Physical Chemistry 20130417 week 3 Wednesday April 17, 2013 page 1
Ea,f-Ea,r = ∆U°
elementary reaction
Consider a two dimensional graph with energy E on the vertical axis and reaction coordinate on the
horizontal axis. A curve starts at the left side curves up and right to a maximum, then curves back down
and right, ending higher than the left side. Ending higher than the left side makes this an endothermic
reaction. The vertical distance from the bottom at the left side to the top is the forward activation
energy Ea,f. The vertical distance from the bottom at the right side to the top is the reverse activation
energy Ea,r.
k=A=e
-Ea⁄
RT
Ea is activation energy for the overall reaction.
For example: a composite reaction with rate constants k1 (forward, first reaction), k-1(reverse, first
reaction), and k2(forward, second reaction).
k=
k 1 k 2 -Ea⁄
=e RT
k -1
Ea =Ea,1 -Ea,-1 +Ea,2
An elementary reaction happens in one step. It can’t be broken down into other reactions.
Relation between rate constant k’s and Kc for composite reactions
For elementary reaction:
kf
=k c
k2
k c is equilibrium constant
assumptions: ideal system(γ=1, activity = molar concentration) and RDS holds
reaction:
kf
2+
3+
2Fe2+ +2Hg 2+ ⇀
↽ 2Fe +Hg 2
kr
2
[Fe3+ ] [Hg 2+
2 ]
kc=
2+
2
2+
[Fe ] [Hg ]2
mechanism:
1.
2Fe2+ +2Hg 2+
2.
2Hg +
k1
⇀
3+
+
↽ 2Fe +Hg
k -1
k2
2+
⇀
↽ Hg 2
k -2
fast
slow
s=1
s=2
Since reaction 1 happens twice, it’s not technically an elementary reaction.
ν = stoichiometric coefficient
s = stoichiometric number
From step #1:
rforward =
1 d[Fe3+ ] 1
= k 1 [Fe2+ ][Hg2+ ]=k f [Fe2+ ][Hg 2+ ]
2 dt
2
rreverse =
1 d[Fe2+ ] 1
= k -1 [Fe3+ ][Hg + ]
2 dt
2
Ignore the 2’s when doing rate law, since those aren’t part of the elementary reaction.
From step #2:
1⁄
2
k -2
[Hg 2+ ] k 2
=
⟹[Hg + ]= ( )
+
2
[Hg ]
k -2
k2
1⁄
2
1
k -2
rreverse = k -1 ( )
2
k2
[Fe3+ ][Hg 2+ ]
1⁄
2
[Hg 2+
2 ]
1⁄
2 =k
1
2+ ⁄2
3+
r [Fe ][Hg 2 ]
set rforward = rreverse
For elementary reaction
kf
= Kc
kr
K c is equilibrium constant
1⁄
2
At equilibrium: k f [Fe2+ ][Hg 2+ ]=k r [Fe3+ ][Hg 2+
2 ]
1⁄
3+
2+ 2
1⁄
k f [Fe ]eq [Hg ]eq
=
=K c 2
2+
2+
k r [Fe ]eq [Hg ]eq
likewise:
kf
1⁄
=K c s
kr
1⁄
2
3+ 2
2+
1⁄
[Fe
]
[Hg
]
2
K c = ( 2+ 2
)
[Fe ] [Hg 2+ ]2
s=stoichiometric number in RDS
unimolecular reactions
Unimolecular reactions can be isomerization or decomposition.
examples of isomerizations:
isopropane turns into propene
Ea=274kJ/mol r=k[cyclopropane]
methyl isocyanide turns into methyl cyanide
Ea=160.5KJ/mol
example of decomposition:
C2H5Cl →C2H4 + HCl Ea=360KJ/mol
Lindeman: A→B isomerization
A→B (+C) unimolecular reaction in gas phase
Lindeman mechanism
M is third body
M could be another A molecule or anything
A+M
k1 *
A +M
→
elementary physical reaction
A* +M
k -1
A+M no reaction
→
A*
k2
B(+C)
→
overall A*
r=
0=k1[A][M]-k-1[M][A*]-k2[A*]
k2
B(+C)
→
d[B]
=k 2 [A* ]
dt
equation I
Solve this for [A*]:
[A* ]=
k 1 [A][M]
k -1 [M]+k 2
Substitute for [A*] in equation I to use steady state approximation.
k uni =
k 2 k 1 [M]
k -1 [M]+k 2
uni means unimolecular
2 limiting cases:
1. If k-1[M]>>k2 then:
r=
k 1 k 2 [A][M]
k1k2
the [M]' s cancel so r=k[A]where k=
and it ' s first order
k -1 [M]
k -1
This happens under high pressure.
2. If k2>>k-1[M], then:
r=
k1k2
[M][A] so r=k 1 [M][A] and it ' s second order
k2
This happens under low pressure.
Whether it’s first order or second order depends on how long A* lasts. If the lifetime of A* is short, then
k2→∞ and A+M→B(+C) with second order. If A* has a nonzero or appreciable lifetime, then A*→B(+C)
and it’s first order.