
The rate of a reaction depends on
how hard it is to achieve the
transition state
i.e. to get over the energy barrier
between the ground states
i.e. to achieve the activation energy Δ
G‡ (free energy of the transition state)
which determines whether a reaction
will occur at a detectable rate
The transition state theory links rates to
activation energy:
The rate of a reaction
depends on the
proportion of molecules
with the transition state
energy
It is often thought that all
molecules are the same,
but all molecules are
dynamic entities and in
any population of
molecules there will be a
distribution of energies:
Boltzmann distribution
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Naturally, molecules are in constant motion and sampling different
conformations: some sample low energy conformations, others higher
energy (less stable conformations (due to different entropies, structures
and bonding interactions))
Average energy in a population molecules – where #of molecules peak in
the Boltzmann distribution; but there is a tail of molecules having higher
energy, a proportion of which even exceed the activation energy (shaded
in diagram) - this proportion has enough energy to undergo transition
For a substrate to form a thermodynamically favoured product, it has to
assume a particular conformation – the transition state
In a population of molecules, only very few molecules assume this state
naturally in a “kinetically stable” reaction (even if it is thermodynamically
favourable i.e. spontaneous)
The probability of single molecules achieving the activation energy
determines the rate at the whole population level
A larger activation energy barrier means the transition state is harder to
achieve, i.e., fewer molecules will achieve it.
What can increase the probability? Energy input - increasing the energy of
the molecules can make the reaction more likely to proceed (in both
directions)
Heat input = Kinetic energy increase = molecules will explore more
possible conformations, including higher energy ones
What will happen to population distribution at different temperatures?
What will happen to the rate constant?
As T rises, distribution will shift to the right and flatten out. More will
achieve activation energy, so reaction rate will increase.
For a molecule to achieve a transition state may mean:
1. Reacting groups are aligned in a particular way (often by physical
contortion of the molecule)
For example, Trans to cis isomerisation of peptide bond in Proline
Proline and alanine residue joined by a peptide bond (trans form) – can
isomerize to cis form. Changing the peptide bond requires reordering of
the orbitals
In cis conformation, it is a little less stable because there is steric
hindrance between 2 groups.
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Document Summary
In a state function, the final state is independent of the path taken from the start e. g. in h, s, & g. The transition between two states requires a molecule to be converted to a higher energy conformation to overcome an activation energy barrier; the transition state". Reactions are reversible: at the top of the barrier things can go either way, in the forward or reverse direction. The rate of a reaction depends on how hard it is to achieve the transition state i. e. to get over the energy barrier between the ground states i. e. to achieve the activation energy . G (free energy of the transition state) which determines whether a reaction will occur at a detectable rate. The transition state theory links rates to activation energy: The rate of a reaction depends on the proportion of molecules with the transition state energy.
