V O L U M E 26, NO. 12, D E C E M B E R 1 9 5 4 Table 11.
1923
Interplanar Spacings and Line Intensities (Continued)
d , A. 5-Ethylamino-1-phenyltetraaole
r/ro
28,
5.9 11.8 12.3 13.2 14.9
15.0 7.49 7.18 6.70 5.94
0.03 0.55 0.91 0.04 0.29
15.5 16.1 16.9 18.2 19.0
5.71 5.50 5.24 4.87 4.66
20 7 21.5 22.8 24 3 25 0
d , A. 5-Picrylaminotetrazole
I/Io
4.7 9.5 11.5 14.3 14.8
18.8 9.29 7.69 6.19 5.98
1.00 0.31 0.11 0.16 0.06
0.06 0.06 0.07 0.05 0.05
18.0 18.6 19.0 19.6 20.4
4.92 4.76 4.66 4.52 4.35
0.12 0.22
4.28 4.13 3.89 3.66 3.56
0.09 0.23 0.07 1.00 0.37
22.0 23.2 23.9 24.4 25.0
4.03 3.83 3.72 3.64 3.56
0.10
26.1 27.0 28.4 29.6 30.8
3.41 3.30 3.14 3.01 2.898
0.25 0.18 0.18 0.08 0.03
3.37 3.30 3.19 3.10 2.993
0.38 0.56 0.11 0.07 0.24
32.0 33.3 37.1 38.0 41.0
2,792 2.686 2,419 2.364 2.197
0.04 0.03 0.03 0.06 0.01
26.4 27.0 27.9 28.8 29.8 30.8 31.6 32.0 36.6 37.0
48.3 44.2 45.6 49.6 50.7
2.086 2.045 1.986 1.835 1.797
0.01 0.01 0.01 0.02 0.02
51.6 53.2 53.0
1.768 1.719 1.698
0.04 0.01 0.01
38.0 39.0 41.3 42.3 43.9 45.0 47.9 49.5 50.6
2.364 2.305 2.182 2.133 2.059 2.011 1.896 1.838 1.801
28,
0
ACKNOWLEDGMENT
The compounds listed were prepared by Ronald A . Henry and William G. Finnegan of this lahoratory. LITERATURE CITED
(1) Burkardt. L. A, and Moore, D. W., A N ~ LCHEM., . 24, 1679 (1962). (2) Fmnegan, W. G., Henry, R. A , , and Lieber, E., J . Org. C h a . , 18,779 (1953). (3) Garbrecht. W. L., and Herbat. Ti &I.,I b i d . , p. 1003.
0
0.10
0.09 0.08 0.38 0.13 0.16 0.19
0.15 0.22 0.14 0.02 0.04 0.02 0.08 0.04 0.01 0.04 0.02 0.02 0.02 0.02
(4) Henry, R. A , and Finnegan, W. G., J . Am. C h m . SOC.,76, 923 (1954). (5) Henry, R. A . , and Finnegan, W. G., to be published. ( 6 ) Henry, R. d.,Finnegan, W. G., and Lieber, E., J . Am. Chem. Soc., 76, 88 (1954). (7) Hofman, K. A., Hock, H.. and Kirmreuther, H., Ann., 380, 136 (1911). (8) StollB, R., and Roser, O., J . prakt. Chem., 139,63 (1933).
RECEIVED for review June 12, 1954. Accepted August 23. 1954. Published with the approval of the Technical Director, U. S. Naval Ordnance Test Station.
Determination of Ionized Calcium and Magnesium in Milk GEORGE CHRISTIANSON, ROBERT JENNESS, and S. T. COULTER Departments of Agricultural Biochemistry a n d D a i r y Husbandry, University o f Minnesota, St. Paul, M i n n .
A method is presented for determining ionized calcium and magnesium in millc, wherein these ions exist in equilibrium with several dissolved and colloidal complexes. The amounts of calcium and magnesium bound by a cation exchanger (IR-100) equilibrated against. milk are employed as measures of activity of these ions. The amounts bound are converted to concentrations of calcium and magnesium ions by comparison with the quantities bound by the exchanger in equilibrium with standard solutions containing sodium, potassium, calcium, and magnesium as the chlorides. The apparent concentrations of these ions in normal bovine skim milk at 22" to 25" C. are 2.0 to 2.3 millimoles of calcium and 0.82 to 0.85 millimole of magnesium per liter. These values are strongly influenced by pH adjustment, addition of citrate, and previous heat treatment. The reproducibility of the method appears to be very satisfactory.
T
HE activity of calcium and magnesium ions in milk has long been presumed to govern the stability of the caseinate particles therein. This belief is based on circumstantial evidence obtained by adding soluble calcium or magnesium salts or reagents which form complexes with these ions. It has not been possible to relate caseinate stability to the actual calcium and magnesium ion activities because of lack of suitable methods of determination. I n milk, as in other biological fluids, calcium and mngnesium ions are in equilibrium n-ith several dimolved and colloidal complexes. Obviously, any analytical method must not displace these equilibria. Reversible electrodes would be ideal for measurement of activities of these ions, but unfortunately satisfactory electrodes for a system as complicated as milk have yet to be devised ( 2 , 8). The method of PvIcLean and Hastings (7), employing the amplitude of contraction of an isolated frog's heart as a measure of ionized calcium, has been employed successfully for blood but it is somewhat cumbersome and is sensitive only in certain ranges of concentration. .4ctually, the concentration of ionized calcium
ANALYTICAL CHEMISTRY
1924 in milk is pmbably close to or even above the upper limit of sensitivity of the frog heart method (2.0 millimoles per liter). Others (2, S, 9-11) have proposed equilibration of the system being studied with a slightly soluble salt of calcium or magnesium and calculation of the ionic concentrations from the amount of dissolved anion and the solubility product of the salt. I n the case of milk, such methods are most conveniently applied to ultrafiltrates or equilibrium dialyzates. Harnapp (S), employing calcium picrolonate a t 30” C., calculated the calcium ion concentration of cow milk ultrafiltrate to be about 1.2 to 1.4 millimoles per liter, and Nordbo (10) estimated the magnesium ion concentration to be 0.5 millimole per liter by use of magnesium tropaeolin 00 a t 37’ C. Recently a colorimetric method has been proposed (12, 13, 16, 21) based on the shift in absorption maximum when calcium combines with purpurate (murexide). Smeets and Seekles ( 2 4 ) have applied this technique to ultrafiltrates from 40 samples of normal cow milk with results for calcium ion concentration ranging from 2.0 to 3.6 millimoles per liter (average 2.75 =t0.39 millimoles per liter). The Pame group (22) has proposed a method based on the extent of formation of calcium stearate when stearic acid is spread on the surface of milk, but no data have been published. Pyne (14) has suggested measuring calcium ion concentration by determination of the rate of clotting of a caseinate solution, equilibrated by dialysis against the unknown solution and then treated with rennin. The “effective” calcium ion concentration thus determined “is a composite value, related closely, no doubt, to the true calcium ion concentration but influenced to some degree by the presence of other ions, especially polyvalent anions.” Values in the neighborhood of 4.0 millimoles of calcium ion per liter were obtained on 17 samples of fresh milk. The present paper reports an attempt to measure calcium and magncsium ion levels in skim milk by the use of cation exchangers. The binding of cations with exchangers has been postulated to follow either the mass action law or an adsorption isotherm (6, 16). I n either event it follows that if such a biological fluid as milk be brought to equilibrium with an exchanger, the amount of any particular cation bound by the exchanger is a function of the activity of that cation and the activities of competing cations. This principle has been employed in determining activity coefficients and ionization constants for certain salts (17-20, 25). In milk the principal cations in addition to calcium and magnesium are sodium and potassium, which are present in amounts of about 20 and 40 millimoles per liter, respectively, and are presumed to be entirely in the ionic form To obtain equilibrium between an exchanger and milk, without upsetting the equilibria existing in the latter, one must use an infinitesimal amount of exchanger with respect to the volume of milk This effect can be achieved by passing the milk over the exchanger in a column or by successive batchwise treatments. The first milk loses appreciable amounts of cations and is thus altered, but successive portions are changed to lesser degrees until finally the influent and effluent are identical. In order to relate the amount of a particular cation bound to the activity of that ration of the milk, one may employ standard curves made with concentrations of competing cations, sodium and potassium, a t the same level as in milk and varying levels of the cations sought (calcium or magnesium). METHOD
Choice of Exchanger. The following qualities are desirable in an exchanger for equilibrium studies:
No binding of anions or of complexes containing anions should occur. The exchanger should have only one kind of active center. Equilibrium should be reached quickly and completely from any state and hysteresis effects should be minimal.
The change in bound cations per unit change in cation activity should be large in the concentration range normally found in milk. The exchanger should wet easily, resist breakage, and consist of particles of uniform size. The total exchange capacity is immaterial Several exchangers n-ere examined, including Permutit, the carboxylic resin Amberlite IRC-50, and the sulfonic resins Amberlite IR-100, Amberlite IR-120, and Chempro C-20. Permutit and IRC-50 were discarded after tests showed that they bound phosphate as well as cations when equilibrated with milk. Most of the work was done with IR-100, even though it resists wetting, fractures easily, consists of particles of uneven size, contains some weakly acid groups in addition to the sulfonic groups, and exhibits some hysteresis effects. IR-120 yielded results similar to those obtained m-ith IR-100 and had better physical properties. I n general, the sulfonic class of cation exchange resins was the only satisfactory type found. Doubtless certain other resin: of this type would be satisfactory. -4sufficient quantity of IR-100 in the sodium state was prepared for the entire study. I t was treated in succession with 111hydrochloric acid, water, and 5770 sodium chloride, washed free of salts with water, air-dried, and stored in a closed bottle. Column. Each column consisted of 3 grams of the air-dried IR-100 in a glass tube 13 to 15 mm. in inside diameter and 50 em. in length with a 7 X 10 em. reserpoir on the top. The reservoir allowed 300 to 400 ml. of fluid to be placed in the column without excessive head pressure. A4three-way micro bore stopcock was fitted with a rubber stopper to the base of the tube in such a way that fluids flowing down the column passed through a constricted tip, while backwashing fluids could be forced relatively rapidly through an unrestricted tube. A piece of glass wool, or preferably glass cloth, slightly larger than the column diameter was held over the end of the tube a s the stopper was inserted. This served to prevent loss of resin through the stopcock. The resin was wetted and classified by backwashing with water. Deionized distilled water was used in all operations and for all solutions. Care was taken to drive all bubbles and air pockets from the column by rotating or tapping the tube. To obtain reproducible results it was necessary to condition the column before use. The most satisfactory conditioning treatment involved equilibrating the resin a i t h standard solutions until the amount of bound calcium was the same for two successive runs. However, washing with 1% hydrochloric acid for 3 or 4 days, followed in turn by sodium chloride solutions and a second acid wash, was usually satisfactory. As milk cannot be added to the resin in the acid state because the casein would be precipitated, a solution of 10% potassium chloride and 6% sodium chloride was passed through the resin to remove hydrogen ions. The column was then reclassified by backwashing with water and the water was drained to just above the top level of the resin. Equilibrating with Milk. Separator skim milk was employed. The slight cream layer that formed on standing was siphoned off. All determinations were made a t room temperature (22” to 25’ C.). From 350 to 500 ml. of the sample to be analyzed was passed through the column to bring the cation distribution on the resin into equilibrium with unchanged milk. The first milk passed through was diluted slightly by the water left on the resin, but by careful layering of the milk in the column this dilution effect was soon reduced to negligible proportions. As the resin lacked calcium initially, appreciable exchange occurred as the milk started to flow through it, and for that reason the first 50 ml. were rapidly passed through. Subsequently, the flow waB reduced to a dropwise rate. Thus, fresh milk was kept on the resin for a 4-hour period of equilibration. At intervals of 10 to 30 minutes, the rate of flow was momentarily increased to the maximum, which was 15 to 20 ml. per minute, in order to dispel any “pockets” of nonmoving milk. The last 20 to 50 ml. of milk was sucked through the column as rapidly a s possible (0.5 to 1 minute) with vacuum. Several washings with water removed the last traces of milk and the column was considered cleaned TThen the effluent water mas not cloudy. All air pockets and bubbles were dispelled by backwashing. Elution of Bound Cations. The cations bound by the resin were eluted by four successive treatments with 50-ml. portions of IK hydrochloric acid. The first 50 ml. was passed through the column as slowly as possible (from 4 to 8 hours). The second portion was passed through in 3- to 5-ml. spurts, flowing a t the maximum rate of 15 to 20 ml. per minute, at intervals of 10 to 15 minutes. Then the first and second steps were repeated. In the case of the first and third elutions, the columns
V O L U M E 2 6 , NO. 1 2 , D E C E M B E R 1 9 5 4 occasionally ran dry at night, in which case it was necessary to backwash with a minimum of water before the next elution could be performed. To avoid possible loss of calcium, the backwashing water was not drained. The combined eluate was made to a volume of 200 ml. Determination of Calcium and Magnesium in Eluate. Aliquots (usually 10 ml.) of the eluate were titrated by the method of Jenness ( 4 )with ethylenediamine tetraacetate and the indicator ammonjum purpurate to determine the levels of calcium and magnesium. As these eluates contained no phosphate, it was not necessary to pass them through a n anion exchanger. Standard Curve. The amounts of calcium and magnesium bound by the resin a t equilibrium are themselves valuable indexes of the status of these ions in milk. Nothing more would be necessary for studies of the effects of various treatments on milk of constant composition. For comparisons among lots of milk, however, the results can be converted to apparent ion conwiltrations by reference to appropriate standards.
.is the sodium and potassium contents of a milk sample must l i e known, a standard curve can be constructed only after analysis
1925 A CaIi ACaR A NgR centrations in milk -~ *and A[Ca+?]’ A [ h l g + + ] ’ A [Mg++] A Mg R are the respective changes in ions bound per unit -
~
change ig ionic concentrations (evaluated from the data obtained with standard solutions). All factors except [Ca++], and [hlg++], can be evaluated and inserted in the equations, which are then solved simultaneously to yield [Ca++], and [Mg++],“. RESULTS
Standard Solutions. The relation between the calcium ion concentration of the standardizing solution and calcium bound by the resin a t equilibrium is plotted in Figure 1. Curves A and B indicate the different binding on conditioned ( B ) and nonconditioned ( A ) columns. Prolonged conditioning alu.:iys brought results into accord. The difference betvieen B, C, and D s h o w the important effect of competing ions-sodium, potassium, and magnesium-in determining the amount of calcium bound a t equilibrium. This point is further illustrated in Tahle I, n-hich also reports magnesium binding in some cases.
OF the milk.
While the milk was being equilibrated against the resin, a sample was ashed and the ash dissolved in hydrochloric acid and analyzed for sodium and potassium with a Perkin Elmer flame photometer using lithium as an internal standard (25’). Standard solutions were then prepared having the same sodium and potassium concentrations (as the chlorides) a s the milk. Calcium and magnesium (also as the chlorides) were included in the solutions a t levels found by past experiments to lie within the expected range for milk. Each standard solution, representing a different calcium concentration and/or different magnesium concentration, was passed through one or two of the exchange columns. Because the ionic coneentiations of these solutions were 1011 and they mere lacking in calcium and magneeium “buffering action,” i t n a s necessarj- to pass much greater amounts over the columns than with milk-usually 15 to 20 liters for 60 to 90 hours. As it was especially important that no other ions be present in the standardization solutions, only deionized distilled water nas used. Columns equilibrated against standardizing solutions w r e washed, bxckwashed, and eluted in the same manner as those equilibrated against milk, and the eluate was analyzed for calcium and magnesium. For milk of “average composition,” convenient levels in the standards are 8 to 10 mg. of calcium and 1.5 to 2.5 mg. of magnesium per 100 ml. Over these small ranges of concentration the relations between inns bound and ionic concentrations are essentially linpar. At least four different combinations should be employpd (two concentrations of ralcium and trvo of magnesium), although nine are better (three concentrations of each ion). Then the following pair of simultaneous equations serve to interpolate for the values of calcium and magnesium ion in milk: CaR,
=
CaRl
+ [A:E+”tl ( [ c ~ + + I-? ~i ~ a + + i l ) ]-
I9t
131 2
t
4 CO++
6 I N SOLUTION
10
(mg./~oorn~,)
Figure 1. Calcium Binding by IR-100 as a Function of Ionic Composition of the Solution A and B made with solutions containing 131 mg. K, 59 mg. N a , and 0.0 mg. h l g per 100 mi. A . Resin not adequately conditioned B. Resin thoroughly conditioned C a n d D made with solutions containing 140 m g . K and 47 mg. N a per 100 ml. C. 1.40 mg. RIg per 100 ml. D. 2.13 mg. RIg per 100 mi.
It is evident that sodium and potassium levels must be carefull!controlled and magnesium taken into account in order to arrivr a t any valid results for the binding of calcium. Effect of Various Factors on Binding from Skim Milk. The resin IR-100 binds 15 to 16 mg. of calcium and l . i to 1.8 mg. of magnesium per gram when equilibrated with skim milk. It was of interest to determine the effects of changes in pH, the
Table I.
Relation of Calcium and Magnesium Bound by 1R-100 to Composition of Solution
Concentrations in Solution, hIg./100 M1. hIg Na K Ca 4.7
0.0
54 59
131 141 118 121
131
where CaR, and hlgR, are the quantities of calcium and magnesium bound per gram of resin in equilibrium with skim milk, C a n l and MgR1 are the quantities of calcium and magnesium bound per gram of resin a t a point on the standard curves corresponding to [Ca++Iland [Mg++]l. (Any point on the curves may be chosen.) [Ca++], and [Mg++], are the respective ionic con-
8
1.0 7.8 9.2
1.5 2.5 1.5 2.5
N o t determined.
144 59 48 48 48 48
131 150 I50 I50 I50
Cations Bound, h l~/~G_ . _ Ca AIK 15 7 15.0 15.9 15.5 15.4 14.7 14.0 15.2
0.0 0 0 0.0 0.0 0.0 $0 1.4
14.3
2.2
16.6 15.8
1.2
1.9
1926
ANALYTICAL CHEMISTRY
addition of a calcium complexing reagent such as citrate, and heating on the extent of binding. The pH of portions of a single lot of skim milk was adjustrd to values between 6 and 7 by adding either 1.5N sodium hydroxide or 1 ON hydrochloric acid. The dilution was negligible in all cases (maximum of 1.5%). The calcium bound has been plotted against pH in Figure 2. The marked effect of pH on binding doubtless largely reflects its effect on calcium activity of the milk rather than on the binding capacity of the resin or increased competition from sodium ions. The binding capacity of this resin does not vary greatly with pH in this region of the scale and in any case it would increase with increase in pH. The decrease in calcium bound produced by adjusting the milk from pH 6.62 t o 6.92 with sodium hydroxide is due in only a small degree to increased sodium ion concentration. This adjustment required only about 5 meq. of sodium hydroxide per liter and the effect is far greater than that produced by adding 5 meq. of sodium ions (see Figure 3 ) The effect of trisodium citrate on the binding of calcium is shown in Figure 3. Because addition of this salt increases the pH of milk, sufficient hydrochloric acid was added in each case to restore it to pH 6.6 (maximum of 3 ml of 1 O N hydrochloric acid per liter). The lowering of calcium binding is due both to the increase in competing sodium ions and to the complexing of calcium by citrate. T o estimate the magnitude of the latter, a series with sodium chloride a t comparable levels was includrd. As expected, the citrate reduced the binding of calcium much more than the chloride.
and 0.82 to 0.85 millimole of magnesium per liter or 8.2 to 9 3 mg. of calcium and 2.0 to 2.1 mg. of magnesium per 100 ml. Comparison of IR-I00 and IR-120. A comparison was made of the binding of calcium by IR-100 and IR-120 in equilibrium with skim milk and standard solutions. All standard solutions in this experiment contained 131 mg. of potassium and 59 mg. of sodium per 100 ml. No magnesium was included. At any given calcium concentration, IR-100 bound about one third as much calcium as IR-120. In equilibrium with skim milk IR-100 hound 15.2 mg. of calcium per gram and IR-120 bound 46.2 mg. per gram. These amounts of calcium corresponded in both cases t o that bound by the respective resins in equilibrium with a standard solution containing 5.2 mg. of calcium per 100 ml. Thus, they would be expected to give comparable results for concentrations of ionized calcium in milk.
16-
t
's
l44 1
I
1
I
0
0
16
MEO.
PER
24
LITER
Figure 3. Effects of Added Sodium Citrate and Sodium Chloride on Binding of Calcium by IR-100 in Equilibrium with Skim Milk
Table 11. Binding of Calcium and Magnesium by IR100 in Equilibrium with Skim Milk and Apparent Ion Concen trationsa Concentration in Milk,
\
t
Sample
\
b
1 2
6.4
6.0
Na
I
