Water
Activity
Prediction
GUSTAVO V. BARBOSA-CÁNOVAS
Washington State University
Pullman, Washington , USA
Water Activity
9Water activity is a critical factor that determines
shelf life, influence how fast organisms will grow
in a product, and may be the most important
factor in controlling spoilage.
9By measuring water activity, it is possible to:
ƒ predict which microorganisms will and will not be
potential sources of spoilage.
ƒ have an insight on the activity of enzymes and vitamins
in foods that can have a major impact their color, taste,
and aroma.
Water Activity: Concept
The water activity scale extends from 0 (bone dry) to
1.0 (pure water)
Water Activity = aw = ρ/ρo
where ρ = water vapor pressure inside the food
ρo = vapor pressure of pure water under the
same conditions of temperature, etc.
Relative humidity = ρ/ρo
Each solute will affect the aw uniquely
WATER ACTIVITY - STABILITY DIAGRAM
Water activity (Aw) of food products
Food Product
Fruits &Vegetables
Meats
Cheese
Jams & Jellies
Honey
Noodles
Dried Milk
Crackers
Aw
0.97-1.00
0.95-1.00
0.68-1.00
0.75-0.94
0.54-0.75
0.50
0.20
0.10
Some devices used to measure water
activity in semimoist foods
LUFF Aw-Wet Messer
(Germany)
NOVASINA Thermoconstanter
(Switzerland)
Fiber-dimensional hygrometer
VAISALA Humicap (Finland)
Electrical capacitance of polymer thin
film
DECAGON Aqualab (U.S.A.)
Dew point by the chilled mirror
technique
OTTAWA aw-Meter (Canada)
Thermometric device suited to establish
compliance or non-compliance of test
samples with a standard
NAGY aw-Kryometer (Germany)
Cryoscopic measurements; initial
freezing point
Electrical conductivity of immobilized
salt solutions
Procedure for calculation of
Aw in semimoist foods
Prediction of Water Activity
%\0DWKHPDWLFDO0RGHOV
Has been limited to aqueous
solutions of electrolyte and
non electrolyte solutes
Raoult’s Law
y i P = xi Pi
0
Where
¾ P is the system pressure
¾ Pi0 is the saturation vapor pressure of the pure solvent
¾ yi and xi are the mole fraction of a particular component
in the vapor and liquid phases respectively
The application of Raoult’s Law to food systems is not
practical because of solvent-solute interactions.
Raoult’s Law
„
Assumes water activity lowering due to
solute (range 0.95 to 1.0)
„ All solute dissolved in all water
„ No between solute interaction
http://courses.che.umn.edu/02fscn43421s/Lecture_Folder/Topic%207-3Color.pdf
Prediction of Water Activity
%\0DWKHPDWLFDO0RGHOV
Water activity can be estimated by
different theoretical and empirical models
considering the types of solutes in the
solution:
¾Electrolytes
¾Nonelectrolytes
¾Mixtures
Prediction of Water Activity
%\0DWKHPDWLFDO0RGHOV
Non-electrolytes solutions
¾Money and Born Equation
¾Grover Equation
¾Norrish Equation
¾Teng and Lenzi
Prediction of Water Activity
0RQH\DQG%RUQ(TXDWLRQ
1.0
aw =
(1.0 + 0.27n )
where n is the number of moles of sugar per 100 g of water.
9This empirical equation is use for calculating Aw of sugar
confections, such as jams, fondant creams and boiled sweets.
Prediction of Water Activity
*URYHU(TXDWLRQ
2
a w = 1.04 − 0.1isici + 0.0045i (sici )
where
¾
Ci is the concentration of component i
¾
Si is the sucrose equivalent for different ingredients
such as lactose (1.0), invert sugar (1.3), 45DE corn
syrup (0.8), and gelatin (1.3).
The Grover model is an empirical approach to estimated Aw
in candy formulations.
Prediction of Water Activity
1RUULVK(TXDWLRQ
log (aw/xw) = -ki(1-xw
2
)
xw = mole fraction of water
ki = Norrish constant for ingredient i
9 Norrish equation takes into account a nonideal thermodynamic
approach to determine the Aw of binary mixtures.
9 Norrish Equation - accounts for water binding properties of the
solute and is more useful for large concentrations of solute.
Example
1RUULVK(TXDWLRQ
„
The water activity of a glucose-water solution (2.44:1
wt/wt) can be estimated by means of the Norrish equation.
The mole fractions are: X1 = 0.804 and X2 = 0.196. The
Norrish constant for glucose.is 2.25. Substituting for the
values in the Norrish equation results in an estimated
water activity of 0.74.
log (aw/xw) = -ki(1-xw
2
)
Example
1RUULVK(TXDWLRQ
„
The experimental water activity of this mixture is
reported as 0.78 (Teng and Seow, 1981).
„
The use of Raoult’s law gives a water activity
estimate of 0.80.
Prediction of Water Activity
7HQJDQG/HQ]L (TXDWLRQ
i
a w = 1 + ∑ i Ai m
For i=1 to k
Where Ai is the polynomial coefficient, m is the
solute molality, and k is the degree of the
polynomial
Prediction of Water Activity
%\0DWKHPDWLFDO0RGHOV
Electrolytes solutions
¾Pitzer Equation
¾Bromley Equation
Prediction of Water Activity
3LW]HU(TXDWLRQ
a w = exp( −0.01802φΣi M i )
Where φ is the
osmotic coefficient,
zm and zx are the
charges of m and x
ions, vm and vx are
the respective
number of ions, M
is the solution
molality. B(0),
B(1), Bmx and C are
the Pitzer
coefficients.
Example
3LW]HU(TXDWLRQ
Example
3LW]HU(TXDWLRQ
9An electrolyte 1:1 type is in solution(e.g., a solution
of NaCl, 2.31 molal at 25°C).
9The Pitzer's Bmx(0), Bmx(l), and Cmx parameters for
NaCl are 0.0765, 0.2664, and 0.00127, respectively.
The following can be defined for the ions: zNa = 1,
zCl = 1, νNa = 1, and νCl = 1.
9The osmotic coefficient is evaluated from equation:
Φ=-1000 lnas/(Ms∑νrmr)
Example
3LW]HU(TXDWLRQ
mNa=2.31
F = -0.211
mCl=2.31
I=2.31
BNaCl = 0.089
zNazCl  =1.0
Φ = 1.001
Water activity is evaluated from Equation:
a w = exp( −0.01802φΣi M i )
aw = exp(-0.01802 x 1.001 X (2.31 + 2.31 a, = 0.92
The experimental water activity of this mixture is 0.92 (Teng
and Seow, 1981).
Prediction of Water Activity
%URPOH\(TXDWLRQ
Where φ is the
osmotic
coefficient, zm
and zx are the
charges of m
and x ions, vm
and vx are the
a w = exp( −0.01802φΣi M i )
respective number of ions. M
is the solution molality, I is
the ionic strength. B, Bm, Bx,
δm, δx are the Bromley
coefficients.
Example
%URPOH\(TXDWLRQ
The Bromley B parameter is equal to 0.0574 for the
NaCl. The ionic strength I=2.31 and the charge product
zNazCl  =1.0.
•Substituting these values gives in the equations
presented above:
T1 = -0.0615
T2 = -0.0226
a = 1.5
The osmotic coefficient (Φ ) and the water activity are:
Φ = 1.0062
aw = 0.919
Prediction of Water Activity
%\0DWKHPDWLFDO0RGHOV
Multicomponents Mixtures
¾Ross Equation
¾Ferro-Fontán-Benmergui-Chirife
Equation
¾Ferro-Chirife-Boquet Equation
¾Lang-Steinberg Equation
¾Pitzer-Kim Equation
Procedure for calculation of
Aw in semimoist foods
Prediction of Water Activity
5RVV(TXDWLRQ
0
aw = Πi (aw )i
aw0=water activity of each component in the binary mixture
Prediction of Water Activity
)HUUR)RQWiQ%HQPHUJXL&KLULIH(TXDWLRQ
Ii
a w = Π i ( a wi ( I )) I
I i = 0 .5 vi m i Z m Z x
awi(I)= water activity of a binary solution of I at the same total ionic strength (I)
of the multicomponent solution. Ii is the ionic strength of component i in the
mixture, vi is the total of ions of the solute i in solution, mi is the molality of the
solute, and zm and zx are the charges of m and x ions.
Prediction of Water Activity
)HUUR&KLULIH%RTXHW (TXDWLRQ
2
(aw)m = X1exp(−Km X2 )
 Mt
K m = ∑ K s C s 
s=1
 Ms
n




 n  Cs
M t =  ∑ 
 s = 1  M s



 
−1
X1 and X2 are the molar fractions of the solvent and solutes, Ks is the Norrish K
value for each solute in the mixture, Cs is the weight ratio of each solute to the
total of solids in the mixture, and Ms is the molecular weight of each component
Example
)HUUR&KLULIH%RTXHW (TXDWLRQ
A solution of glucose (5.96% wt/wt) and sucrose
(46.01%wt/wt) has a measured water activity of
0.926 (Teng and Seow,198l). The K values of
glucose and sucrose are 2.25 and 6.47,
respectively. The Km and Mt values are evaluated
from equations mentioned above.
Km = 5.65
Mt = 310.82
Then, the predicted water activity using FerroChirife-Boquet equation is 0.923.
Prediction of Water Activity
/DQJ6WHLQEHUJ (TXDWLRQ
Log(1 − a ) = ( MW − ∑ ai wi ) / ∑ bi wi
w
Where ai and bi are the Smith equation constants for each component i in
the mixture. M is the moisture content of the mixture, W is the total dry
material of the mixture, wi is the dry material of each component i in the
mixture.
9The model may predict water activities over the
range 0.30 to 0.95 of a multicomponent mixture
Example
/DQJ6WHLQEHUJ (TXDWLRQ
A mixture of starch (0.79 g/g of total sample) and
sucrose (0.09 g/g of total sample) has a moisture
con- tent of 0.219 g of water/g of solids at an aw of
0.90. The Smith constants for each component are
(Lang and Stein- berg, 1981):
Starch: ai = 0.0989
bi = -0. 1485
Sucrose: ai = -0.5944
bi = 1.2573
Example
/DQJ6WHLQEHUJ (TXDWLRQ
Rearranging the data in terms of the Lang and
Steinberg model:
M=0.29gofwater/g of solid
W=0.89g of solids
(ai wi)starch= 0.08 g of water
(ai wi)sucrose = -0.06 g of water
(biwi)starch=-0.12g of water
(biwi)sucrose=0.13g of water
Replacing the above values in Lang-Steinberg equation
and taking the log10 to base 10:
aw = 0.90
Prediction of Water Activity
3LW]HU.LP (TXDWLRQ
{
φ − 1 = (∑ mi )−1 IF'−F ) +∑ i ∑ j mim j (λij + Iλ'ij ) + 2∑ i ∑ j ∑ k mim jmk µijk
F = − 0 . 392 I 0 . 5 /( 1 + 1 . 2 I 0 . 5 )
F = dF / dI
λ ' ij = d λ ij / dI
Where m is the molality of a particular ion (i,j,or k). λij is the second
virial coefficient, µijk is the third virial coefficient, and I is the ionic
strength.
}
Example
3LW]HU.LP (TXDWLRQ
An aqueous solution of NaCl (9.29% wt/wt) and LiCl (1.57%
wt/wt) has an experimental water activity of 0.9312 (Tsong and
Seow, 1981). Pitzer and Kim equation can be expressed as
where Bij, F and I are
evaluated by
Example
3LW]HU.LP (TXDWLRQ
I = 2.198
CNaCl = 0.00127
F = -0.2087
CLiCl = 0.0036
BNaCL = 0.0902
∑ mi = 4.408
BLiCl = 0.1652
∑ mz = 4.408
¾The predicted values for the osmotic coefficient and water
activity are the following:
Φ = 1.0811
aw= 0.92
Prediction of Water Activity
6DOZLQ6ODZVRQ (TXDWLRQ
∑ i ai si wi
aw =
∑ i si wi
Where ai is the initial water activity of component i used in the mixture, si
is the sorption isotherm slope of component i at the mixture temperature,
and wi is the dry weight of component i.
Prediction of Water Activity
5RD7DSLD0RGHO
Based on the concept proposed by Salwin and Slawson, and
the linear relationship of Favetto and Chirife (1985).
awM =1− ∑ Kimi
i
Where awM= water activity in equilibrium state o final of a
complex mixture, k = constant of Faveto and Chirife equation at
25°C[kg w/g mol], m = molality and i= number of solutes in a
complex mixture.
Prediction of Water Activity
%\&RPSXWHU3URJUDPV
ÂVega-Mercado H., Romanach B.,
Barbosa-Cánovas G.V. et al, Developed
an Interactive Computer Program to
accurately predict the Aw of
multicomponent systems containing
fiber, proteins and fats
Prediction of Water Activity
%\&RPSXWHU3URJUDPV
ÂProgram Capabilities
ƒ Predict Aw of model food systems by several well
accepted equations (Bromley, Pitzer, Norrish,
Ferro-Cherife-Boquet, Ross, Ferro BenmerguiCherife)
ƒ Establish similarity levels between foods of
known aw and composition to new products
where composition is available
Prediction of Water Activity
%\&RPSXWHU3URJUDPV
ÂProgram Capabilities
ƒ Calculate deviation factors based on
previously established similarity levels,
where the presence of fibers, fats and
proteins is taken into account
ƒ Programmed in MS-DOS QBASIC 1.0,
available from the authors
Prediction of Water Activity
%\&RPSXWHU3URJUDPV
ÂThe accuracy of the predicted aw is affected
when the algorithm is applied to food systems
which contain fats and proteins.
ÂFood products containing fats and proteins
show a deviation factor of 1.07, on average,
after one iteration.
ÂThe discrepancy in aw values, awpred and awrep,
can be explained in terms of water bound on
proteins or associated with fatty mesomorphic
structures.
Procedure for calculation of
Aw in semimoist foods
•http://courses.che.umn.edu/02fscn4342-1s/default.html
•http://fscn.che.umn.edu/Ted_Labuza/PDF_files/Presentations/A
w&Kinetics.pdf
•http://fscn.che.umn.edu/Ted_Labuza/PDF_files/Presentations/
AwTgKinetics.pdf
•http://fscn.che.umn.edu/Ted_Labuza/PDF_files/Presentations/
Multidomain.pdf
•http://courses.che.umn.edu/02fscn43421s/Lecture_Folder/Topic%202-Water%20bonding3color.pdf
Thank you!!