A kinetic study on the isomerization of hop α-acids

Article abstract of DOI:10.1021/jf8004965

In this article, a detailed study on hop α-acid isomerization kinetics is presented. Because of the complex wort matrix and interfering interactions occurring during real wort boiling (i.e., trub formation and α-acids/iso-α-acids complexation), this investigation on α-acid isomerization kinetics was performed in aqueous buffer solution as a function of time (0-90 min) and heating temperature (80-100°C). Rate constants and activation energies for the formation of individual isc-α-acids were determined. It was found that iso-α-acid formation follows first-order kinetics and Arrhenius behavior. Differences in activation energies for the formation of trans- and cis-isomers were noticed, the activation energy for the formation of trans-iso-α-acids being approximately 9 kJmol^-1 lower.

Full text of DOI:10.1021/jf8004965

6408 J. Agric. Food Chem. 2008, 56, 6408–6415
A Kinetic Study on the Isomerization of Hop r-Acids
BARBARA JASKULA,*,†,‡ PAWEL KAFARSKI,§ GUIDO AERTS,†,‡ AND
†,‡
LUC DE COOMAN
Laboratory of Enzyme, Fermentation and Brewing Technology, KaHo St.-Lieven, Gebroeders
Desmetstraat 1, B-9000 Gent, Belgium, Leuven Food Science and Nutrition Research Centre
(LFoRCe), Department M2S, Katholieke Universiteit Leuven, Kasteelpark Arenberg 20,
B-3001 Leuven, Belgium, and Wroclaw University of Technology, Institute of Organic Chemistry,
Biochemistry and Biotechnology, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland
In this article, a detailed study on hop R-acid isomerization kinetics is presented. Because of the
complex wort matrix and interfering interactions occurring during real wort boiling (i.e., trub formation
and R-acids/iso-R-acids complexation), this investigation on R-acid isomerization kinetics was
performed in aqueous buffer solution as a function of time (0-90 min) and heating temperature
(80-100 °C). Rate constants and activation energies for the formation of individual iso-R-acids were
determined. It was found that iso-R-acid formation follows first-order kinetics and Arrhenius behavior.
Differences in activation energies for the formation of trans- and cis-isomers were noticed, the activation
energy for the formation of trans-iso-R-acids being approximately 9 kJmol-1 lower.
KEYWORDS: Hop r-acids; trans-/cis-iso-r-acids; isomerization yield; kinetics; rate constant; activation
energy
INTRODUCTION
on the trub being formed. Furthermore, factors such as pH, wort
gravity, hopping rate, hop product(s) used, presence of divalent
cations, duration and temperature of the boil, and the degree of
dispersal of the R-acids upon addition of hops all have important
influences on the R-acid isomerization yield and final utilization
(3–10).
Hops (Humulus lupulus L.) have long been used in brewing
as they are a natural preservative, and part of the early use of
hops in beer was to preserve it. Hops have been used for
centuries to flavor the beer and are considered, along with water,
malt, and yeast, to be an essential ingredient. Nowadays, it is
recognized that hops are implicated in the main quality features
of beer, i.e., taste and aroma, foam, color, and final product
stability (1, 2).
Hop R-acids and the essential hop oils are at the origin of
key flavor attributes of beer, namely, typical beer bitterness and
hoppy aroma. With respect to conventional hopping, a most
important chemical conversion occurs during wort boiling,
namely, the thermal isomerization of the hop R-acids to the bitter
tasting iso-R-acids via an acyloin-type ring contraction (Figure
1). Conversion of each R-acid results in two epimeric iso-R-
acids, distinguished as a trans- and cis-iso-R-acid. Consequently,
six major iso-R-acids are present in beer, i.e., the trans- and
cis-isomers of isocohumulone, isohumulone, and isoadhumulone.
Unfortunately, upon wort boiling, the isomerization yield of
R-acids into iso-R-acids is invariably low (at most 50-60%)
and also subject to variations, even from brew to brew. At the
origin of the poor R-acid isomerization are the limited solubility
of R-acids in wort, incomplete isomerization during the boil,
and depletion of R-acids and iso-R-acids because of adsorption
Final overall R-acid utilization is related to the beer, and this
value is still significantly lower than the isomerization yield,
amounting to only 30-40% or even as low as 10-20% (11).
This is due to further losses of iso-R-acids postwort boiling,
i.e., further losses during wort clarification, fermentation,
maturation, and beer filtration.
Knowledge of R-acid utilization is of prime importance for
each brewery in calculating accurate hopping rates to aim at
precise bitterness levels, and, in particular, detailed knowledge
of the isomerization kinetics should allow more precise control
of iso-R-acid levels achieved in finished beer. However,
published literature has only modestly characterized the kinetics
of R-acid isomerization into their corresponding iso-R-acids.
In 1964, Spetsig (13) found that R-acid isomerization follows
the pattern of a first-order reaction. At about the same time,
Askew (3) also found the reaction kinetics for R-acid conversion
to be of first-order by heating R-acids in aqueous solution and
further quantifying both R-acids and iso-R-acids using spec-
trophotometric methods. Later on, Mosˇtek et al. (14) stated that
during the first 10 min of hop boiling, the rate of the
isomerization of R-acids varied with concentration and time and
did not follow the pattern of first-order reaction kinetics.
However, in the subsequent 10-120 min of boiling, R-acid
isomerization did occur as a first-order reaction. McMurrough
* Corresponding author. Phone: +32-(0)9-265 86 13. Fax: +32-(0)9-
265 87 24. E-mail: barbara.jaskula@kahosl.be.
† KaHo St.-Lieven.
‡ Katholieke Universiteit Leuven.
§ Wroclaw University of Technology.
10.1021/jf8004965 CCC: $40.75  2008 American Chemical Society
Published on Web 07/04/2008

Hop R-Acid Isomerization Kinetics
J. Agric. Food Chem., Vol. 56, No. 15, 2008 6409
Figure 1. The mechanism of R-acid isomerization into iso-R-acids (12).
et al. (15) demonstrated that decreases in R-acids upon boiling
follow first-order reaction kinetics and that the rate is influenced
by temperature, pH, and the concentration of divalent cations.
Furthermore, it was observed by McMurrough et al. (15) that
decreases in R-acids during boiling with hop extract were always
greater than the corresponding increases in iso-R-acids through-
out the boiling period. When looking at the individual R-acids,
the isomerization yield of cohumulone was always highest,
suggesting a faster conversion of cohumulone than n- and
ad-humulone (16–18).
Recently, Malowicki and Shellhammer (9) confirmed the
reaction kinetics of iso-R-acid formation to be of first-order.
However, in contrast to previous work (16–18), these authors
claim that the isomerization of cohumulone to isocohumulone
proceeds at a rate similar to that of the conversion of humulone
and adhumulone to their corresponding iso-R-acids. Malowicki
and Shellhammer (9) were the first to report on essential kinetic
parameters of iso-R-acid formation, i.e., the rate constant and
activation energy amounting to (7.9 × 1011) e(-11858/T) min -1
and 98.6 kJmol-1, respectively.
In this work, we aimed at the reliable determination of basic
kinetic parameters (rate constants and activation energies) related
to the formation of iso-R-acids, including individual trans- and
cis-iso-R-acids. To perform the isomerization reactions, a model
buffer system was selected in order to allow characterization
of the isomerization as such, i.e., without interference of the
reaction by the removal of R-acids/iso-R-acids due to trub
formation, as observed in wort boiling.
MATERIALS AND METHODS
Determination of Rate Constant and Activation Energy of Iso-
r-acid Formation. Boiling Experiments 1 and 2. An all-glass round-

6410 J. Agric. Food Chem., Vol. 56, No. 15, 2008
Jaskula et al.
Figure 2. First-order linearization for total iso-R-acids, isocohumulone, isohumulone, and isoadhumulone upon heating of hop R-acids in buffer system
at 100 °C (A), 90 °C (B), and 80 °C (C); experiment 1.
Table 1. Influence of Heating Temperature on the Rate Constant k (s-1) of Iso-R-Acid Formation: Experiment 1 and Experiment 2a
temperature
compoundb
100 °C
90 °C
80 °C
experiment 1
experiment 2
experiment 1
experiment 2
experiment 1
experiment 2
total iso-R-acids
isocohumulone
isohumulone
0.84 × 10-4
1.00 × 10-4
0.76 × 10-4
0.85 × 10-4
0.34 × 10-4
0.65 × 10-4
0.23 × 10-4
0.53 × 10-4
0.28 × 10-4
0.55 × 10-4
0.82 × 10-4
1.00 × 10-4
0.73 × 10-4
0.80 × 10-4
0.38 × 10-4
0.66 × 10-4
0.22 × 10-4
0.51 × 10-4
0.28 × 10-4
0.54 × 10-4
0.34 × 10-4
0.40 × 10-4
0.31 × 10-4
0.33 × 10-4
0.14 × 10-4
0.26 × 10-4
0.09 × 10-4
0.22 × 10-4
0.11 × 10-4
0.22 × 10-4
0.36 × 10-4
0.43 × 10-4
0.33 × 10-4
0.38 × 10-4
0.15 × 10-4
0.28 × 10-4
0.10 × 10-4
0.24 × 10-4
0.12 × 10-4
0.28 × 10-4
0.14 × 10-4
0.17 × 10-4
0.13 × 10-4
0.14 × 10-4
0.07 × 10-4
0.10 × 10-4
0.05 × 10-4
0.09 × 10-4
0.05 × 10-4
0.09 × 10-4
0.14 × 10-4
0.18 × 10-4
0.13 × 10-4
0.14 × 10-4
0.07 × 10-4
0.10 × 10-4
0.04 × 10-4
0.09 × 10-4
0.05 × 10-4
0.10 × 10-4
isoadhumulone
trans-isocohumulone
cis-isocohumulone
trans-isohumulone
cis-isohumulone
trans-isoadhumulone
cis-isoadhumulone
a Calculation of rate constants was based on common equations and procedures as published by Tinoco et al. (22). b Compound identification based on reference
preparations of R-acids and iso-R-acids, respectively (see Materials and Methods).
bottom flask (500 mL) with 3 necks was used in two separate laboratory
scale boiling experiments (250 mL scale). The first neck was used for
online measurement of the temperature, the second neck was fitted to
a reflux condenser to prevent evaporation, and the third opening was
closed with a rubber septum for sampling as a function of time using
a syringe. Boiling experiments were performed in aqueous buffer
solution (0.1 M), prepared with 3,3-dimethylglutaric acid and NaOH
(sodium hydroxide) to maintain a wort representative pH of 5.20. The
flask containing buffer solution (250 mL) was heated in a laboratory
stirrer/hot basket and continuously homogenized during the experiment
with a magnetic stir bar. When the buffer achieved the required
temperature (80, 90, or 100 °C), 2 mL of an ethanolic solution of
commercial nonisomerized hop extract (International Calibration Extract
ICE 2 containing 49.39% R-acids (w/w) and 24.94% ꢀ-acids (w/w);
Labor Veritas, Zu¨rich, Switzerland) was added.
Deskpro 2000 (software: Merck HPLC-System-Manager Software
D-7000 Rev.2.1), and an Alltima C18 5 µm column (150 mm × 4.6
mm i.d., Alltech Associates, Deerfield, IL, USA).
Chromatographic conditions were as described by De Cooman et
al. (21). Eluent A: milli-Q water adjusted to pH 2.80 with phosphoric
acid (85%, Merck, Darmstadt, Germany). Eluent B: HPLC-grade
acetonitrile (Acros Organics, Belgium). Isocratic elution was using 52%
(v/v) B and 48% (v/v) A. Analysis time: 50 min. Flow rate: 1.8
mL.min-1. Temperature: ambient temperature. UV-detection: 270 nm
(iso-R-acids) and 314 nm (R-acids). A dicyclohexylamine (DCHA)-
iso-R-acids ICS-I1 complex (66.5% (w/w) iso-R-acids; Labor Veritas,
Zu¨rich, Switzerland) with known composition was used as external
standard for quantification of iso-R-acids. The International Calibration
Extract ICE 2 (49.39% (w/w) R-acids, 24.94% (w/w) ꢀ-acids; Labor
Veritas, Zu¨rich, Switzerland) with known composition was applied for
the quantification of R-acids. The trans/cis iso-R-acids ratio (T/C-ratio)
was based on the measured concentrations by HPLC of trans- and cis-
isocohumulone, and trans- and cis-isohumulone.
Initial R-acids levels were 60 mg/L. At selected time intervals (5,
10, 15, 20, 30, 45, 60, and 90 min), heated samples (5 mL) were taken
using a syringe and cooled immediately in liquid nitrogen (-196 °C).
Frozen samples were kept at -24 °C until further extraction and HPLC
analysis.
[trans-isocohumulone] + [trans-isohumulone]
[cis-isocohumulone] + [cis-isohumulone]
T/C (%) )
× 100%
Extraction of r-Acids and Iso-r-acids from the Aqueous Buffer
System. R-Acids and iso-R-acids were isolated from the boiled buffer
samples by liquid-liquid extraction, on the basis of the modified IOB
method 9.16 (19) by Jaskula et al. (20). Buffer sample (5 mL) was
acidified with H3PO4 (0.5 mL; 12 M; Merck, Darmstadt, Germany)
and partitioned in a separating funnel with 10 mL iso-octane (Acros
Organics, Belgium). After phase separation, the iso-octane layer (10
mL) was collected. This extraction with 10 mL iso-octane was
performed three times, and the collected iso-octane fractions were
concentrated to dryness under reduced pressure (30 °C). The residue
was redissolved in 1 mL ethanol/H3PO4 (99.75/0.25; v/v). Before HPLC
analysis, the extract was filtered through a 13 mm syringe filter (0.20
µm PTFE) (Alltech Associates, Deerfield, IL, USA).
HPLC Analysis of r-Acids and Iso-r-acids. HPLC separations
were performed on a Merck Hitachi Liquid Chromatograph (Merck,
Darmstadt, Germany), consisting of a programmable HPLC pump
L-7100 with a quaternary low pressure gradient system, a diode array
detector L-7450A, an interface module D-7000, a solvent degasser
L-7612, an autosampler L-7200 (sample loop: 100 µL), a Compaq
RESULTS AND DISCUSSION
R-Acid isomerization kinetics was investigated in a simple
model system (3,3-dimethylglutaric acid/NaOH buffer solution;
0.1 M; pH 5.20). Hop R-acids were added to heated buffer
solution in the form of nonisomerized hop extract, predissolved
in ethanol. Two independent series of heating experiments were
performed in order to determine rate constants and activation
energies. Iso-R-acid formation was measured by HPLC as a
function of heating time and temperature (for more experimental
details, see Materials and Methods).
According to previously published work (9, 13, 14), iso-R-
acid formation from hop R-acids follows first-order kinetics.
Thus, as shown by eq I, the rate of iso-R-acid formation upon
heating of the reaction mixture is proportional to the instanta-
neous concentration of R-acids at any time during the reaction.

Hop R-Acid Isomerization Kinetics
d[iso-R-acidst]/dt ) k[R-acidst]
J. Agric. Food Chem., Vol. 56, No. 15, 2008 6411
Table 2. Total Isomerization Yield (%) and Isomerization Yield of
Individual R-Acids (%) as a Function of Heating Time at Different
Temperatures: Experiment 1
(I)
In eq I, [iso-R-acids ] is the concentration (mol/L) of iso-R-
t
acids at reaction time t, [R-acids t] is the concentration (mol/L)
of R-acids at reaction time t, and k is the rate constant (s-1).
Following integration, eq II is derived from eq I:
Heating Temperature 80 °C
time (min)
isomerization yield (%)
5
10
15
20
30
45
60
90
ln 1-[iso-R-acids ] ⁄ [R-acids ] ) -kt
(II)
(
)
t
0
total iso-R-acids
cohumulone
humulone
0.0 0.9 1.5 2.1 2.5 3.7 4.9 7.4
0.0 1.2 1.7 2.6 3.1 4.6 5.9 8.5
0.0 0.8 1.4 1.9 2.1 3.2 4.4 6.9
0.0 0.9 1.3 2.0 2.4 3.8 4.8 7.5
where [iso-R-acids t] is the concentration (mol/L) of iso-R-acids
at reaction time t, [R-acids ] is the concentration (mol/L) of
0
R-acids at reaction time t ) 0 (s), k is the rate constant (s-1),
and t is the reaction time (s).
adhumulone
A graph of -ln(1-[iso-R-acidst]/[R-acids0]) versus t, when
linear, proves that the reaction follows first-order kinetics.
The kinetic data on R-acid isomerization obtained via
experiment 1 are shown in Figure 2. Apparently, at each heating
temperature (80 °C, 90 °C, and 100 °C), iso-R-acid formation
follows first-order kinetics, and the higher the applied heating
temperature, the higher the rate constant of the reaction (k). Rate
constants corresponding to the formation of total iso-R-acids,
isocohumulone, isohumulone, and isoadhumulone are further
shown in Table 1.
In addition, Table 1 contains the rate constants of individual
iso-R-acids, i.e., the trans- and cis-isomers, as a function of the
applied heating temperature for both experiments 1 and 2. For
determination of the rate constants of each pair of trans- and
cis-isomers derived from the same R-acid, kinetics of parallel
reactions was applied (22).
Heating Temperature 90 °C
time (min)
isomerization yield (%)
5
10
1.5 2.5 3.1 3.9 5.2
1.9 3.3 4.2 4.8 6.6 10.5 13.3 19.1
15
20
30
45
60
90
total iso-R-acids
cohumulone
humulone
8.7 11.7 16.7
1.3 2.0 2.5 3.5 4.6
1.5 2.5 3.1 3.7 4.7
7.9 10.8 15.6
8.2 12.2 16.3
adhumulone
Heating Temperature 100 °C
time (min)
isomerization yield (%)
5
10 15 20
30
45
60
90
total iso-R-acids
cohumulone
humulone
2.2 4.4 5.7 7.7 13.0 21.4 27.9 36.0
2.7 5.3 7.7 9.2 15.4 24.9 32.0 41.0
2.1 3.9 4.8 6.9 11.5 19.6 25.7 33.3
1.8 4.3 5.3 7.6 13.7 21.4 28.0 36.0
adhumulone
In agreement with previous work on wort boiling at a pilot
scale (Jaskula et al., unpublished results), it can be seen that
the rate constants for the formation of cis-isomers are always
higher than the rate constants for the formation of trans-isomers.
Especially at the highest heating temperatures (100 and 90 °C),
the difference in rate constant between cis- and trans-iso-R-
acids is very pronounced. This is related to the higher required
activation energies and higher pre-exponential factors as found
for the formation of cis-isomers (see further). The rate constant
for the formation of the major iso-R-acid, i.e., isohumulone, is
always the lowest. Obviously, depending on the iso-R-acid
produced, there are clear differences in rate constants, which
contradicts the previous work by Malowicki and Shellhammer
(9).
The observed differences in rate constants, as a function of
heating temperature and nature of the iso-R-acid (see Table 1),
are further reflected in clear differences in isomerization yields,
as can be derived from Table 2. Clearly, in order to obtain
relatively satisfying isomerization yields, a sufficiently high
heating temperature is required, which is related to the value
of the free energy of activation of the isomerization reaction
(approximately 97 kJmol-1; see further). When looking at the
efficiency of the reaction for the individual R-acids, the
isomerization yield of humulone is the lowest at each time
interval and at each applied heating temperature. On the basis
of kinetic data (rate constants) and calculated isomerization
yields, R-acid conversion occurs more efficiently for cohumu-
lone, followed by adhumulone, and humulone.
Table 3. T/C-ratio (%)a as a Function of Reaction Time and Temperature:
Experiment 1
time (min)
temperature (°C)
5
10
15
20
30
45
60
90
80
90
100
153.1 111.6 89.7 84.1 70.7 53.9 57.6
100.0
60.8
77.5
54.1
75.6 55.4 55.4 49.3 49.1 46.7
61.8 54.9 47.3 47.3 47.1 46.3
a T/C (%) ) (trans-isocohumulone+trans-isohumulone)/(cis-isocohumulone+cis-
isohumulone) × 100%.
T/C-ratios after short heating periods, in particular at the lowest
heating temperature (80 °C). As heating continues, T/C-ratios
become lower. The higher T/C-ratios observed at the lower
heating temperatures (80 and 90 °C) are connected with the
lower free energies of activation for the formation of trans-
isomers. However, the reaction is thermodynamically controlled
because of the higher stability (less free energy) of the cis-
isomers, and therefore, the T/C-ratio declines as a function of
reaction time.
As R-acid isomerization kinetics was monitored at different
temperatures, rate constants were related to the heating tem-
peratures in order to find out whether the reaction follows
Arrhenius behavior. According to the general Arrhenius eq III,
the relationship between the rate constant of the reaction and
the absolute temperature is as follows:
Also in agreement with the kinetic data (see Table 1) are
the iso-R-acids T/C-ratios measured in the course of the heating
period (Table 3). The lower the heating temperature, the higher
the T/C-ratios, i.e., the more trans-isomers and the less cis-
isomers are proportionally formed. This is due to the lower free
energy of activation of trans-isomers versus cis-isomers (see
further).
k ) Ae-E ⁄(RT)
(III)
a
where k is the rate constant (s-1), A is the pre-exponential factor
(s-1), Ea is the free energy of activation (kJmol-1), R is the gas
constant (8.314 J K-1 mol-1), and T is the absolute temperature
(K).
Moreover, when considering the evolution of the T/C-ratio
as a function of heating time, it is interesting to notice the highest
Equation III can also be expressed as follows:

6412 J. Agric. Food Chem., Vol. 56, No. 15, 2008
Jaskula et al.
Figure 3. Arrhenius behavior of formation of total iso-R-acids from R-acids; experiment 1 and experiment 2.
Figure 4. Arrhenius behavior of formation of isocohumulone, isohumulone, and isoadhumulone; experiment 1.
The activation energy related to the formation of total iso-
R-acids amounts to 96-97 kJmol-1. This result is in agreement
with the activation energy of iso-R-acid formation as measured
by others (98.6 kJmol-1; 9). Furthermore, as apparent from
Table 4, activation energies related to the formation of
isocohumulone, isohumulone, and isoadhumulone are nearly
identical. This can be ascribed to the fact that within the
transition state, the same bonds are being broken and formed
during acyloin ring contraction, regardless of the nature of the
R-acid being converted. A similar enthalpy of activation will
lead to a similar free energy of activation (Ea). Consequently,
the influence on the activation energy of the hydrocarbon residue
in the acyl side chain at C-2 of the R-acid appears to be
negligible.
ln k ) -Ea/(RT) + ln A
(IV)
A plot of ln k versus the reciprocal of the absolute temperature
1/T should be straight provided that the reaction follows
Arrhenius behavior. The slope of the line (-Ea/R) allows
calculation of the activation energy (Ea), whereas from the
intercept of the graph with the ordinate (ln k), the value of the
pre-exponential factor can be derived.
As obvious from the correlation coefficients, Figures 3, 4,
and 5 clearly demonstrate that R-acid isomerization in our
kinetic experiments follows Arrhenius behavior. This holds
true for both total iso-R-acid formation (Figure 3), formation
of isocohumulone, isohumulone, and isoadhumulone (Figure
4), and formation of individual trans- and cis-iso-R-acids
(Figure 5).
However, with respect to the formation of trans- and cis-
iso-R-acids, a difference in activation energy was always noted,
regardless of the iso-R-acid analogue being formed (see Table
4). Activation energies associated with the formation of trans-
The experimentally determined Arrhenius equations and
activation energies derived thereof are summarized in Table 4.
Clearly, when comparing the results of both independent
experiments 1 and 2, reproducible data have been obtained.

Hop R-Acid Isomerization Kinetics
J. Agric. Food Chem., Vol. 56, No. 15, 2008 6413
Figure 5. Arrhenius behavior of formation of trans-isocohumulone, cis-isocohumulone, trans-isohumulone, cis-isohumulone, trans-isoadhumulone, and
cis-isoadhumulone; experiment 1.
Table 4. Arrhenius Equation and Free Energies of Activation for Total Iso-R-acid and Individual Iso-R-acid Formation
experiment 1
Arrhenius equation
experiment 2
Arrhenius equation
Ea (kJmol-1
)
Ea (kJmol-1
)
total iso-R-acidsa
isocohumulone
isohumulone
3.13 × 109 e-11661/T
3.83 × 109 e-11673/T
3.08 × 109 e-11690/T
3.68 × 109 e-11722/T
0.07 × 109 e-10576/T
19.8 × 109 e-12443/T
0.06 × 109 e-10661/T
3.16 × 109 e-11833/T
0.23 × 109 e-11104/T
2.96 × 109 e-11797/T
97.0
97.1
97.2
97.5
87.9
103.5
88.6
98.4
92.3
98.1
2.43 × 109 e-11567/T
2.45 × 109 e-11499/T
1.77 × 109 e-11492/T
1.81 × 109 e-11456/T
0.15 × 109 e-10847/T
16.6 × 109 e-12363/T
0.09 × 109 e-10838/T
1.31 × 109 e-11505/T
0.23 × 109 e-11102/T
1.03 × 109 e-11386/T
96.2
95.6
95.5
95.3
90.2
102.8
90.1
95.7
92.3
94.7
isoadhumulone
trans-isocohumulone
cis-isocohumulone
trans-isohumulone
cis-isohumulone
trans-isoadhumulone
cis-isoadhumulone
a According to Malowicki and Shellhammer (9), the rate constant and activation energy for total iso-R-acids amount to (7.9 × 1011) e(-11858/T) min -1 and 98.6 kJmol-1
,
respectively.
iso-R-acids were on average approximately 9 kJmol-1 lower
than activation energies measured in relation to their cis-
counterparts.
of trans-iso-R-acids). As a result, the hydrogen of the hydroxyl
group at C-6 should be more readily released in the conformer
that leads to the trans-iso-R-acids, and consequently, activation
energies for the formation of trans-isomers are lower than those
of the cis-iso-R-acids.
Just like the overall free energy change of a reaction (∆G°),
the free energy of activation (∆E a) is composed of an enthalpy
factor (∆Ha) and an entropy factor (∆Sa). ∆Ea ) ∆Ha - T∆Sa.
The enthalpy of activation (∆Ha) is the difference in bond
energies between the reactant(s) and the transition state; the
entropy of activation (∆Sa) is the difference in entropy between
the reactant(s) and the transition state
For the moment, it is not clear whether the higher activation
energy associated with the formation of cis-compounds is due
to a higher change in enthalpy of activation and/or entropy of
activation, although changes in entropy with respect to the
formation of transition states are usually considered relatively
small (22).
A possible explanation of the higher activation energies
involved in cis-iso-R-acid formation may lie in the conforma-
tional differentiation of the keto form of the R-acids in the
transition state, whereby the intramolecular (very weak) hydro-
gen bond between the tertiary alcohol at C-6 and the carbonyl
at C-5 guides the outcome. Indeed, in intermediary states, the
hydrogen bond in the conformer in which the carbonyl is
pointing downward at a syn-position with the hydroxyl at C-6
(formation of cis-iso-R-acids) should be stronger than in the
conformer in which the carbonyl is pointing upward (formation
In particular, the free energy of activation associated with
the formation of cis-isocohumulone is relatively high (ap-
proximately 103 kJmol-1), when compared with the other cis-
iso-R-acids (96-97 kJmol-1). This observation may be ascribed
to the lower pKa value of cohumulone, causing more easy
formation of the anion in the ꢀ-triketo system, thus a higher
electron density within this system, which in turn may induce
a slightly higher, partial negative charge on the oxygen of the
carbonyl at C-5 in the transition state, resulting in an energeti-
cally unfavorable situation when the cis-isomer is being formed.
Notwithstanding, the lower free energy of activation associ-
ated with the formation of trans-iso-R-acids, rate constants of
trans-iso-R-acid formation are significantly lower than rate
constants of cis-iso-R-acid formation (Table 1). At first sight,
this seems to be contradictory when looking at the Arrhenius
eq III, in that normally a reaction with a lower free energy of
activation should occur faster than a reaction with a higher one.
However, further inspection of Table 4 reveals that the
explanation of this apparent contradiction lies in the differences
of the pre-exponential factors related to trans- and cis-iso-R-
acid formation, respectively. cis-Isomer formation always

6414 J. Agric. Food Chem., Vol. 56, No. 15, 2008
Jaskula et al.
cis-iso-R-acids are becoming the dominant ones because cis-
iso-R-acids are thermodynamically more stable. In accordance
with this proposed free energy diagram and thermodynamic
control of R-acids isomerization, partial conversion, i.e., reverse
isomerization, of trans-iso-R-acids via R-acids into cis-iso-R-
acids has been demonstrated by us in both heated buffer systems
and boiling wort, starting from pure trans-iso-R-acids (data not
shown). Furthermore, trans-cis interconversion was also
reported previously by Verzele and De Keukeleire (25).
In conclusion, the ionization of the ꢀ-triketo system in the
R-acids is considered as the rate-limiting step of the isomer-
ization reaction. Electron density within this ꢀ-triketo system
will be influenced by the nature of the acyl group at C-2 of the
R-acid analogue. While conforming the known basic mechanism
of hop R-acid isomerization, the kinetic study carried out in
this work, in particular results on activation energies of
individual trans- and cis-iso-R-acids, reveals new and more
detailed insight into the mechanism of the key reaction of hops
in brewing.
Figure 6. Proposed free energy diagram for the formation of trans- and
cis-iso-R-acids from R-acids (∆G °t, overall free energy change related
to the formation of trans-iso-R-acids; ∆G °c, overall free energy change
related to the formation of cis-iso-R-acids; Eat, free energy of activa-
tion related to the formation of trans-iso-R-acids; Eac, free energy of
activation related to the formation of cis-iso-R-acids).
ABBREVIATIONS USED
involves higher pre-exponential factors, which explains the
higher rate constants, despite the higher activation energies
required to attain their transition state. The higher pre-
exponential factor related to cis-iso-R-acids may suggest a higher
probability of the cis-iso-R-acid transition state to end up in
the finished product (a cis-iso-R-acid), which indeed has a lower
free energy, i.e., a higher stability from the thermodynamic point
of view than its trans-counterpart.
Finally, it can be seen from Table 4 that the pre-exponential
factor associated with isocohumulone formation is higher than
that of isohumulone and isoadhumulone formation. As men-
tioned previously, the rate constant of isocohumulone formation
is always significantly higher than the rate constants of the
formation of the other analogues. Because the activation energy
related to isocohumulone formation is not different form the
other activation energies (Table 4), its higher rate constant can
be associated with the higher pre-exponential factor, which in
turn may be related to the lower pKa value of cohumulone versus
the pKa value of the other R-acid analogues (pKa cohumulone,
4.7; pKa humulone, 5.5; pKa adhumulone, 5.7; (23)). The lower
pKa of cohumulone will lead to more efficient formation of the
required stabilized anion in the ꢀ-triketo system of the transition
state, thus resulting in a higher probability of the reaction taking
place and, ultimately, higher isomerization yields.
HPLC, high performance liquid chromatography; T/C-ratio,
(trans-isocohumulone + trans-isohumulone)/(cis-isocohumulone
+ cis-isohumulone) × 100%; PTFE, polytetrafluoroethylene.
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Received for review February 17, 2008. Revised manuscript received
April 21, 2008. Accepted May 4, 2008.
JF8004965