Hoofdstukken betreffend reactie kinetiek en diffusie
May 2, 2022
6
2020/2021
Summary
Subjects
reaction kinetics
rate law
photochemistry
integrated rate law
reaction order
enzyme kinetics
michaelis menten
michaelis menten plot
lineweaver burk plot
eadie hofstee plot
stern volmer plot
stern volmer equation
diffusion
stokes einstein
eyrin
ficks law
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Formulas physical organic
chemistry 1
Rate of reaction aA + bB + cC pP
v = kr[A]a[B]b[C]c
for reaction R P
zeroth order
integrated rate law
[R]t = [R]0 – krt
First order
d [R ]
Change in R over time = -kr[R]
dt
[R]t = [R]0e-krt
t1/2 = (ln2)/kr
second order
integrated rate law
[R]t ¿ ¿
t1/2 = 1/k[R]0
half life of order n:
(2n−1−1)
t1/2 =
( n−1 ) k r ¿ ¿
for reaction A + B P
integrated rate law: ln ¿ ¿ = ([B]0-[A]0)krt
For A B C (with ka and kb)
rate laws:
d[A]
rate (vA) = = -ka[A]
dt
d [B]
rate (vB) = = ka[A] – kb[B}
dt
d [C ]
rate (vC) = = kb[B]
dt
integrals
[A] = e-kat[A]0
[B] = k a ( e−k t−e−k t ) ¿ ¿
a b
(
k a e−k t −k b e−k t
)
a b
[C] = 1+ ¿
k b −k a
for reaction A + B ⇋ C P (with ka, ka’ and kb and equilibrium constant K)
d [P ] ka
fast equilibrium ka, ka’ >> kb: = kb[C] = kbK [A][B] = kb ' [A][B] = kobs [A][B]
dt ka
, [C ]
as K = such that [C] = K[A][B]
[ A ] [B]
d [P ] ka
slow equilibrium ka, ka’ << kb: = kb[C] = kb ' [A][B] = kobs[A][B]
dt k a +k b
as ka[A][B] – ka’[C] – kb[C] = 0
k a [ A ] [B]
such that [C] = '
k a +k b
relaxation of an equilibrium A ⇋ B after a temperature jump
with relaxation time: τ = 1/(kr + kr’) x = x0e-t/τ
Arrhenius equation: kr = Ae-Ea/RT
Arrhenius plot: ln ( ) (
kt 2
kt 1
=
Ea 1
−
R T1 T2
1
)
dln(k r )
activation energy: Ea = RT2( )
dT
catalysis (with kcat)
exp( −ERT ) exp E −E
a , cat
k cat
=
exp (
( ) =
a a ,cat
RT )
kr −E RT
a
Condensation polymerisation
fraction of condensed groups p = k r t ¿ ¿
1
degree of polymerisation: 〈N〉 = = 1 + krt[A]0
1− p
Chain polymerisation
rate of polymerisation: vp = kr[In]1/2[M] = kp [M][M•]
kinetic chain length if SSA in M•: λ = kr[M][In]-1/2 with kr = kp(4fkikt)-1/2
degree of polymerisation: <N> = 2kr[M][In]-1/2
( )
1/ 2
f ki
SSA in M• yields vp = kp [M] [In]1/2
kt
Enzymatic reactions: E + S ⇋ ES P + E with ka, ka’, kb = kcat
k a k b [ E ] [S ]
Vp = = kcat[ES] = Michaelis-Menten equation
k 'a + k b
v max
Michaelis-Menten equation: v= KM
1+ ¿
¿¿
k 'a +k b
with KM =
ka
and Vmax = kb[E]0
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