An Automatic Reaction Rate Method for Determination of Phosphate S. R. Crouch and H. V. Malmstadt Department of Chemistry and Chemical Engineering, Unioersity of Illinois, Urbana, Ill. A new method for the determination of phosphate in aqueous solution and in blood serum is described that utilizes an automatic digital readout of the initial rate of formation of molybdenum blue from phosphate, molybdate, and ascorbic acid. Phosphate concentrations in the range 1-12 ppm P are determined with 1-274 relative error in aqueous solution. Blood serum inorganic phosphate concentrations in the range 3-6 mg P/100 ml are determined with similar relative errors. The method is rapid, requiring about 20-30 seconds of reaction time per sample. Advantages over the conventional method of phosphate analysis are discussed.
THE MOLYBDENUM BLUE PROCEDURE is widely used for the determination of inorganic phosphate in biological samples ( I ) . The method suffers from susceptibility to interferences, instability of the blue product, and long measurement times. These problems are especially significant in biological materials where hydrolysis of phosphate esters, catalyzed by molybdate, can occur over the long analysis period (generally several minutes). In addition, turbidity of deproteinized samples can lead to large errors in spectrophotometric results. A new automatic reaction rate procedure that is based on an experimental study of the mechanism of the molybdenum blue reaction has led to increased speed and reliability in the determination of phosphate. Under controlled conditions the initial rate of formation of phosphomolybdenum blue from phosphate, molybdate, and ascorbic acid is directly proportional to the phosphate concentration. Automatic instrumentation is used to provide a digital readout proportional to the phosphate concentration. The rate procedure is precise and accurate in the range of 1-10 ppm phosphorous and requires less than 1 minute of reaction time per sample. The short measurement time minimizes errors due to hydrolysis of phosphate esters in biological materials and allows many determinations to be carried out in a short time. In addition, because the rate of change of absorbance of phosphomolybdenum blue is measured and not the absolute absorbance value, turbid samples may be analyzed with little error. The phosphate procedure is simple. Ascorbic acid is injected into the reaction cell containing the acid-molybdate reagent and the phosphate sample, and the result is read off a digital voltmeter about 20 seconds after the reaction is started. Phosphate results for both aqueous solutions and blood serum samples are precise and accurate to about 1 - 2 z . GENERAL CONSIDERATIONS
Reaction Mechanism. A mechanistic study of the molybdenum blue reaction (2) has led to the following relationship between the rate of absorbance change a t 650 mp and the concentrations of reagents: (1) 0. Lindberg and L. Ernster, “Methods of Biochemical Analysis,” 0. Glick ed., Vol. 111, Wiley, New York, 1956, pp. 1-22. (2) S. R. Crouch and H. V. Malmstadt, ANAL.CHEM.,39, 1084 (1967).
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ANALYTICAL CHEMISTRY
dA _ _- Kl[POI-3][Mo(VI),I6[Ascorbic acid] dt Kp[Hf]lo K3[Ascorbic acid]
+
(1)
where [Mo(VI),] refers to the total concentration of Mo(V1) in the mixture and [H+] refers to the total acid concentration. If the starting concentrations of sulfuric acid, Mo(VI), and ascorbic acid are the same for each sample, the initial rate of absorbance change is directly proportional to the phosphate concentration
Optimum Reagent Concentrations. For the procedure described here, the sulfuric acid concentration is greater than 0.8N to ensure that the reaction is slow enough to provide an easily measured rate of change of absorbance. Under these conditions Equation 1 simplifies to
dA - _ - K’[P0,-3][Mo(VI)t]6[Ascorbic acid] dt [H+]’O
(3)
K’ can be empirically evaluated from recorded curves by measuring the initial rate of change of absorbance in an experiment in which all initial reactant concentrations are known. The following procedure is used to optimize reagent concentrations: 1 . The range of phosphate concentration to be measured is noted. 2. The Mo(V1) concentration is chosen to ensure complete reaction with phosphate (large excess). 3. The ascorbic acid concentration is similarly chosen to ensure complete reduction to phosphomolybdenum blue. 4. The sulfuric acid concentration necessary to give a chosen rate is calculated from K’ and the reactant concentrations; the desired rate is chosen such that initial kinetics prevail for at least 30 seconds with the highest phosphate concentration (not more than of the total reaction occurs in 30 seconds). For the procedure described here the phosphate concentration in the reaction cell varies from 0.38 to 2.3 ppm P, corresponding to a blood serum range of 2-12 mg PjlOO ml. The Mo(V1) concentration in the reaction cell is O.OlM, and the ascorbic acid concentration is 0.057M. The sulfuric acid concentration is 0.845N. Temperature Control. Temperature variations have a large effect on the reaction rate, and therefore a reaction cell thermostated at 25.0” i 0.1 O C is employed. Reagents and samples are also kept at this temperature to ensure rapid thermal equilibrium in the reaction cell. Induction Period. Under the conditions employed in this procedure, a short induction period must pass before steady initial rates are obtained. Usually 10-20 seconds are required. Therefore, digital voltmeter readings are not taken until after this period is over, Because the absorbance C’S. time curve is also recorded, it is easy to observe when the induction period is over.
5z
Working Curve. Although the rate of reaction is directly proportional to the phosphate concentration, instrumental factors lead to a small but reproducible intercept when standards are plotted against digital readout. Therefore, a standard curve is rapidly established using two or three aqueous phosphate standards. The same standard curve may be used for periods up to one week, after which decomposition of the ascorbic acid can lead to erroneous results. Blood Serum Determinations. The automatic rate procedure is easily adapted to the determination of phosphate in blood serum. Trichloroacetic acid (TCA) is used to precipitate the protein. Because of the large effect of the acid concentration on the reaction rate, it is necessary to neutralize the serum supernatant before the measurement step. Attempts to add the appropriate amount of TCA to aqueous standards led to erroneous and irreproducible results because of the difficulty of duplicating the acidity of the serum supernatant. Therefore a simple neutralization t o pH 4-8 is used. EXPERIMENTAL
Instrumentation. The basic spectrophotometric reaction rate measuring system has been previously described (3). The operational amplifier system is stabilized by a Heath (EUA-19-4) chopper stabilizer unit. Voltages proportional to the slopes of reaction curves are measured on an integrating digital voltmeter (UDI, Heath Model EU-805 X) with provision for a 10-second integration period. In addition, several readings are taken with the digital voltmeter during each reaction for additional averaging. These readings are taken only during the initial, straight-line portion of the absorbance cs. time curve. Reagents. All reagents are prepared in deionized water. The molybdate solutions are stored in polyethylene bottles to avoid possible contamination from silicon. Stock phosphate solutions are prepared by dissolving 0.4393 grams of oven-dried K H 2 P 0 4and diluting to 1 liter. This solution is 100 ppm phosphorous. Working standards of 1, 2, and 3 ppm P are prepared from this stock. These standards represent actual serum inorganic phosphorous concentrations of 2, 3, and 6 mg/100 ml, as the sample is diluted by 1-20 during the deproteinization and neutralization step. For phosphorous concentrations outside the normal range, additional standards representing 8, 10, and 12 mg PjlOO ml can be prepared and carried through the same measurement step. A 0.018M Mo(V1) solution in 1.48N H2S04is prepared by dissolving either 1.089 grams of N a 2 M o 0 4 . 2 H 2 0or 0.794 gram of ( N H ~ ) ~ M o ~ O ~ in ~ .deionized ~ H ? O water in a 250-ml volumetric flask. Then 10 ml of concentrated H2S04 is added and diluted to volume. The solution is stored in a plastic bottle. For best results, the acid-molybdate reagent should be prepared one day before using it. This solution is replaced after about two weeks. A 0.10M ascorbic acid solution is prepared by dissolving 1.76 grams of ascorbic acid in water and diluting to 100 ml. This solution is replaced every week. A 9 % (wjv) solution of trichloroacetic acid in water is prepared. Concentrated NaOH, 0.1N NaOH, and thymol blue indicator (0.1 %> are prepared. Procedure. PREPARATION OF EQUIPMENT.The SpectroElectro titrator is turned on about 30 minutes before the measurements are started. The 650-mp filter on the titrator is used in conjunction with a yellow ultraviolet cutoff filter. The recording photometer is calibrated to read 100% transmittance full scale with deionized water in the cell and then switched to 10% transmittance full scale by increasing the current sensitivity 10-fold. Appropriate suppression
voltage is used to bring the pen on-scale with deionized water in the cell. The operational amplifiers with chopper stabilizers are turned on and allowed a 30-minute warm-up period. The balance switches on the ratemeter are used to ensure that the stabilizers are properly balanced. For this work the ratemeter noise suppression resistor R, was 300 K . The integrating digital voltmeter (1-volt range, 10-second integrate time) is connected directly to the ratemeter output. For calibration purposes, the phosphate standard of highest concentration (usually 3 ppm P) is carried through the measurement step, and the calibrating potentiometer on the ratemeter is adjusted to give a reading of about 100 mV on the digital voltmeter. PREPARATION OF BLOODSERUM SAMPLES.Two procedures can be used for deproteinizing and neutralizing the serum samples. In the first procedure the serum and deproteinizing agent are mixed and rapidly filtered through a glass-fiber filter ( 4 ) . In this manner deproteinization can be accomplished in less than 1 minute. Alternatively, the sample can be centrifuged and the supernatant utilized for analysis. For the filtration procedure 0.25 ml of serum is transferred with a hypodermic syringe into a 5-ml beaker and 2.25 ml of 9 % trichloroacetic acid is added. The solution is mixed thoroughly and drawn by vacuum into the calibrated tip of a three-way Teflon (DuPont) stopcock through a glassfiber filter (4). The single arm of the stopcock is drawn out and calibrated to deliver 1.5 ml. When the tip is filled with filtrate, the stopcock is turned turn to remove the vacuum. The stopcock is then turned another 1/4 turn and the sample is allowed to drain into a 3-ml volumetric flask to which 1 drop of thymol blue indicator is added. Concentrated NaOH is then added dropwise until the indicator begins t o change from red to yellow (noted by localized yellow color). Then 0.1N NaOH is slowly added until the yellow color remains after shaking. The pH is now between 3.5 and 8. Above pH 8 the indicator turns blue, and 9 % TCA can be used to readjust to the yellow color if the endpoint is overshot. After neutralization, the solution is diluted to 3.00 ml. A 2.00-ml aliquot is taken for analysis. The entire deproteinization-neutralizationstep takes 2 to 3 minutes. In addition, this step can be completely automated with the addition of automatic pipets (4). For the centrifuging procedure, the same quantities of serum and 9 % TCA are mixed in a small centrifuge tube and centrifuged for about 5 minutes. The supernatant (1.50 ml) is transferred to a 3-ml volumetric flask and neutralized as described above. MEASUREMENT STEP. Three milliliters of the acid-molybdate reagent is pipetted into the reaction cell and the stirring is started. Two milliliters of the neutralized sample or phosphate standard is pipetted into the cell. The recording photometer is adjusted until the pen is a few divisions from the end of the scale representing 100% transmittance. The reaction is started by injecting 0.25 ml of ascorbic acid into the cell. As soon as the recording photometer indicates a steady initial rate, 3 or 4 readings are recorded from the integrating digital voltmeter and these readings are averaged. Individual digital voltmeter readings for successive 10-second integration periods during a single reaction can vary by 5-10 %, but averaged rates on duplicate samples agree within 1-2 %. If the recording photometer indicates the presence of noise, the stirring is turned off 10-20 seconds after injecting the ascorbic acid. Between samples the cell is emptied with an aspirator tube and rinsed once or twice with deionized water. CALCULATIONS. Standard phosphate solutions are plotted as 2, 4, and 6 mg PjlOO ml against the average initial rates. The concentrations of samples are read directly from the
(3) H. V. Malmstadt and S. R. Crouch, J . Chem. Educ., 43, 340
(1966).
(4) H. V. Malmstadt and H. L. Pardue, C/h. Cliem., 8, 606 (1962). VOL. 39, NO. 10, AUGUST 1967
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standard curve. Standards representing as much as 12 mg PjlOO rnl can be run using this same procedure. For phosphate solutions outside this range, a different procedure is necessary.
Table I. Automatic Results for Phosphate Based on Two Standards
Direct rate readout'"
Phosphorous concentration in ppm Taken Foundb Error
z
1 .oo 1.50 2.00 2.50 3.00
34.6 49.9 66.0 79.0 95.5
...
...
1.50 2.03 2.46
+1.5 -1.6
0.0
... Averages of triplicate runs, * Based on 1.00 and 3.00 ppm standards.
, . .
a
Table 11. Precision of Automatic Results for Aqueous Phosphate Solutions 2.00 ppm Phosphorous Direct rate readout Deviatfon 65.6 66.5 66.0 66.6 65.4 Average 66.0 Rel. std. dev. 0 , 8
0.4 0.5 0.0 0.6 0.6
z 3.00 ppm Phosphorous
95.4 95.2 96.3 96.0 95.0 95.0 Average 95.5 Rel. std. dev. 0 : 6 %
0.1 0.3 0.8 0.5 0.5 0.5
Table 111. Automatic Results for Phosphate in Control Blood Serum Phosphorous, mg per 100 ml serum Error Reporteda Found
z
3.0 3.4 3.5 4.6 6.1
2.98 3.41 3.56 4.59 6.12
-0.7 +0.3 +1.7 -0.2 +O. 3
a Manufacturer's values, obtained by classical molybdenum blue procedure ( 5 ) (Averages of 1000 determinations).
Table IV. Precision of Automatic Results on Control Sera Phosphorus, mg per 100 ml serum Reported Found 3.0
Unassayed 4.6
2.97,2.95,3.02,2.99 3.45, 3.52, 3.37 4.57, 4.65, 4.55
Rel. std. dev., Z 1.2 2.1 1.2
Table V. Recovery of Phosphate Added to Serum Phosphorous concentration in mg/100 ml Present in serum Addeda Found Recovery
z
3.45 3.45 3.45 3.45
1.09 1.51 1.87 2.18
4.55 5.00 5.30 5.60
101 103 99 99
RESULTS AND DISCUSSION
Aqueous Phosphate Solutions. Under the conditions chosen the direct digital rate readout varies linearly with the phosphate concentration over the range of 0-12 ppm. Because of a small instrumental blank, a working curve of two points is necessary. Results calculated on the basis of two phosphate standards are given in Table I. These data indicate that an accuracy of 1-2% can be expected for aqueous phosphate solutions using the automatic rate procedure. Table I1 shows results of reproducibility studies on two aqueous standards. Data from duplicate and triplicate runs also indicate a precision of about 1%. Preliminary results indicate that the precision of replicate samples can be improved by using solutions which are free from particles, and by taking care to exclude all other potential noise sources. The data in Table I1 were taken with no particular precautions to illustrate the precision which can be expected on a routine basis. Phosphate in Blood Serum. The normal range of phosphorous in human blood serum is 2.5-4.0 mg per 100 ml of serum. Using a 0.25-ml sample of serum and carrying it through the 1-20 dilution necessary for deproteinization and neutralization, the final concentration is 1.25-2.00 ppm, which is within the useful range of the procedure. Several deproteinization reagents were tested, including perchloric acid, trichloroacetic acid, and silicotungstic acid. Results were satisfactory using all but the latter. Perchloric acid was discarded because it introduced a phosphate blank. The deproteinization and neutralization procedure was tested on control serum standards containing both normal and abnormal amounts of phosphorous, and the quantitative results are shown in Table 111. These data are based on a working curve constructed from 1, 2, and 3 ppm aqueous phosphate standards. The differences between measured values and manufacturer's results (based on averages of 1000 determinations) are within 1-2 %. The reproducibility of the overall procedure for phosphate in 0.25 ml of serum is illustrated in Table IV. These results indicate a precision comparable to that obtained on aqueous phosphate standards. The data in Table V show the recovery of aqueous phosphate standards added to a serum sample which was analyzed by the rate procedure. Recoveries of phosphate varied from 99 to 103 with an average recovery of 100%. Interferences. A quantitative study of interferences has not been attempted; however, results indicate no major interferences in deproteinized serum samples. It should be noted that many of the deproteinized serum samples were turbid which caused the initial absorbance to be higher than that of a deionized water or TCA blank. Also, the slight indicator color from the neutralization step causes a n additional initial absorbance. Neither of these sources contribute to the rate of absorbance change and hence d o not lead to errors in the rate procedure. Preliminary results indicate that the reaction rate procedure should be advantageous in other biological samples, where results are often limited by hydrolysis of phosphate esters such as adenosine triphosphate (ATP). Because the rate measure-
a Standard phosphate solutions were added to serum originally containing 3.45 mg PjlOO ml.
( 5 ) C. H. Fiske and V. Subbarow, J . B i d . Chem., 66, 375 (1925).
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ments are obtained within a few seconds, the contribution of organic phosphate to the measured values should be very small. Further work on this aspect is under way. Ionic strength variations were seen to have little effect on the measured reaction rates. Phosphate standards prepared in 3000 ppm NaCl gave the same rate as deionized water standards. Alternate Analysis Procedures. The rate measurements described here can be made manually by determining the slopes of recorded absorbance us. time curves. Comparable results can be obtained; but the automatic procedure is less time-consuming and less subject to operator bias. Alternatively, the variable time procedure (6) can be used in which (6) W. J. Blaedel and G. P. Hicks, “Advances in Analytical Chemistry and Instrumentation,” C. N. Reilley Ed., Vol. 3, Wiley, New York, 1964, pp. 130-3.
the time interval is measured for a fixed absorbance change. Generalizations. The automatic reaction rate method should be applicable to other phosphate-containing materials. In addition, it should be possible to eliminate many interferences in the classical molybdenum blue procedure by the rate method. For example, silicate reacts with molybdate and a reducing agent to give a similar blue product, whose rate of formation can be made negligibly slow in comparison to the rate with phosphate by proper control of pH. Hence a kinetic separation or a differential kinetic analysis of phosphate and silicate is possible. Preliminary work in this area is under way. RECEIVED April 3, 1967. Accepted June 2, 1967. Presented at the Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, March 1967.
Selection of Wavelengths for Atomic Absorption Spectrometry Marvin Margoshes Spectrochemical Analysis Section, National Bureau of Standards, Washington, D. C . 20234 The theoretical basis for the absorption of light by atoms is examined for atomic absorption spectrometry with a line source and with a continuum source. A method is described for selection of wavelengths to be measured from published atomic constants. The most sensitive line can be selected; but if the absorbance measured with this line is too large, another line having an appropriate sensitivity can be chosen. The methods have been tested with published data for atomic absorption spectrometry with hollow cathode lamps and with new data for atomic absorption spectrometry with a continuum source. I n both cases, the accuracies of the predictions are adequate for the purpose of line selection, Examples are discussed for which the theory does not agree with experiment.
The purpose of this publication is to describe simple methods for predicting the relative sensitivities of two or more absorption lines of the same element. The predictions are shown to be in agreement with experimentally determined relative sensitivities in most cases. However, instances are also discussed of disagreement between predicted and measured relative sensitivities, Often, such differences can be anticipated when the causes of disagreement are understood. In general, the selection of lines by the methods here described can best serve as a guide for experimental measurements, rather than as a replacement for experiment. THEORY
SELECTION OF A WAVELENGTH for measurement in atomic absorption spectrometry is ordinarily based on published data on suitable lines or on direct measurements on a number of lines of the analyte (element being determined) of either the concentration required to give a selected absorbance or the absorbance at a fixed concentration. Direct measurements on many lines are time-consuming, and reliance on published data may not result in the selection of the best possible wavelength. Differences in instrumentation must be taken into account, and the necessary information may not be given in the literature. For example, the most sensitive line of an element may be in a wavelength region that was not accessible with the spectrometer employed in the original measurements. The particular filler gas in the hollow cathode lamp is an experimental variable which can affect the choice of wavelengths, because the gas may have emission lines nearly coincident with one or more lines of the analyte. When there are such adjacent interfering lines, either from the filler gas or the analyte, the spectral band pass of the spectrometer becomes an important factor. When two or more analytes are to be determined in the same solution, it will not always be possible to make use of the most sensitive line of each element, as only a limited concentration range can be covered with a particular absorption line. There has been little information published on wavelengths suitable for the determination of elements present at high concentrations.
The Beer-Lambert law states that the absorbance, A , is equal to 0.43 abc, where 0.43 is the log lee, a is the absorptivity, b is the absorption path length, and c is the concentration of the absorbing species. In practice, the factor 0.43 is often incorporated into the absorptivity. This law will hold only when the absorptivity is constant over the band pass of the spectrometer, and it will be only approximately correct for atomic absorption spectrometry where the band width, which is effectively determined by the width of the emission line from the hollow cathode lamp, is comparable to the absorption line width in the flame. If the absorbance is measured over the entire width of the absorption line, then a is equal tof,~irc2/mc, where hiis the oscillator strength for the transition from the lower energy level, i, to the upper energy level, j , E , and rn are charge and mass of the electron, and c is the velocity of light
(0. When the lower energy level is the ground state of the atom, the concentration of the absorbing species is simply the population in the flame of atoms in the ground state, No. For absorption lines due to transitions from energy levels above the ground state with an energy Et, the population, N,, of
(1) H. G. Kuhn, “Atomic Spectra,” Academic Press, New York, 1962, p. 63. VOL. 39, NO. 10, AUGUST 1967
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