GE HEALTHCARE Biacore T100, Руководство пользователя

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10 Thermodynamic analysis
10.1 Background
198
Biacore T100 Software Handbook BR-1006-48 Edition AE
A value for the standard heat capacity change
Δ
C
P
° can thus be obtained in
addition to
Δ
H° and
Δ
S° from non-linear fitting of the data to this extended
equation.
10.1.2 Transition state thermodynamics
Transition state theory holds that the equilibrium constant for formation of the
transition state in a reaction can be related to the rate constant for the overall
reaction by the
Eyring equation :
Applying a similar rearrangement of the thermodynamic equations for the
transition state gives:
so that the thermodynamic transition state constants for the forward and
backward reactions can be obtained from plots of ln(k
a
/T) and ln(k
d
/T)
respectively against 1/T.
Note that the Eyring equation does not have a corresponding non-linear form
that takes account of the heat capacity change for transition state formation.
Non-linear fitting to obtain values for
Δ
C
P
° can only be applied to equilibrium
thermodynamic analysis.
where
Δ
C
P
° is the heat capacity change under standard conditions
T
0
is the reference temperature (25°C = 298.15 K for standard
conditions)
where K
‡
is the equilibrium constant for formation of the transition state for
the forward or back reaction
k is the kinetic rate constant for the interaction in the corresponding
direction (k
a
or k
d
)
h
is Planck’s constant
k
B
is Boltzmann’s constant
RT K
D
ln
Δ
H
T
0
°
T
Δ
S
T
0
°
–
Δ
C
P
°
T T
0
–
( )
T
Δ
C
P
°
T
T
0
-----
⎝ ⎠
⎛ ⎞
ln
– + =
K
‡
k
h
k
B
T
--------
=
k
h
k
B
T
--------
ln
Δ
H
o‡
RT
------------- –
Δ
S
o‡
R
------------ + =