The Brønsted catalysis relationship is a Linear Free Energy Relationship (LFER) that relates ionization of an acid or base which catalyzes a reaction and the rate of the reaction. Contributed by: Quincy Davis, Jonathan Greenhalgh, Joshua Visser (Undergraduates), University of Utah, 2016

1. Organic Pedagogical Electronic
Network
Brønsted Catalysis
Quincy Davis
Jonathan Greenhalgh
Joshua Visser

2. Overview
References: Anslyn, E.V.; Doughert, D. A.; Modern Physical Organic Chemistry, University Science Books: Saulisito CA, 2006
Wiki Page: https://en.wikipedia.org/wiki/Br%C3%B8nsted_catalysis_equation
Other References: Buncel, E.; Um I. H.; Hoz, S. Solvent-Independent Transition-State Structures for Acyl-Transfer Reactions. A Novel Strategy for Contruction of a Brønsted Correlation. J. Am.
Chem Soc. 1989, 111, 971-975; Sengerová, B.; Tomlinson, C.; Atack, J. M.; Williams, R.; Sayers, J. R.; Williams, N. H.; Gasby, J. A. Brønsted Analysis and Rate-Limiting Steps for the T5 Flap
Endonuclease Catalyzed Hydrolysis of Exonucleolytic Substrates. Biochemistry 2010, 49, 8085-8093
The Brønsted catalysis relationship is a
Linear Free Energy Relationship (LFER) that
relates ionization of an acid or base which
catalyzes a reaction and the rate of the
reaction. The equations used to relate these
quantities are:
log(k)=αlog(Ka)+C
log(k)=-βlog(Ka)+C’
The constants, α and β, are measured
factors that connect k to Ka. C and C’ are
constants relating to the fit of the line, but
they have no physical meaning. The
constants are typically between 0 and 1,
where a higher value for α refers to a highly
acid catalyzed reaction – where protonation
is the rate determining step.
A higher value of β refers to a reaction that is
base catalyzed – where deprotonation is the
rate determining step. The constants α and
β must add up to 1 due to the relationship
between Ka of the acid, and the Ka of the
conjugate base. Any LFER, including a
Brønsted plot, is an evaluation of an effect
on the transition state of the rate determining
step. Therefore, for a Brønsted catalyzed
reaction, if the acid-base step isn’t rate
limiting, then a plot of log kcat vs pKa to
assess the Brønsted coefficients of α and β
will be inconclusive as to the effect of acid or
base on the rate and give smaller than
expected values. This is due to the rate of
reaction being ultimately unaffected by the
acid-base catalysis when a different step is
determining the rate.
In a plot of log k vs. pKa to evaluate α or β a
positive slope would correlate to a β value
and a negative slope to an α value.

3. Determination of Mechanism
References: Um, I. H.; Im, L. R.; Kang J. S., Bursey, S. S.; Dust, J. M. Mechanistic Assessment of SNAr Displacement of Halides
from 1-Halo-2,4-dinitrobenzenes by Selected Primary and Secondary Amines: Brønsted and Mayr Analyses J. Org. Chem. 2012,
77, 9738-9746
X=F 1a
X=Cl 1b
X=Br 1c
X=I 1d
Brønsted-type plots for
reactions of 1a−d with cyclic
secondary amines 1−5 in
MeCN at 25.0 ± 0.1 °C: 1a
(●, βnuc = 1.00), 1b (■, βnuc
= 0.53), 1c (○, βnuc = 0.53),
1d (◊, βnuc = 0.52).
Bursey et. al. performed the following analysis of 1-halo-
2,4-dinitrobenzenes. The pKa was varied by using
several amine bases. Because the value of β for
reaction 1a in MeCN is 1.00 it was determined that the
loss of the proton ( k3 ) was rate limiting for X=F while for
1b-d it was determined that formation of MC-1-Z ( k1 ) is
rate limiting because β=0.52 or 0.53. The value of β in
this case shows that for 1a the loss of the proton is base
catalyzed, whereas for 1b-d the reaction is less sensitive
to what base is used. It was also found that β is solvent
dependent for 1a because in water the value of β was
found to more closely match the values of 1b-d.
Base
1 Piperadine
2 Piperazine
3 1-(2hydroxyethyl)
piiperazine
4 1-formylpiperazine
5 Morpholine

4. Linear Free Energies in an Enzymatic Reaction
References: Mihai, C.; Kravchuk, A. V.; Tsai, M.; Buzik, K. S. Applications of Brønsted-Type LFER in the
Study of the Phospholipase C Mechanism. J. Am. Chem. Soc. 2003, 125, 3236-3242
pKa Aryl: 7.1 to 10.2 pKa Alkyl: 12.4 to 15.9 pKa Alkyl: 13.3 – 15.9
X = O, S X = O, S X = O, S
R = Aryl, pKa = 7.1 - 10.2 R = Alkyl, pKa = 12.4 – 13.9 R = Alkyl, pKa = 13.3-15.9
Nonhydrophobic Nonhydrophobic Hydrophobic
Figure 2. Brønsted dependence of log kcat
vs pKa for PI-PLC catalyzed cleavage of
hydrophobic O-alkyl inositol phosphates (□, β
= 0.12 ± 0.11), hydrophobic Rp-O-alkyl
phosphorothiolates (∆, β = 0.27 ± 0.15), and
hydrophobic Sp-O-alkyl inositol
phophorothiolates (●, β = 0.46 ± 0.16)
compared to that of short-chain alkyl and aryl
esters of the inositol phosphate (○, β = 0.58 ±
0.06).
The authors tested three different sets of R groups on the inositol phosphates
(where X = O) and phosphorothiolates (where X = S), where each set of R
groups has a pKa range given in Figure 1. Using a Brønsted LFER, plotting log
kcat vs pKa, Figure 2 was obtained. From this plot – which was plotted with the
assumption of a negative β value giving a negative slope as opposed to the
traditional positive one– it is seen that the reaction conditions of
nonhydrophobic aryl and nonhydrophobic alkyl give the same dependence on
pKa and a Brønsted β coefficient value of 0.58, indicating a strong base
catalyzed dependent RLS. Additionally, from Figure 2, it is shown that for the
hydrophobic alkyls tested, there is a smaller β of 0.12 which gives an α of .88,
showing an acid catalyzed RLS. From this data, the authors conclude that the
RLS is changed based on the aryl or alkyl chain, where a specific Histidine
residue that facilitates acid catalyzed loss of the alcohol is excluded from the
transition state.
Figure 1
Note: The Rp and Sp values given in the
above plot for the hydrophobic chains were
for the system where X = S
(phosphorothiolates), and similar
phosphorothiolate results were not given in
this plot for the nonhydrophobic chains.

5. Problems
References: Buncel, E.; Um I. H.; Hoz, S. Solvent-Independent Transition-State Structures for Acyl-Transfer Reactions. A Novel
Strategy for Contruction of a Brønsted Correlation. J. Am. Chem Soc. 1989, 111, 971-975
1. What does it mean if α is zero?
a. Deprotonation is the rate determining step
b. Protonation is the rate determining step
c. There is no protonation occurring at the rate determining step
d. α cannot be 0
2. A Brønsted plot is depicted here. Which of the following is true?
a. The reaction is acid catalyzed
b. The reaction is base catalyzed
c. It can’t be determined if it’s acid or base catalyzed based on this plot
3. At low pKa the slope of the Brønsted plot is near zero. As the pKa is increased, the slope approaches a
steady value of α. What might be the reason for this behavior?
a. Proton transfer becomes less rate limiting at high acidity
b. Proton transfer becomes more rate limiting at high acidity
c. Proton transfer approaches the diffusion limit
d. A and C
e. B and C
4. What is the relationship between α and β?
a. α and β are related by a proportionality constant
b. α + β= =1
c. They are not mathematically related
d. α = β-1

6. Solutions
1. C
2. B
3. D
4. B

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Contributed by:
Quincy Davis, Jonathan Greenhalgh, Joshua Visser (Undergraduates)
University of Utah, 2016