CALCIUM CONTENT OF MILK
FINAL REPORT FOR BE 210 – BIOENGINEERING LAB II
DR. MITCHELL LITT
APRIL 29, 1998
Group W8
MINHTHE LUU
SOFIYA KUCHUK
ANIL SEETHARAM
ADRIAN SHIEH
Abstract
The objectives of the experiment were to experimentally determine the
calcium content in milk through atomic absorption spectrophotometry and to
ascertain whether the standard method described by Perkins-Elmer Co. for
calcium determination in milk using atomic absorption spectrophotometry is the
most viable procedure.
The calcium content of four different types of commercially available cow’s
milk was determined using a flame atomic absorption spectrophotometer. Milk
was treated with one or both of two reagents, trichloroacetic acid and lanthanum
chloride. The addition of lanthanum only was found to be most efficient on the
basis of accuracy, speed, and cost. Using this method, the calcium content (in
ppm) of whole, 2%, 1% and skim milk were found to be 1218  5.21%, 1158 
0.79%, 1175  1.53% and 1154  1.53%, respectively.
1
Background
Milk is a complex mixture of emulsified lipids and proteins, in addition to
other dissolved components such as lactose, vitamins, and minerals. Milk is
known for its high calcium content. In milk, calcium exists both as an ion and as
Ca9(PO4)6 bound to the protein casein (Dairy Science & Technology). Casein is
the major protein in milk, and it forms spherical submicelles due to its
hydrophobic nature. These submicelles clump together due to the interactions
between Ca9(PO4)6 and -casein (Figure 1). Anywhere from 75% to 90% of the
calcium present in cow’s milk is bound to casein (Hurley) (Dairy Science &
Technology).
Milk must undergo several different stages of processing before it can be
sent to the market (Figure 2). The first stage is clarification, standardization, and
separation. The milk is centrifuged to remove fat and solid impurities. Cream is
reintroduced to the purified milk if necessary (to make non-skim milk).
The
second stage, pasteurization, is a process that eliminates most bacteria from milk
by heating it over an extended period of time.
The third process,
homogenization, reduces the size of fat globules in milk. Finally, the milk is
fortified with nutrients such as vitamins A & D, and possibly calcium if the milk is
of the calcium-enriched variety (Dairy Science & Technology). It is important
that, in processing the milk, there is no mechanism by which dairy producers
change the calcium concentration. Except for enriched milk, the calcium present
in the raw milk is essentially unchanged after processing. Therefore, the calcium
concentration in milk depends on the calcium in the diet of the cows.
To determine the total calcium content in milk, it is necessary to dissociate
the calcium ion from the calcium-casein complex. This is typically accomplished
by acid precipitation of casein. Acid liberates calcium from casein, causing the
insoluble
phosphoprotein
to
precipitate
(Laboratory
of
Crystallography).
Precipitation of the protein also means that it can be easily removed to prevent
clogging of the spectrophotometer. Another consideration is interference with
calcium caused by the formation of calcium-phosphorus and calcium-sulfur
2
compounds. These compounds cannot be easily dissociated in the flame.
Lanthanum or strontium are added to compete with calcium for phosphorus, to
prevent formation of Ca-P molecules (McKenzie, 174). Sodium, magnesium and
potassium can also cause interference, but only at concentrations of 500 ppm or
more, higher than concentrations typically found in milk (Stable Isotope Lab, U. of
Ga.).
Methods and theory related to the use of the atomic absorption
spectrophotometer can be found in the Bioengineering Laboratory II Manual.
3
Figure 1: Diagram of the casein submicelle and micelle structures(Dairy Science & Technology).
Figure 2: A flow chart of the processing milk undergoes from a raw state to
packaging (Dairy Science & Technology).
4
Materials & Apparatus
1. Trichloroacetic acid, Sigma-Aldrich (100% w/v, 6.1N)
2. Lanthanum chloride, Sigma-Aldrich
3. Milk (Wawa brand – skim, 1% milk fat, 2% milk fat, whole)
4. Perkin-Elmer Model AA 4000 atomic absorption spectrophotometer
5. Miscellaneous glassware
6. 15 & 50 mL plastic flasks
7. Stir plate
8. International Equipment Company Model PR-7000 centrifuge
9. Digital micropipetters- P-20, P-200, P-1000
10. Pipet-Aid
Procedure
Overview
This lab required the preparation of three stock solutions to be used to
calibrate the AAS. These solutions were diluted calcium stock solutions with the
following reagents: (1) TCA + La, (2) La only, and (3) TCA only. In addition,
twelve test milk solutions were prepared by treating each of the four milk samples
with the above reagents. The following is a detailed outline of the preparation of
these solutions.
Day One
The first task was preparation of the necessary solutions. The solutions
and subsequent dilutions were made with deionized water.
The lanthanum
solution was made by taking 8.828g of LaCl3 and mixing with 100 mL of
deionized water, to produce a 5% w/v solution. The lab coordinator provided a
1000 ppm Ca standard and 100% w/v TCA. Before the measurements were
taken on the AAS it was configured to test for calcium. Bulb two was selected
with the current at 10 mA, slit size 0.7L, and wavelength of 422.7 nm. The
5
optimum fuel rate, after experimenting with tap water (which is calcium-rich) and
different fuel-air settings, was determined to be 18 fuel to 45 air.
The first task was to prepare the different kinds of calibration solutions.
The solutions made were calcium plus TCA and La solution, calcium with TCA
only, and calcium with La solution only. The only solutions used the first day
were the TCA plus La solutions, the rest were stored for days two and three.
1. Preparation of calibration stock
Prepared stock Ca solutions (1-6 ppm) with TCA + La/TCA/La and blanks
(no Ca). For X ppm, use X * 10 L Ca stock
a. for TCA-lanthanum: (e.g. 1ppm) 10L Ca stock + 120L TCA + 1mL
lanthanum and diluted up to 10mL

the blank was constructed by taking 120L TCA + 1mL lanthanum
and diluting up to 10mL
b. for TCA only: 10L Ca stock + 120L TCA and diluted up to 10mL

the blank was constructed by taking 120L TCA and diluting up to
10mL
c. for lanthanum only: 10L Ca stock + 1mL lanthanum and diluted up to
10mL

the blank was constructed by taking 1mL lanthanum and diluting up
to 10mL
On day one, the milk samples were prepared. The milk was treated with
TCA to precipitate out the proteins.
After the milk was centrifuged, the
supernatant was used to make three different dilutions of calcium. An equal
amount of La was added to each. These samples were tested in the AAS. For
the first day, only the milk samples containing both TCA and La were tested.
2. Preparation of milk sample
Milk types: Skim, 1% low fat, 2% low fat, whole
A. For sample with TCA & Lanthanum:
6
a. 500 L milk + 1.2 mL TCA dilute to 10mL
b. shake at five minute intervals for 30 minutes
c. centrifuge at 8oC, 2500 RPM, 5 min.
d. transfer the supernatant into a different vial to store for future use
e. three concentrations of each milk sample were made from the
supernatant

200L milk stock + 500L lanthanum and diluted up to 5mL

300L milk stock + 500L lanthanum and diluted up to 5mL

400L milk stock + 500L lanthanum and diluted up to 5mL
f. the samples were tested using AAS
The calibration stock and supernatant from the milk was saved for use on
days two and three.
Day Two
On day two, using the supernatant from day one two different treatments
were performed. One of them contained both TCA and La, the other contained
only TCA.
From the original milk stock a treatment containing La only was
performed. During this treatment the milk was diluted and centrifuged as before,
except no TCA was added to precipitate the proteins.
treatments only one concentration was prepared.
From all the three
Instead of making three
different concentrations, a dilution factor of 333 was used since it was found to
be the most favorable concentration.
2. Preparation of milk sample (continuation from day one)
B. For sample with TCA and lanthanum:
a. using the supernatant from A, a 3ppm concentration of each milk type
was made

300L milk stock + 500L lanthanum diluted up to 5mL
b. calibration curve was constructed using stock (part 1a)
c. samples were analyzed using AAS
7
C. For sample with TCA only:
b. using the supernatant from A. a 3ppm concentration of each milk type
was made

300L milk stock diluted up to 5mL
b. calibration curve was constructed using stock (part 1b)
c. samples were analyzed using AAS
D. For sample with lanthanum only:
a. 500 L milk was diluted to 10 mL
b. centrifuge at 8oC, 2500 RPM, 5 min
c. no pellet formed, consider all as a supernatant
d. three concentrations of each milk sample were made from the
supernatant

300L milk stock + 500L lanthanum and diluted up to 5mL
e. calibration curve was constructed using stock (part 1c)
f. samples were analyzed using AAS
Day Three
On day three, the focus was on two treatments only, TCA + La and La
only.
It was decided that further testing of TCA only samples would not be
performed, since on day two the results obtained made it obvious that La was a
necessary component in the solution. For the two treatments performed new
milk stock was prepared for both as well a calibration stock for TCA with La.
Three aliquots were taken from each milk sample to provide a larger sample size
to facilitate statistical analysis of the results.
sections B and D from day two are unchanged.
8
Otherwise, the procedures for
Results
A calibration curve was constructed for each milk treatment (See
Procedure for more details about stock preparation). The equation of the best-fit
line of each curve was used to calculate the concentration of Ca2+ in the samples
given the AAS-generated absorbance measurements. Figure 1 is an example of
a calibration curve. Concentrations used to plot these curves were selected to lie
within the optimum detection range of calcium for the AAS: 0.2 ppm to 7 ppm.
Calibration curve for TCA + La treatment
0.4
Absorbance
0.3
A = (0.0514 ppm-1) C - 0.002
R2 = 0.9995
0.2
0.1
0
0
1
2
3
4
5
6
7
Concentration Ca (ppm)
Figure 1: A representative calibration curve, in this case, the plot for the TCA + La
treatments series, Day 3.
The following graphs give the measured mean concentrations for each
milk type and treatment. A clear observation that can be made is that all
experimental results are less than the expected (USDA) results. A second
observation is that the measured concentrations for all samples tested with TCA
alone were significantly lower than those of the other tests.
9
Calcium content of Whole milk, by treatment
Concentration (ppm)
1400
1200
1000
1230
1202
1218
TCA + La
800
TCA
600
La
Fed. Std
661
400
200
0
Figure 2: A comparison of measured calcium content using the three methods
described in Procedure. Note: Approximately 50% decrease in calcium
detection when using TCA only.
Calcium content of 2% milk, by treatment
1400
Concentration (ppm)
1200
1255
1000
800
1158
1111
TCA
La
600
400
TCA + La
Fed. Std.
659
200
0
Figure 3: Summary of calcium content for 2% milk for three procedures tested.
10
Calcium content of 1% milk, by treatment
1400
Concentration (ppm)
1200
1268
1000
1226
1175
TCA + La
800
TCA
600
La
Fed. Std.
669
400
200
0
Figure 4: Summary of calcium content for 1% milk for the three procedures tested.
Calcium content of Skim milk, by treatment
1400
Concentration (ppm)
1200
1276
1000
1154
1130
TCA + La
800
TCA
600
La
400
Fed. Std.
630
200
0
Figure 5: Summary of calcium content for skim milk for the three procedures tested.
Statistical Analysis
Two statistical tests were used to compare the data collected in the
experiment.
To determine whether or not a significant difference existed
between the calcium content of different types of milk, a single-factor analysis of
variance (ANOVA) test was employed. This statistical test is used typically to
analyze populations of data where more than two different treatments of one
11
factor are used, e.g. four different milk types (Devore, 390). A two-sample t-test
was used to compare different treatments of the sample milk type.
The
variances of the two samples were not assumed equal (12  22). This test is
typically used to compare two distinct groups of data. In this case, the distinction
between the populations is the treatment method used on the milk samples
(Devore, 357).
t-Test: Two-Sample between two treatments
(TCA & La and La only)
Milk Type
t-stat
t-critical
Whole
2%
1%
Skim
-0.505
1.76
-6.186
1.70
4.381
1.71
-2.385
1.73
Table 1: Two-Sample t-test with unequal variances shows there is no significant statistical
difference within whole, 2% and Skim between TCA & La versus La only treatments, while for 1%
there is a difference.
ANOVA single factor: between milk types
Treatment
F
F-critical
TCA & La
68.83
2.72
La
TCA
2.94
2.81
13.23
4.07
Table 2: ANOVA single factor test was performed within milk treatment groups between the four
milk types. The test showed a significant difference for TCA & La treatment as well as the TCA
only treatment. For the La only treatment a smaller, but still significant, difference was found.
Milk Type
Dairy Council
(ppm)
USDA (ppm)
Whole
2%
1%
Skim
1230
1194+0.41%
1255
1216
1268
1230
1276
1234+4.02%
Table 3: The data in the left column were quoted as Federal standards by the Dairy Council of
California. The USDA standards in the right column are drawn from a nutrient database collected
from different independent research groups. The database listed standard error and number of
samples for the whole and skim standards. This data was used to determine the 95% confidence
interval shown in the table.
12
The sum of the 95% confidence and propagated error data listed in Table
4 gives the percent-wise interval around the mean that is valid for each result.
For example, this interval for whole milk treated with TCA + La would be  8.18%
about the mean.
Milk
Type
Whole
2%
1%
Skim
Milk
Propagated
95%
Treatments
Error
confidence
intervals
TCA & La
TCA
La
TCA & La
TCA
La
TCA & La
TCA
La
TCA & La
TCA
La
6.79%
11.74%
6.24%
6.98%
11.77%
6.35%
6.74%
11.67%
6.32%
6.96%
12.06%
6.36%
1.39%
1.34%
5.21%
1.06%
1.55%
0.79%
1.10%
1.32%
1.53%
1.10%
1.32%
1.53%
% Error,
Dairy
Council
% Error,
USDA
2.27%
46.24%
1.00%
11.48%
47.54%
7.72%
3.35%
47.24%
7.31%
11.47%
50.65%
9.57%
0.67%
44.62%
1.98%
8.62%
45.84%
4.74%
0.37%
45.61%
4.45%
8.43%
48.96%
6.46%
Table 4: Summary table of error found in each milk type and treatment given with respect to the
Dairy Council of California and USDA values. The propagated error was determined using the
exact differential approach (See Appendix).
13
Discussion
The experimental results showed statistically significant differences
between the calcium concentrations of the four milk types tested, in all treatment
groups. The statistical analysis (using the single-factor ANOVA method) shows
that calcium content does depend on the type (fat content) of milk. It does not
elucidate the nature of the correlation. Literature values report a general trend of
increasing calcium concentration with decreased milk fat.
This is a logical
conclusion since the lipids in milk do not contain calcium. As the fraction of fat by
volume increases, the amount of protein and water (where the calcium resides)
per unit volume decreases.
Three methods of treating the milk were compared to determine if the
protocol described in the Perkins-Elmer spectrophotometry manual and Milk
Proteins (McKenzie) was the most efficient procedure available. The results of
the milk treated with TCA only showed a significantly lower measured content of
Ca2+ ions. This is attributed to interference caused by the formation of calcium
compounds, such as calcium phosphate and sulfate, which are not easily
dissociated in the flame. Without the addition of lanthanum to compete with
calcium for these anions, these compounds form readily and result in
approximately 45-50% reduction in detectable calcium content. The data clearly
shows that lanthanum is necessary to prevent interference with calcium caused
by sulfur and phosphorus.
The addition method, the protocol of adding
lanthanum or strontium to milk to prevent interference, is the accepted procedure
when determining the content of calcium in milk (McKenzie, 174-175).
The results for the lanthanum only treatment and the TCA and lanthanum
treatment (described by Perkins-Elmer) did not show significant differences in
calcium content.
TCA was selected as a reagent to precipitate the protein
casein. These proteins bind with calcium and account for 75% of total calcium
content of cow’s milk. It was necessary to liberate the calcium from the protein
molecule. The data collected, however, does not show any significant variation
between the two different treatment groups. The conclusion is that the flame was
14
sufficiently hot to denature the protein and dissociate the calcium from the casein
micelles. If this is the case, prior degradation of the protein molecules is not
necessary. The conclusion from the results is that the addition of lanthanum, or
any other element that exhibits similar favorable properties, is important in
preventing interference with calcium due to the formation of calcium sulfate and
calcium phosphate. However, acid precipitation of casein is not necessary. The
most cost-effective and least labor-intensive method is the dilution of pure milk
and addition of lanthanum only.
The conclusion regarding the most efficient treatment to determine the
calcium concentration of milk may seem incongruous: sources cited in this paper
recommend treating milk with TCA as well. The results of this report seem to
suggest that not only is lanthanum treatment the most effective way to treat milk,
but prevention of interference with lanthanum is the more important treatment
step when testing milk. This is further evidenced by the observation that the TCA
only treatment released just half of the total calcium in milk.
Precision & Error Analysis
Atomic absorption spectrophotometry is typically considered a very
precise method for the determination of ion concentrations. The instrument itself
provides excellent readings, and, when properly used, can yield excellent results.
The primary sources of systematic error in this experiment, as determined by
using the exact differential method, were the calibration curve and precision of
instruments used in diluting the samples (see Appendix). The calibration curve
regressions showed a good degree of fit (R2 > 0.995), but there are statistical
uncertainties in the calculated slopes and intercepts of the calibration curves in
the form of 95% confidence limits. The dilution factor is similarly a source of
propagated uncertainty. Successive dilutions using the digital micropipetters can
result in as much as a 2.70% variation in the dilution factor.
15
Further Considerations
One possible avenue of continued experimentation is determining the
calcium content of milk from alternative sources. Currently, cow’s milk is by far
the most prevalent dairy source. There does exist a small market for exotic dairy
products derived from goat and yak milk, among others. There are also nondairy alternatives like soymilk. One question that could be asked is whether
cow’s milk is the ideal source for nutritional calcium.
Clearly, other
considerations besides the calcium content of determine milk’s nutritional value,
including the presence of proteins, sugars, and other dissolved nutrients. For
example, lactose intolerance prevents a significant portion of the population from
consuming cow’s milk and derivative products. Dairy products, however, are
nutritionally important primarily because they are the most enriched source of
calcium found among the four food groups. Some studies have already been
done on milk from different species of mammals, and these could serve as
starting points (Hurley).
Another possible experiment would be to determine the amount of
interference caused at different concentrations of calcium.
This could be
accomplished using recovery spiking. Furthermore, a relationship between the
concentration of lanthanum and the amount of interference (if any) that occurs
could also be quantified. Knowing the optimum amount of lanthanum to inhibit
interference of a given concentration of calcium would allow researchers to limit
the amount of lanthanum used.
16
References
1.
Bioengineering Laboratory II Manual.
Spring 1998.
2.
“Dairy Nutrition”. Dairy Council of California.
http://www.dairycouncilofca.org. © 1997
3.
“Dairy Science and Technology”. University of Guelph.
http://www.foodsci.uoguelph.ca/dairyedu/home.html.
4.
“Determination of Metals in Milk.” FP-11. Perkins-Elmer AAS Manual.
5.
Devore, Jay L. Probability and Statistics for Engineering and the Sciences,
4th ed. Duxbury Press: New York, 1995.
6.
Hurley, Walter L. “Lactation Biology”. Department of Animal Sciences,
University of Illinois. http://classes.aces.uiuc.edu/AnSci308/index.html.
Jan. 26, 1997.
7.
McKenzie, Hugh A., ed. Milk Proteins, Vol. 1. Academic Press: New York,
1970.
8.
“Metals Analysis by Flame Atomic Absorption Spectrophotometry”. Stable
Isotope Laboratory, Institute of Ecology, University of Georgia.
http://www.uga.edu/~sisbl/aaspec.html. July 22, 1997.
9.
“Preparation of Casein from Skim Milk.” Laboratorium voor kristallografie,
Universiteit van Amsterdam.
http://krop.chem.uva.nl/bart/casein_prep.html.
10.
“USDA Nutrient Database for Standard Reference, Release 12”. Nutrient
Data Laboratory, United States Department of Agriculture.
http://www.nal.usda.gov/fnic/foodcomp/. March 30, 1998.
17
Department of Bioengineering,
Appendix: Determination of Systematic Error
Systematic error was quantified using the exact differential method,
summarized in the following equation:
F(x,y,z) = F/xx + F/yy + F/zz, where x, y, and z
are the uncertainty values associated with their respective variables
The equation used to determine the concentration of milk is:
Cmilk = [D(A – b)]/m
D = dilution factor of sample; A = absorbance of sample; b = y-intercept of
calibration curve; m = slope of calibration curve (in ppm -1)
The dilution factor was calculated using the equation:
D = (V1V2)/(VmilkVtreated)
V1 = final volume of initial dilution; V2 = final volume of final dilution; Vmilk =
volume of milk used in initial dilution; Vtreated = volume of treated milk used
in final dilution
Using these two formulas, the systematic error in the dilution factor and in the
concentration of calcium can be determined:
D = V2/(VmilkVtreated) V1 + V1/(VmilkVtreated) V2 +
(V1V2)/(VtreatedVmilk2) Vmilk + (V1V2)/(VmilkVtreated2) Vtreated
V1 = 0.1 mL; V1 = 10 mL
V2 = 0.05 mL; V2 = 5 mL
Vmilk = 5 mL; Vmilk = 0.001 mL
Vtreated = 0.001 mL; Vtreated = 0.2-0.4 mL
Cmilk = D/mA + -D/mb + D(b-A)/m2m + (A - b)/mD
Values inputted for this equation depend on the sample and test group to
which it belonged.
These two formulas were used to calculate the propagated error values quoted in
Results, Table 4.
18