simplified method fortheestimation ofinorganic phosphorus ......ports that phosphorus excretion...
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Simplified Method for the Estimation of InorganicPhosphorus in Body Fluids
Harry Goldenberg and Alberto Fernandez
A simplified procedure is described for the determination of inorganic phosphate in
body fluids. The method employs two stable reagents and requires a minimum num-
ber of steps. Serum is deproteinized with trichioroacetic acid containing ferrous ion
and thiourea. The supernatant is decanted and mixed with a small volume of
molybdic acid. The phosphomolybdate formed is immediately reduced in situ by the
ferrous ion to produce a blue color that is stable for several hours. The intensity of
color is insensitive to changes in concentration of acid, molybdate, ferrous ion, and
thiourea, and to losses in decanting the serum supernatant. Excellent conformity to
Beer’s law is demonstrated over a wide range of phosphorus concentrations. Recoveries
of phosphorus added to serum and urine are shown to be quantitative. A comparison
is presented between this method and that of Fiske and SubbaRow (1).
PHOSPHORUS is distributed throughout every cell of tile body and plays
all important role in intermediary metabolism, skeletal formation,
dentition, and acid-base balance. It is present in blood in the form of
both inorganic and organic piloSphate. The inorganic phosphate occurs
almost exclusively in the plasma or serum, while the erythrocytes con-
tain most but not all of the organic phosphate. Clinical studies indi-
cate that the phosphate coiitent of body fluids varies in a characteristic
manner in health and disease. Serum and urinary phosphorus are de-
pressed in rickets, osteonlalacia, and idiopathic steatorrhea. Both in-
dexes are similarly depressed following the administration of insulin,
glucose, and adrenalin, and following anesthesia with ether or chloro-
form. Hypophosphatemia is also encountered in ilyperparatllyroidism,
but tile urinary phosphate excretion tends to increase. There are re-
ports that phosphorus excretion is increased in mental disease. Ele-
vated serum phosphorus levels are most generally encountered in
renal failure, less of ten ill healing fractures.
Numerous colorimetric nIetilods have been proposed for tile esti-
Froln the Bio-Science Laboratories, 7600 Tyrolle Ave., \all Nuys, Calif. 91405.
JTeeeived for publication May 23, 1966; accepted for publication Julie 28, 1966.
871
872 GOLDENBERG & FERNAND� Clinical Chemistry
mation of inorgallic phosphate. In these methods the phosphorus is
usually treated with molybdate and the phosphomolybdate, formed is
subsequently reduced to molybdeiium blue. The reducing agents em-
ployed by previous authors include aminonaphtholsulfonic acid (1),
stannous chloride (2), p-methylaminophenol (3), ascorbic acid (4),
ferrous sulfate (5, 6) and p-semidine (7). Experience has shown that
most reductants in use are not completely acceptable for the analysis
of phosphorus. Some reducing agents are unstable and have a short
shelf life. Others yield molybdenum blue colors that are unstable,
deviate from Beer’s law, or are sensitive to small changes in the acidity
of the medium. lii our study of various reducing agents, ferrous ion
was found to offer the greatest advantages for routine use. When em-
ployed in the form of Mohr’s salt the compound appears to suffer from
few or none of the objections to other reductants.
The present method is based on the use of Mohr’s salt and was de-
veloped to provide the clinical laboratory with a simplified procedure
for the determination of phosphorus in body fluids. Toward this end,
the analytical approach adopted by previous workers has been re-
appraised. It is customary to add the reductant after the molybdate.
Taussky and Shorr (6) combined their reductant and molybdate solu-
tions to give a mixed reagent that would react directly with phosphate.
This mixed reagent is not stable for more than several hours. in the meth-
od to be described here the Mohr’s salt is combined with the protein
precipitant (trichioroacetic acid, TCA) and stabilized by the addition
of thiourea. Only two reagents are required for the analysis. Serum is
deproteinized with the iron-TCA and the supernatant solution decanted
into a cuvet for color development with inolybdate. Because of the
small volume of molybdate reagent used, the sample loss sustained in
decantation is shown to have no effect on the final absorbance measure-
ment.
Material and MethodReagents
Iron-TCA, stabilized Transfer 50 gm. of trichloroacetic acid to
a 500-ml. volumetric flask with distilled water. Add 5 gm. of thiourea
(Eastman Kodak Co.)* and 15 gm. of Mohr’s salt (ferrous ammonium
sulfate hexahydrate), dissolve and dilute to mark with water. Store in
an amber bottle. A deposit of sulfur begins to form after a week but
�Some commercial preparations of thiourea may contain small anfounts of phosphorus.
Thiourea is purified by recrystallizing from water. Dissolve 60 gm. of the compound in 100 ml.
of hot distilled water, filter if necessary, and place overnight in the refrigerator. Tile Crys-
talline deposit is filtered off on a Buchner funnel, washed with a little cold distilled water,
and dried in a desiccator. Yield, 45 gm.
Vol. 12, No. 12, 1966 INORGANIC PHOSPHORUS 873
does not interfere with the analysis. The shelf life of this reagent is
6-12 months.Molybdate Add 45 ml. of concentrated 112S04 with cooling to a
500-ml. volumetric flask containing 200 ml. of cold distilled water. Add
22 gm. of ammonium molybdate, previously dissolved in 200 ml. of
water, dilute to mark, and mix. This reagent is stable for several years.
Phosphorus standard, 5 mg./100 ml. Dissolve 0.2197 gm. of pure,
anhydrous KH2PO4 (dried for an hour at 1100) in distilled water and
dilute to a liter. A small amount of chloroform is added as a preserva�
tive. Discard if there are signs of mold growth.
Procedure for Serum (or Plasma)
1. Place 0.2 ml. of serum in a test tube and add 5 ml. of iron-TCA
with shaking. Let stand for 10 mm. and centrifuge.
2. Decant the supernatant into a clean tube.
3. Prepare a blank containing 0.2 ml. of water + 5 ml. of iron-TCA,
and a standard containing 0.2 ml. of 5 mg./100 ml. P + 5 ml. of iron-
TCA.
4. Add 0.5 ml. of molybdate reagent to each tube and mix by in-
version. The color develops rapidly and is measured after 20 mm. or
within 2 hr.
5. Read the absorbance of the serum unknown (An) and standard
(A8) versus the blank at 660 m� (Klett filter No. 66) or at any desired
wavelength between 640 and 750 mjj.
Calculation
The amount of phosphorus in the serum or plasma is calculated by
the formula
A.
mg. phosphorus/100 ml. serum = -i-- X 5 (1)
Comments
In decanting the centrifugate, it is unnecessary to transfer the last
few drops of solution, since a loss of 0.5 ml. (10 drops) produces an
analytical error of only 1%.
The procedure as described above requires 0.2 ml. of serum but can
be readily adapted to other volumes. For 0.1 ml. of serum: Use 3 ml. of
iron-TCA, centrifuge, decant, and add 0.3 ml. of molybdate. The blank
contains 0.1 ml. Qf water + 3 ml. of iron-TCA + 0.3 ml. of molybdate;
the standard, 0.1 ml. of 5 mg./100 ml. of P + 3 ml. of iron-TCA + 0.3
ml. of molybdate. Read in a photometer and use equation 1. For 0.5 ml.
of serum: Use 10 ml. of iron-TCA, centrifuge, decant, and add 1 ml.
874 GOLDENBERG & FERNANDEZ Clinical Chemistry
of molybdate. The blank contains 0.5 ml. of water + 10 ml. of iron-
TCA + 1 ml. of molybdate; the standard, 0.5 ml. of 5 mg./100 ml. P +
10 ml. of iron-TCA + 1 ml. of molybdate. Read and substitute in Equa-
tion 1. It may be noted that a loss of 1 ml. iii decanting the supernatant
(from 0.5 ml. of serum) decreases tile photometer reading by only 0.9%.
The decantation procedure is recommended for accuracy as well as
speed of analysis. As an alternative, the analyst may withdraw an
aliquot of the supernatant and mix it with one-tenth its volume of
molybdate reagent for color development. If a centrifuge is not avail-
able, the deproteinized solutions are filtered and an aliquot mixed with
a one-tenth volume of molybdate.
Procedure for Urine
1. To 0.2 ml. of urine, diluted 1 to 20 with water, add 5 ml. of iron-
TCA and 0.5 ml. of molybdate reagent. Mix by inversion.
2. A blank and standard are prepared in like manner, using 0.2 ml.
of water and 0.2 ml. of phosphorus standard respectively in place of
the diluted urine.
3. Zero the photometer with the blank at 660 m� (or other selected
setting) and measure the absorbance of the urine unknown (An) and
standard (A8).
Calculation
The amount of phosphorus in the urine is calculated by the formula
111g. phosphorus/100 ml. urine = -�- X 100 (2)
Comments
The urine dilutions most commonly used are 1 to 20 or 1 to 10, but
this may be varied at the discretion of the analyst.
Urine specimens containing protein will develop a turbidity upon
addition of iron-TCA. If this happens, allow the protein to settle for
15 mill. before centrifuging. Decant the supernatant and add molybdate
(0.5 ml.) in tile usual manner.
Experiment Results
A detailed study of the parameters involved in the phosphorus analy-
sis was made in order to establish the optimum conditions of assay.
The reagent concentrations and procedure used in these experiments
were similar to those described above under “Material and Method,”
except for the parameter(s) under evaluation.
Fig. 1. Color intensity produced by
phosphorus (16 �tg.) as function of
amillolliuni molybdate reagent con-
centration. Readings were taken at
700 m�i in a Beckman DU spectro-
photometer.
0.4
0.3Lu0z
� 0.2lfl
0.1
% AMMONIUM MOLYBDATE
Vol. 12, No. 12, 1966 INORGANIC PHOSPHORUS 875
Molybdate Reagent
The influence of variations iii concentration of amnionium molybdate
on the intensity of the color is shown in Fig. 1. The absorbance reaches
a maximum at a reagent concentration of about 2.3% and remains on
a plateau through the highest value tested, viz., 10%. Molybdate is
employed in the stock reagent at a concentration of 4.4%, which can
be decreased by almost one-half or doubled with no effect on the color
intensity. This insensitivity to changes in concentration of the color
reagent is mandatory for a valid application of the decantation prin-
ciple. Unlike the substances present in the TCA supernatant (phos-
phorus, Mohr’s salt, and thiourea), tile molvbdate undergoes a large
dilution when mixed with sample, yielding a fluial concentration that
is dependent on the decantation loss. A ma,�or decantation loss, such
as 50%, would approximately double the fiuial niolybdate concentration.
As seen in Fig. 1, the system call tolerate this increase with no effect
on the intensity of color.
The ability of the system to tolerate increased amounts of molybdate
is intimately related to a factor not previously considered, namely
the concentration of acid iii the mixture. If insufficient acid is present,
the molybdate may undergo reduction to form molybdenuni blue in the
absence of phosphorus. The amount of acid required to give a colorless
blank increases with tile amount of molybdate employed for analysis.
The iron-TCA solution contains 10% (0.GN) TCA; this is sufficient to
prevent spontaneous development of color even when the one-tenth
volume of molybdate used contains distilled water, rather than sulfuric
acid, as the solvent. However, increasing tile ratio of unacidified
molybdate to iroii-TCA to 1 :5 results in a colored blank whose intensity
876 GOLDENBERG & FERNANDEZ Clinical Chemistry
deepens on standing. The possible development of colored blanks is
eliminated by adding sulfuric acid (approximately 3N) to the
molybdate reagent. When prepared in this manner, the molybdate
reagent has a shelf life of several years.
The effect of sulfuric acid on the color reaction was studied by
varying the acidity of the molybdate reagent from 0 to 6N, which
corresponds to 0 to 0.55N in the final mixture, exclusive of the TCA
contribution. No significant differences in color intensity were noted
in any of the tubes over a 2-hr. period. If the acidity due to TCA
(0.53N) is included with the sulfuric acid, the permissible range of
acid used in the system varies from 0.53 to 1.06N or higher.
lron-TCA Reagent
Sumner (5) noted that the color obtained when ferrous ion is added
to phosphomolybdate is instantaneous and stable, increasing no more
than 2% in 2 hr. He reported the shelf life of his ferrous sulfate reagent
to be 2 hr. The ferrous molybdate reagent of Taussky and Shorr (6)
was also found to be unstable after several hours. In view of the
rapidity and stability of color development obtained using ferrous ion,
an effort was made to establish conditions for its stabilization.
Mohr’s salt is comparatively stable toward oxidation by air, and is
employed as a primary standard in quantitative analysis. Combining
Mohr’s salt with TCA provided a reagent with a shelf life of several
days. This was not satisfactory. Miscellaneous reducing agents and
antioxidants were therefore tested as possible stabilizing agents for
the ferrous ion. Hydroquinone and diphenylamine were not satisfac-
tory since on aging they imparted yellow or pink colors to the reagent.
Other agents were also tested, including hydroxylamine, hydrazine,
and sodium sulfite, but in each case the compound underwent oxidation
to produce a marked yellow or green color. Thiourea was found to give
the most satisfactory results. Its principal oxidation product, sulfur,
precipitates from solution, hence the reagent remains colorless. The
stabilized iron-TCA reagent assumes a yellow appearance on aging
but this is largely an illusion due to the sulfur precipitate. The reagent
was found to be usable for periods up to 1 year.
The optimum concentrations of thiourea and ferrous ion were de-
termined by studies that are summarized in Tables 1 and 2. For the
first study the Mohr’s salt was fixed at 3% and the thiourea varied
from 0 to 5% in the iron-TCA reagent (Table 1). Stable colors were
obtained in 10-40 mm. with no apparent effect by thiourea at concen-
trations up to 1%. At the higher concentrations of thiourea, small but
definite increases in readings were noted, approximating 2-4% over
Vol. 12, No. 12, 1966 INORGANIC PHOSPHORUS 877
the indicated 30-mm. interval. On the basis of these data, 1% thiourea
was selected as optimal. Table 2 illustrates the effect of increasing
ferrous ion in the presence of a 1% concentration of thiourea. It is
clear from the first line in the table that thiourea reduces phospho-
molybdate in the absence of iron, but the color formed is not stable.
Other concentrations of thiourea were also tested, with the same gen-
eral results. The effect of adding Mohr’s salt is to stabilize the color;
this is apparent at concentrations of 3, 5, and 10%. Five per cent
Mohr’s salt probably represents the optimum concentration. How-
ever, a 3% solution has been chosen to maximize the shelf life of the
reagent. The change (increase) in color intensity using 3% Mohr’s
salt is about 4% in 2 hr., as compared with a 2% increase for 5%
Mohr ‘s salt.
The question arises whether the Mohr’s salt or thiourea is to be
regarded as the reductant. The stability and magnitude of the color
intensities (Table 1) suggest that ferrous ion is the effective reducing
agent, with the thiourea serving as an antioxidant and supplementary
reductant.
Absorption Spectrum
The molybdenum blue chromophore has a broad absorption maxi-
mum between 700 and 800 m� with a peak at 725-750 m� (Beckman DU
spectrophotometer). The absorbance decreases to 90% of its peak
Table 1. EFFECT o� THIOUREA ON COLOR INPENSIPr (PHOSPHORUS = 20 Mo.)
Thiourea (%) #{149}
Ktett reading (rain.)
10 20 40
0
0.5
1.0
3.0
5.0
252
250
252
260
263
253
251
250
262
266
252
252
251
266
273
Table 2. EFFEcT 05’ FERROUS ION ON CoLoR INTENSITY (PHOSPHORUS = 20 Mo.)
Mohr’s salt (%)
Klett readi ng (mm.)
10 20 30 40
0 268 276 280 284
0.5 237 247 253 256
1.0 244 249 253 255
3.0 251 251 252 253
5.0 263 263 262 264
10.0 269 269 271 269
0 8 16 24 32 40
MICROGRAMS PHOSPHORUS
878 GOLDENBERG & FERNANDEZ Clinical Chemistry
value at 660 m� and to 84% at 640 m� before it reaches a minimum at
450 m�. Wavelength settings above 700 m�t provide maximum sensi-
tivity for phosphorus analysis. However, settings at 660 or 640 m� are
also acceptable because they do not involve much loss of sensitivity
and offer the advantage of being compatible with the upper wave-
length limits of most clinical photometers.
Conformance to Beer’s Law
Phosphorus standards ranging in concentration up to 20 mg./100 ml.
were tested under the routine conditions of assay, and read after
20-30 � in 3 different photometers. The results are given in Fig. 2.
Each instrument provided a linear response with n� indications of
Lu0zH
H
Fig. 2. Evaluation of phosphorus
method for conformity to Beer’s law.
deviation from Beer’s law at the highest phosphorus concentration.
Conformity to Beer’s law was also obtained using an iron-TCA reagent
containing 5% Mohr’s salt.
Recovery Studies
Phosphorus was added in 10-pg. amounts (0.2 ml.) to 0.2 ml. of serum
or urine (diluted 1 :20) and analyzed in the routine manner. The re-
coveries obtained from 6 serums averaged 97.0%, falling in a range of
94.3 to 100%. The phosphorus recovered from 6 urine specimens varied
Vol. 12, No. 12, 1966 INORGANIC PHOSPHORUS 879
from 95.0 to 101%, with an average of 98.0%. Quantitative recoveries
from serum and urine were also obtained when the pilosphorus was
added in amounts of 4, 8, 12, 16, and 20 �g.
Comparison to Reference Methods
A series of 12 serums was analyzed in duplicate by the present pro-
cedure and by the method of Fiske and SubbaRow (1). As indicated in
Table 3, the 2 methods yielded comparable results, with a mean dif-
ference of 0.03 mg./100 ml. This difference is equivalent to 1% of the
average phosphorus value for serum. When the comparison of methods
was extended to urine analyses, the present method gave results 5%
higher than the Fiske-SubbaRow values (Table 4) and the difference
Table 3. COMPARATIVE RESULTS OP SERUM PHOSPHORUS ANALYSES
Sevom sample
Fiske.S,LbbaRo,v Present method De�’iat ion
(mg./I0O ml.) (mg/100 nil.) (mg/ICC ml.)
1 3.61 3.53 -0.08
2 3.36 3.27 -0.09
3 3.94 3.91 -0.03
4 3.78 3.75 -0.03
5 4.64 4.51 -0.13
6 3.80 3.79 -0.01
7 4.03 4.12 +0.09
8 3.23 3.26 +0.03
9 3.70 3.64 -0.06
10 3.92 3.99 +0.07
11 3.28 3.22 -0.06
12 3.75 3.71 -0.04
MEAN 3.75 3.72 -0.03
Table 4. COMPARATIVE RESULTS op URINE PHOSPHORUS ANALYSES
Urine sample
Deviation
Fiske-SubbaRon’ Present method
(mg/ICC ml.) (mg/ICC ml.) (mg/ICC ml.) (%)
1 59.4 62.7 +3.3 + 5.6
2 48.4 50.0 +1.6 + 3.�
3 50.3 53.2 +2.9 + 5.8
4 69.7 72.6 +2.9 + 4.2
5 34.2 35.5 +1.3 + 3.8
6 60.1 63.8 +3.7 + 6.2
7 48.5 50.0 +1.5 + 3.1
8 93.6 98.8 +5.2 + 5.6
9 49.2 50.9 +1.7 + 3.5
10 78.2 80.6 +2.4 + 3.1
11 8.9 10.1 +1.2 +13.5
12 47.1 48.6 +1.5 + 3.2
% MEAN DEVIATION + 5.1
880 GOLDENBERG & FERNANDEZ Clinical Chemistry
was statistically significant by the t test (p < 0.001). Repetition of this
study at a later date led to similar findings.
The small but significant differences noted in the urine phosphorus
analyses prompted the use of a second reference method. The pro-
cedure of Taussky and Shorr (6) was adopted and found to give the
same results as the present method (p > 0.5). This reference method
is unlike the present one in a number of respects, but resembles it in
the use of ferrous ion as the reductant. The reductant employed in the
method of Fiske and SubbaRow is aminonaphtholsulfonic acid. It is
suggested that the 5% discrepancy in urine phosphorus values noted
above is attributable to the difference in reductants used in the methods.
The origin of this discrepancy has not been determined.
Effects of Anticoagulants
The effect of anticoagulants on the phosphorus determination was
tested using phosphorus standards and serum before proceeding with
the collection of plasma samples. Sodium heparin, potassium oxalate,
sodium citrate, and disodium ethylenediamine tetraacetate (EDTA)
were added in 1-5-mg. quantities (0.1 ml.) to 0.2 ml. of phosphorus
standard or serum. There was no evidence of interference by any of
these agents in the amounts used. Their influence on plasma phosphorus
values was evaluated by comparison with serum analyses on the same
blood specimens, which were distributed among 5 tubes. The anti-
coagulants were added in the following amounts: heparin, 0.2 mg./ml.
of blood; oxalate, 2 mg./ml.; citrate, 5 mg./ml.; and EDTA, 1 mg./ml.
The results obtained with heparinized plasma and serum were identical.
Plasma prepared with oxalate and citrate tended to yield somewhat
lower phosphorus values than did serum (average difference, 5%).
This effect by citrate and oxalate is a fairly common one for otherplasma components and may be attributed to a dilution caused by a
shift in water from erythrocytes to plasma. Using EDTA as the anti-
coagulant, erratic differences were noted between plasma and serum
values in a small series of tests (6 blood specimens).
Discussion
The simplicity of the phosphorus method has been achieved by com-
bining the reducing and deproteinizing agents, by employing the de-
cantation principle (8), by eliminating unnecessary dilutions, and by
eliminating volumetric flasks for final adjustment to mark. Quality
control studies indicate that these changes in the classical approach
to the analysis of phosphorus involve no sacrifice of accuracy or
reliability. These observations have been confirmed by 4 major lab-
Fig. 3. Analytical errors resulting
from application of decantation prin-
ciple to determination of serum phos-
phorus. Serum = 0.2 ml., iron-TCA =
S ml., molybdate = 0.5 ml.
z
5.
z5.
rI,
0
20 30 40
% LOSS OF SAMPLE DURING DECANTATION
Vol. 12, No. l�, 1966 INORGANIC PHOSPHORUS 881
oratories in New York that are now using the method. According to
private communicatioiis from Dr. Julius Carr* and Albert Haiiokt, tile
procedure can be readily adapted to tile determination of acid and
alkaline phosphatase in serum.
It is recognized that the analyst who is unfamiliar with the de-
cantation principle may have reservations about its validity. The
chemist, by training and experience, is inclined toward the use of
pipets for transfer of samples. Pipets or related devices are necessary
for measuring out serum and precipitant, but upon fixing the con-
centration of phosphate in the mixture the pipet becomes superfluous
for further sampling. Decantation offers greater speed than pipetting,
less chance of random contamination, and accuracy surpassing the
sensitivity of the clinical photometer.
The acceptability of sampling by decantation is contingent upon a
number of requirements (8). Foremost among these is that the super-
natant must not be diluted appreciably before the absorbance measure-
ment. If the color reagents are added in infinitesimally small volume,
theoretically 99% of the supernatant could be lost during decantation
with no effect on the analysis, provided enough sample remained for
the photometric reading. Under the conditions of the phosphorus
analysis the volume of color reagent (molybdic acid) used is finite, viz.,
one-tenth the volume of supernatant. As shown in Fig. 3, the analytical
error resulting from a 10% decantation loss is 1%; a 20% loss yields
about a 2% error. If the molybdate were double-strength and used in
one-half volume-i.e., one-twentieth the volume of supernatant-a 20%
loss of sample would result in an analytical error of only 1%.
Figure 3 was plotted from Equation 3, given below, and confirmed
*Methodist Hospital, Brooklyn, N. Y.
tBronx Municipal Hospital Center, Bronx, N. Y.
882 GOLDENBERG & FERNANDEZ Clinical Chemistry
by experiment. In this equation V� represents the volume of color
reagent (molybdate) alid V�1 is the volume of the superiiatant.
Analytical error (%) = X decantation error (%) (3)
The validity of this expression is easily checked by an example. For
ease of calculation it is assumed tile supernatant is exactly 10 ml. and
that the procedure calls for 1 ml. (one-tenth volume) of color reagent.
Suppose that 20% of the supernatant is lost during transfer. An ana-
lytical error of 20% would result if the sample (8 ml.) and color reagent
(1 ml.) were diluted to a prescribed volume before reading in a pho-
tometer. On the other hand, the error would be zero if the 8-mi. sample
were mixed with 0.8 ml. of color reagent to give a final volume of 8.8 ml.
It may be seen from purely volumetric considerations that the analyti-
cal error made in mixing 8 ml. of sample with 1 ml. of color reagent is
not equal to the 20% sample loss, but instead corresponds to diluting
the 8.8 ml. of color mixture to 9.0 ml. with excess color reagent. The
error is clearly (0.2/9.0) X 100 = 2.2%. A similar result is obtained
from Equation 3 by substituting 1 ml. for V�, 8 ml. for V,1, and 20%
for the decantation error as follows: (1/9) X 20 = 2.2%.
The decantation formula can be derived intuitively by following the
reasoning used in the example just given, or it may be derived by ele-
mentary geometry (8). The ratio, Ve/(V(. + Vd), is referred to as the
telescoping factor. For example, when the volume of color reagent is
one-twentieth the supernatant, a decantation error of 40% is telescoped
into an analytical error of about 2%.
References
I. Fiske, C. 11., and SubbaRow, Y., The colorlinetric determination of phosphorus. J. Biol.
Chests. 66, 375 (1925).
2. Kuttner, T., and Cohen, H. R., Micro colorimetric studies. I. A molybdic acid, stannous
chloride reagent. The micro estimation of phosphate and calcium in pus, plasma, and
spinal fluid. J. Biol. Chem. 75, 517 (1927).
3. Gomori, G., A modification of the colorimetric phosphorus determination for use with the
photoelectric colorimeter. J. Lab. GUn. Med. 27, 955 (1942).
4. Lowry, 0. H., and Lopez, J. A., The determination of inorganic phosphate in the presence
of labile phosphate esters. J. Biol. Chen,. 162, 421 (1946).
5. Sumner, J. B., Method for the colorimetric determination of phosphorus. Science 100, 413
(1944).6. Taussky, H. H., and Shorr, E., A microcolorimetric method for the determination of in-
organic phosphorus. J. Bud. Chem. 202, 675 (1953).
7. Dryer, R. L., Tammes, A. B., and Routh, J. I., The determination of phosphorus andphosphates with N-phenyl-p-phenylenediamine. J. Biol. Chem. 225, 177 (1957).
8. Goldenberg, H., Decantation as a precision step in colorimetrie analysis. Anal. Chesn. 28,1003 (1956).