Summary Formula sheet physical organic chemistry 1 (NWI-MOL157)

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