Transcript L25-Conc Acids

Acid Catalysis in Concentrated Solutions
Protonation of the substrate is
most often the first step of
acid-catalyzed reactions.
 The extent to which the
substrate is protonated
influences the reaction
rate.
 It is often desirable to
raise [H3O+] to increase
the degree of substrate
protonation, thereby
enhancing the reaction
rate.
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Standard Measure of Acidity - pH
The most familiar measure of the acidity (tendency to protonate a
base) of a solution is pH:
pH   log[ H ]
For the protonation of a base B:

BH  H2 O
KA
[B]  [H3 O  ]
we relate the extent of reaction to the pH through the acid
dissociation constant, Ka:
[B]
[B]
pH

pK

log
K a  [H ]
or
a

[BH ]
[BH ]
For concentrated solutions of strong acids, we find two problems:
 Measuring the pKa of strong acids with respect to H2O
protonation.
 Accounting for the non-ideality of concentrated acid solutions
that are much more “acidic” than their pH would suggest.

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Hammett Indicators
Given that we are interested in knowing the extent to which our
substrate (S) is protonated (SH+) in a given acid solution, a relevant
question is:
 For a range of acidic solutions (0 mol% H2SO4 to anhydrous
H2SO4), to what extent is a neutral base protonated?
Hammett and coworkers have addressed this issue by measuring
the tendency of an acidic solution to protonate various neutral
bases, called Hammett Indicators. For example,
O
+
N
O
+
pKa=0.99
O
NH3
+
N
O
p-Nitroanilinium ion
NH2
+
+
H
p-Nitroaniline
The concentrations of BH+ (nitroanilinium ion) and B (nitroaniline)
can be measured by a spectrophotometric technique.
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Hammett Acidity Function
O
+
N
O
+
pKa=0.99
O
NH3
+
N
O
p-Nitroanilinium ion
NH2
+
+
H
p-Nitroaniline
The Ka for this reaction is known:
aH aB
aH  B [B]
Ka 

aBH
 BH [BH ]
Taking logs yields:
 log K a 
 log
aH  B
 BH
 log
[B]
[BH ]
We define a new parameter, Ho, the Hammett Acidity Function:
aH  B
Ho   log
 BH
which reduces our equilibrium relationship to:
[B]
pK a  Ho  log
[BH ]
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Hammett Acidity Function
To a series of acid solutions of varying concentration, an indicator
of known pKa is added, and the ratio of [B] to [BH+] measured.
 The Hammett acidity function is easily calculated for each
solution by:
Ho  pK a  log
[B]
[BH ]
The acidity function accounts for solution non-ideality by lumping
the activity of H+ (an essentially indeterminable quantity) with the
activity coefficients B and BH+.
 In dilute solutions, aH+[H+], B1 and BH+1, leaving
Ho   log
aH  B
 BH
  log[ H ]  pH
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Hammett Acidity Function
The acidity function is by no
means a universal indication of
the tendency of an acid solution to
protonate a base.
 B and BH+ relate to the
Hammett indicator, and may
not relate to your substrate.
 H0 measures the tendency
of a solution to protonate a
neutral base, not to a base
of any other electrical
charge.
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Ho and Acid Catalyzed Reaction Kinetics
For those acid catalyzed reactions in which protonation of a neutral
substrate is a kinetically significant step, there may exist a
relationship between the reaction rate and the acidity function.
Consider a reaction proceeding by the following mechanism:
RH
r 1:


K
RH
k2
RH  H  P
r 2:
where reaction 2 is rate limiting:
r2  k 2 [RH ]
and reaction1 is at equilibrium:
Ka 
CHEE 323
aRaH
aRH

 [RH ] 
J.S. Parent
aH  R
K a RH
[R]
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Ho and Acid Catalyzed Reaction Kinetics
If we assume that our neutral substrate has great chemical
similarity to the Hammett indicator used to determine Ho of the acid:

[RH ] 
aH  R [R]
 RH K a

aH  B [R]
 BH K a
The rate of the reaction becomes:

r2  k 2 [RH ]  k 2
aH  B [R]
 BH K a
The observed rate constant for the reaction,
k obs
k 2 aH  B

K a  BH
relates to the acidity function according to:
aH  B
log k obs  cons tan t  log
 BH
 cons tan t  Ho
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Ho and Acid Catalyzed Reaction Kinetics
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