CLIN. CHEM. 22/7,
1084-1088
(1976)
Concurrent Determination of Total Serum
Calcium and Magnesium by Thermometric
Titration with Ethylenediaminetetraacetate
Robert H. Callicott2 and Peter W. Carr”3
Total serum calcium and magnesium may be determined
in one thermometric
titration, with disodium ethylenediaminetetraacetate
as the titrant. A 1-mi serum sample is
diluted with 1 ml of tris(hydroxymethyl)aminomethane
buffer (pH 8) and titrated ata constant rate with a motonzed
syringe buret. Results by the thermometric method compared well with those by atomic absorption spectroscopy.
Additional Keyphrases:
thermal analysis
#{149}ethylene glycol
bis(2-aminoethyl ether)-N,N,N’ ,N’ -tetraacetic acid #{149}cyclohexane-diaminetetraacetic
acid #{149} nitriotriacetic acid #{149}
atomic absorption spectroscopy compared
#{149} pediatric
chemistry
Because of its very narrow range in normal serum,
total calcium must be determined
accurately
and precisely if the results are to have any clinical significance.
Because
the normal range for total serum calcium is
about 2.25 to 2.75 mmol/liter
(1), an error exceeding 0.1
mmol/liter
is intolerable
(2). The normal range for total
serum magnesium
is also narrow (0.8 to 1.0 mmol/liter)
(1), and so it must also be determined
accurately.
Many methods are available for determining
calcium
or magnesium,
including complexometric
titrations
with
either visual (3), photometric
(4), or fluorometric
(5)
end-point,
atomic absorption
spectroscopy
(6), or colorimetry
with the use of complexing
dyes (7).
Complexometric
titrations
for determining
ions of
alkaline earth metals were introduced
by Biedermann
and Schwarzenbach
in 1948 (8). Since then, many papers have described
the determination
of calcium or
magnesium,
or both, with use of complexing
agents and
of various means of end-point
detection.
Atomic absorption
spectroscopy
was introduced
to the clinical
laboratory
in 1960 by Willis (6); its application
to
analysis
for metal ions in the clinical laboratory
has
grown steadily; e.g., more than 20 papers deal with determination
of total serum calcium (2). The method of
‘Department
30602.
2
University
Procter and Gamble Co., Cincinnati,
3To
whom
Received
1084
of Chemistry,
requests
for reprints
May 8, 1975; accepted
CLINICAL CHEMISTRY,
should
April
of Georgia,
Ohio 45252..
be addressed.
13, 1976.
Vol. 22, No. 7, 1976
Athens,
Ga
colorimetrically
determining
calcium by complexing
it
with a dye such as cresolphthalein
complexone
(7) has
proven to be useful and easily adapted
for mechanization. Several methods
have also been proposed
for the
simultaneous
determination
of calcium and magnesium.
These include a titration
procedure
with an end-point
obtained
photometrically
(9) and a dual-beam
atomic
absorption
system (10).
Here, we describe the concurrent
measurement
of the
individual
concentrations
of calcium and magnesium
via a single thermometric
titration
with ethylenediaminetetraacetate.
The accuracy and precision
of this
method
compare
very favorably
with the atomic absorption
method and therefore
may be useful as an alternative
method
for determining
total calcium
and
magnesium
in serum.
Materials and Methods
instruments
All of the thermometric
titrations
were performed
in
a 2-ml Dewar flask immersed
in a water bath controlled
to 25 ± 0.005 #{176}C
(range). Temperature
changes were
monitored
with an ac Wheatstone
bridge incorporating
a phase-lock
amplification
system (11). The titrant was
continuously
added from a 50-ml Model 1705 syringe
(Hamilton
Co., Reno, Nev. 89510) driven by a Model
234-2 pump (Sage Instruments,
Inc., Cambridge,
Mass.
02139). The titrant
was pumped
into the Dewar flask
through narrow-bore
Teflon tubing (Hamilton
Co., No.
KF28TF)
and entered the flask below the surface of the
water bath so that temperature
mismatch
was minimized, The contents
of the flask were stirred with a
four-bladed
glass stirrer driven by a high-torque
“Inframo”
motor (Model RZRI-64;
Poly Science Corp.,
Evanston,
Ill. 60201) at about 900 rpm. The titration
curves were recorded with a Model EU-205-11
recorder
(Heath/Schlumberger,
St. Joseph,
Mich. 40985) at a
rate of 4 s/cm.
The results
from the thermometric
method
were
correlated
with calcium and magnesium concentrations
as measured
with a Model 305B atomic
absorption
spectrophotometer
(Perkin-Elmer
Corp.,
Norwalk,
Conn. 06856).
Reagents
All chemicals
were reagent
grade or better,
unless
otherwise
indicated.
All solutions
were prepared
with
de-ionized water from a mixed-bed
umn (Continental
Demineralization
ion-exchange
colService, Atlanta,
Ga. 30329).
Tris (hydroxymethyl)aminomethane
buffer, pH 8.0,
1 mol/liter.
Dissolve 121 g of tris(hydroxymethyl)ami-
nomethane
(Baker
Chemical
Co., Phiilipsburg,
N. J.
08865) in about 900 ml of water. Adjust the pH to 8 with
HC1 or KOH, and dilute to 1 liter.
Ethylenediaminetetraacetate
stock
solution,
I
mol/liter.
Dissolve about 25 g of disodium
ethylenediaminetetraacetate
(Aldrich Chemical
Co., Atlanta,
Ga.
30326) in 100 ml of water by adding KOH until the pH
is about 8.
Ethylenediami
net etraacet ate titrant
solution,
0.5
mol/liter.
Dilute 25 ml of the ethylenediaminetetraacetate stock solution with 25 ml of 1 mol/liter
tris(hydroxymethyl)aminomethane
buffer. Adjust to pH 8.0
± 0.02.
Stock calcium standard
solution,
127.1 mmol/liter.
Calcium carbonate
(Baker’s Analyzed Reagent, or NBS
Standard Reference Material No. 915) was dried overnight at 150 #{176}C
and stored in a vacuum desiccator until
needed. Calcium carbonate,
1.2726 g, was transferred
to a 1-liter volumetric
flask and dissolved in about 6 ml
of concentrated
HC1. When all the salt was dissolved,
the solution was diluted to the mark with water.
Calcium
working
solutions,
2 mmol/liter.
Desired
concentrations
of calcium were obtained by appropriate
dilutions
of the stock calcium standard
solution. There
were no apparent
differences
between
calcium
carbonate from the two sources.
Stock magnesium
solution,
10.37 mmol/liter.
Magnesium ribbon (Matheson,
Coleman and Bell) was first
scraped clean, then 252.2 mg was transferred
to a 1-liter
volumetric
flask. The magnesium
was dissolved
in a
minimum
amount of concentrated
HC1, then diluted to
the mark with water.
Magnesium
working solutions,
1 mmol/liter.
Desired
concentrations
of magnesium
were obtained by diluting
the stock magnesium
solution.
Procedures
Thermometric
titrations.
The titrant
was initially
by titrating 2 ml of a 1 mmol/liter
solution
of calcium
carbonate
in 0.5 mol/liter
tris(hydroxymethyl)aminomethane
(no protein present). Before the
standardized
titration,
a small air bubble was introduced
into the tip
of the titrant delivery line to prevent mixing of the two
solutions.
The delivery tip was held below the surface
of the solution in the Dewar flask. The temperature
of
the contents of the Dewar flask was quickly equilibrated
with the water bath by means of a small resistance
heater inside the flask. Once the flask was heated to the
desired temperature
(3 to 4 mm), the Wheatstone
bridge
was nulled and any temperature
change compensated
for by means of a constant-slope
generator
to obtain a
flat baseline on the recorder
(11). The pump was then
started and the titration
curve recorded.
For determining
calcium and magnesium
in serum,
we used a 1-mi pipet (calibrated
“to contain”)
to deliver
the sample into the flask. The last drop from the pipet
was blown out into the Dewar flask and the residue in
the pipet was flushed into the flask by admitting
1 ml
of 1 mol/liter tris(hydroxymethyl)aininomethane
buffer
through the back of the pipet. The pipet was allowed to
drain for at least 1 mm and then the contents
of the
Dewar
flask were titrated
After the titration,
coholic potassium
the Dewar
hydroxide
as mentioned
previously.
flask was rinsed with al(0.1 mol/liter)
and soap
solution. The end-points for the titration were obtained
by visual extrapolation
of the two linear segments of the
titration
curve as shown in Figure 1.
Atomic
absorption
spectroscopy.
The method described by Pybus et al. (12) was used to determine
total
calcium
by atomic
absorption,
without
the internal
strontium
reference.
The method
suggested
by Perkin-Elmer
was used to determine
magnesium
(13).
Results
Although
a mixture
of magnesium
and calcium
had
been previously
analyzed
by thermometric
titrimetry
at concentrations
and in amounts much greater than in
serum, we noticed effects that were present
in the titration of the mixture
that we did not observe for calcium or magnesium
alone and had not been previously
reported.
-Jo--.,
These effects included
initial curvature
and
elongation
of the time to the first end-point;
we attributed these effects to slow exchange
kinetics.
The exchange
reaction
of calcium
with the magnesiumethylenediaminetetraacetate
complex is being investigated further and results will be published
elsewhere.
‘0-s-c
START
Since the exchange
lyzed, the reaction
reaction
appeared
to be acid cata-
rate was increased by lowering the
pH from 9.5 to 8.0. Since the effective formation conFig. 1. Recording of the thermometric titration with ethyIenediaminetetraacetate of a 2-mi sample containing 1.265 mmol of
calcium and 1.037 mmol of magnesium per liter in 0.5 mol/Iiter
tris(hydroxymethyl)aminomethane
buffer (pH 8)
stant is reduced
to see if calcium
pH. The titration
as the pH is lowered, it was important
and magnesium
could be titrated at this
curves for calcium
and magnesium
CLINICALCHEMISTRY.Vol.22,No.7,1976 1085
SSCORO
cR0 -po,,i
respect to concentration. Next a solution containing the.
average concentrations
of calcium and magnesium
found in serum was prepared in the absence of protein
and titrated by the procedure outline for serum samples.
This titration is shown in curve A of Figure 2. Curve B
of Figure 2 shows the. thermometric
titration of an actual serum sample. The protein evidently has very little
effect on the titration curve. The effect of protein was
further investigated by titrating a solution that was 2.5
mmoi of calcium and 1.0 mmol of magnesium per liter
START
with no protein
tion was titrated
,o-1c
present. Afterwards,
an identical solucontaining
70 g of protein per liter. The
protein had no effect on the shape of the titration curve
or on the volumes required to reach the end-points.
2. Curve A. Thermometric titration ofa 1-misampleof 1.068
mmol/lfter magnesium and 2.266 mmol/llter calcium diluted with
FIg.
1 ml of 1 mol/liter tris(hydroxymethyl)aminomethane
8 (no protein present)
buffer, pH
Curve B. Titration of 1 ml of serum containing 2.50 mmol/llter
calcium and 1.30 mmol/liter magnesium diluted with 1 ml of 1
mol/liter tris(hydroxymethyl)aminomethane
buffer, pH 8
Both were titrated with ethylenedlaminetetraacetate
&oxymethyl)aminomethanebuffer(pH 8)
in 0.5 mol/Ilter trls(hy-
Table 1. AnalytIcal Recovery of Calcium and
Magnesium (Four Samples)
Calcium
Added
Found
Magnesium
Recovery
Found
97.7
3,42
101.7
1.78
96.8
3.39
100.5
1.76
#{192}y
99.2
#{192}y
respectively.
Analytical Recovery
%
1.52
1.43
0.937
0.776
1.52
1.52
0.801
0.801
We evaluated the short-term
precision of the thermometric method by performing four replicate titrations on a sample of pooled serum. The relative standard deviations (coefficients of variation) for calcium
and magnesium
were 1.1% and 2.8%, respectively.
Day-to-day
precision
was evaluated
by running 13
replicates from a serum pool during 20 days. During this
time four inexperienced
operators
obtained
results
having a relative standard deviation of 1.6% for the
calcium assay and 6.4% for the magnesium assay, with
means of 2.1 and 0.83 mmol/liter, respectively. An experienced operator (RHC) obtained a day-to-day relative standard deviation of 1.6% and 3% for calcium and
magnesium,
Recovery
mmol/llter
%
mmol/iit.r
3.50
1.75
3.50
1.75
Added
Precision
100
94.0
116.9
96.8
101.9
We first
#{149}
Each determination Is the average of two runs. Tilrant, ethylenediaminetetraacetate (pH 8). Titration rate, 61 nmol/s.
removed
102%, with a range
show
some
end-point
curvature
at the pH used,
but
because this is a linear titration procedure we may extrapolate to the end-points as shown in Figures 1 and
2. Even though
the heat of formation
of magnesium
with
ethylenediaminetetraacetate
is endothermic
[H = 16.8
kJ/mol (+ 4 kcal/mol)] (14) and that of calcium with
ethylenediaminetetraacetate
is exothermic [H = -25.2
kJ/mol (- 6 kcal/moi)] (14), both reactions appear
exothermic because of the large heat of protonation
of
the tris(hydroxymethyl)aminomethane
buffer [LH =
-50.4 kJ/mol (- 12 kcai/mol)] (15). We titrated a solution
containing
1 mmoi
of calcium
and
1 mmol
of
magnesium per liter, to determine if any differentiation
was possible. The titration of a 2-ml sample of the
mixture
is shown
in Figure
1. The distance
to the first
end-point corresponds
to total calcium; the distance
from the first to the second end-point corresponds to
the total magnesium. These distances are linear with
1086
CLINICAL CHEMISTRY, Vol. 22, No. 7, 1976
all the
calcium
and
magnesium
from a pool of serum by passing it through an ion-exchange column, as outlined by Lott and Herman (16).
We next added known amounts of calcium and magnesium and titrated the samples thermometrically.
The
results are shown in Table 1. The average recovery for
calcium was 99.2%, with a range for the four results of
96.7% to 101.7%. The average magnesium recovery was
Correlation
of 94.1% to 117%.
Studies
A series of human sera were analyzed for both calcium
and magnesium by atomic absorption spectroscopy and
thermometric
titration
(Table 2). The calcium concentration varied from 1.8 to 3.8 mmol/liter, and a correlation coefficient of +0.98 was obtained from a linear
least-squares
regression analysis of the data. Because
the correlation coefficient is affected by the range of the
data (17), it would improve if a wider range of sample
calcium concentrations
had been available.
The absence of bias was also assessed for both species
by performing a t-test for the paired observations
(18)
and a Wilcoxon signed-ranks
test (18). No significant
difference was obtained in either statistical test at the
95% confidence interval.
To further verify the technique, we also studied a set
of three different commercial control sera (Versatol).
The results (Table 3) indicated good agreement except
Table 2. Total Calcium and Magnesium as
Measured in 12 Sera by Atomic Absorption and
Thermometric Tltrlmetry
CalcIum
At. absorp.
Th.rm.
Added
Therm. titrIm.
At. ab.orp.
tltrlm.
Table 4. DetermInation of Calcium In Three Sera
by Thermometric Titration with Ethylene Glycol
BIs( 2-aminoethyl ether )-N,N,N’,N’ -tetraacetlc
Acid a
1.99
0.88
0.88
1.71
1.71
1.5
2.56
3.42
2.55
3.39
0.2
2.30
2.07
2.13
2.27
1.98
2.09
0.79
0.82
0.77
0.81
0.80
0.82
2.36
2.23
0.82
0.84
2.31
2.23
0.81
0.83
2.24
2.20
2.27
2.29
0.82
0.80
0.81
0.83
2.19
2.18
0.78
0.79
#{149}
Titration rate, 58.29 nmol/s,
2.34
2.29
0.71
0.81
3.08
3.08
0.65
0.73
2.23
0.776
0.806
SD of differen ce ±0.06
±0.04
(19). This ligand was tested to determine
whether calcium could be titrated more precisely if only
one break occurred in the titration curve. At pH 8 no
heat was observed upon titration of magnesium when
it was present at a concentration
fourfold the normal
value for serum and a virtually ideal-i.e.,
rectilineartitration
curve
amounts
Table 3. AnalysIs of Versatol Samples by
Thermometric Tltrlmetry
Calcium
Magnesium
Reported
Found
2.50
2.49
0.864
0.873
required
Versatol-A
Versatol-A-Alternate
1.70
3.14
1.77
3.11
1.32
0.352
1.20
0.511
DIscussion
small
is difficult.
Interferences
Thermometric
volume
Titration
of Calcium
with
Ethylene Glycol Bis(2-aminoethyl ether)..
N,N,N’ ,N’ -tetraacetic
Acid
The titration of calcium with ethylene glycol bis(2aminoethyl ether)-N,N,N’,N’-tetraacetic
acid was also
studied. This titrant reacts quantitatively
with calcium,
but the magnesium complex is so weak that magnesium
calcium.
amount
Known
of magne-
to a de-ionized
serum
of titrant.
In general,
less than
20 jl is
to reach the end-point.
Although Jordan and Alleman (14) indicated that
calcium and magnesium could be determined
by thermometric ethylenediaminetetraacetate
titration at pH
10, their work yielded only modest precision (-‘3%)
upon titration of relatively large volumes (25 ml) at
concentrations
of about 2 mmol/liter.
No accuracy
or
precision
it is possible that various metal ions such as iron, zinc,
and copper, which are present in serum or introduced
as reagent contaminants,
would cause erroneous measurements, because ethylenediaininetetraacetate
reacts
quantitatively
with these metals. Concentrations
of
these metals up to 10-fold normal were added to a
pooled serum. We found that addition of sodium sulfide,
10 mmol/liter, to the sample effectively eliminated interferences from these three ions. We observed no statistically significant increase in the end-point volumes
when sodium sulfide was added to solutions containing
no contaminants.
for
are presented in Table
4. The average analytical recovery for added calcium
was 99.6%. Precision of replicate determinations
is
better than 1%. The major factor limiting precision in
these titrations
is our ability reproducibly
to deliver the
Versatol
for Versatol-A-Alternate.
In this case the ratio of calcium to magnesium was so high that the end-point ex-
obtained
and a constant
sium (1 mmol/liter)
were added
pool. Results of several titrations
Found
mmol/Iltsr
was
of calcium
R.ported
trapolation
pH 8.
added to do-Ionized serum. Each sample con-
is untitratable
0.78
0.88
2.27
A Known amounts of calcium
0.5
tained1 mmol of magnesium per liter.
2.32
2.41
Av
CV, %
mmol/ilt.r
mmoi/lIter
2.11
Found
b
data were quoted
for the titration
of a mixture.
Our work focused on the problems involved in scaling
the method down to a clinically more reasonable sample
size (1 ml) and overcoming
the
kinetic
problems
in-
volved in titrating a mixture.
The main drawback of ethylenediaminetetraacetate
titrations in the area of clinical chemistry has been the
limited means of end-point location. Many visual indicators, along with a variety of chemical procedures,
have been tested in attempts to improve it. A major
feature of thermometric
titrations
is their complete
insensitivity to both the optical characteristics
and the
properties of the matrix. As indicated above, there is
essentially no effect of serum protein on the titration
curve. An additional virtue of thermometric
titrations
is that although magnesium is often an interferant
in
most visual titrations
for calcium, it may be simultaneously assayed when the end-point is located thermometrically.
Several other chelating agents were tested to assess
their utility. For various reasons both nitrilotriacetic
CLINICAL CHEMISTRY, Vol. 22, No. 7, 1976
1087
acid and cyclohexane-diaminetetraacetic
acid gave no
improvement
in the titration curves. Nitrilotriacetic
acid gives a very poorly shaped titration curve because
it forms very weak complexes with both calcium and
magnesium. Cyclohexane-diaminetetraacetic
acid gives
results comparable to ethylenediaminetetraacetate,
but
no improvement
was observed.
The precision and recovery studies indicate that the
thermometric
titration is precise and accurate for simultaneously
measuring calcium and magnesium
in
serum. The results compare well with those by atomic
absorption
spectroscopy
(Table 1). Sample volume is
limited to a minimum of 1-ml, because the size of our
Dewar flasks is limited by their heat-loss characteristics
to about 2 ml. One cannot dilute the sample more than
two-fold because the net temperature
change would
become so small that noise would become evident in the
curve. We believe that smaller samples could be accommodated
by using isothermal
calorimetry
or by
compensating for the heat-loss characteristics of a small
Dewar flask. Each of the above modifications entails the
use of more complex instrumentation.
One major drawback of the thermometric
technique
is the poor determination
of magnesium at high ratios
of calcium to magnesium.
As the concentration
of
magnesium becomes small, the difficulty in finding a
linear region from which to extrapolate increases, as can
be seen in the poor results for Versatol-A-Alternate
(Table 3).
2.Lott,
J.A.,Determination
of total and ionic calcium. CRC Crit. Rev.
Anal. Chem. 3, S. Meites, Ed., Chemical Rubber Co., Cleveland, Ohio,
We acknowledge the Athens General Hospital and the University
of Georgia Health Services for supplying the serum samples. One of
us (RHC) would like to acknowledge support from the University of
Georgia Graduate School and the support of an Analytical Summer
Fellowship sponsored by the Olin Charitable Trust Corporation. This
work was supported by grant GM 17913 from the NIH.
16.Lott, J. A., and Herman, T. S., Increased AutoAnalyzer
dialysis
of calcium and magnesium in presence of protein. Clin. Chem. 17,614
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