V O L U M E 28, NO. 8, A U G U S T 1 9 5 6
1357 limit as 2 , and setting i? equal t o it, a n d further substituting a for t h e ratio z l / i l , Equation 4 becomes
centration is due entirely t o errors in il a n d 1 2 , the diffusion currents before a n d after t h e standard addition, respectively. It is apparent, however, t h a t a noticeable contribution is due to t h e error in t h e residual current io. This is so because in this t y p e of analysis there is no M ay t o measure io directly a n d i t must be assumed equal t o zero, extrapolated from t h e residual before the diffusion plateau, or estimated from t h e residual of solutions similar t o t h e sample. B y retaining this io t e r m a n d assuming, as did Meites, t h a t t h e volume of t h e standard is negligible compared to t h a t of the sample, it can be shown easily t h a t
T h e conditions for minimum error can be determined 1)). dlfferentiating Equation 5 with respect to a and setting the rerult equal to zero, bearing in mind the earlier assumptions t h a t E , and SOare independent of il and z? and hence of a. T h e folloning equation for optimum a results.
where C', is the roncentration of the sample and k is a constant which includes the concentration of t h e s t a n d a r d and the volumes of sample and s t a n d a r d . T h e s t a n d a r d deviation of C, can be expressed approximately l)y a n equation of t h e following form ( 1 )
I n Table I a comparison is given of the relative errors calculated from Equation 5 using a = 10 as recommended by hleites, 01 = 2 as recommended by t h e earlier norkers, a n d aG calculated from Equation 6. EI was set equal t o 1% in cases I and I1 and 0.1 % of i, in case I and 1% in cases I1 and 111.
where S,is the standard deviation of C',: and S,, SI, and S:! are tht. s t a n d a r d deviations of io, il, and i?,respectively. T h e relative error of C,, denoted by E,, is obtained by substituting Equation 1 into 2 and dividing both rides of the resiilt b y
Table I. Relative Error of Sample Concentration under Several Representative Conditions Using a's Recommended by Various Authors 70Error -
c'
S'
a
10
I
I1
111
1.8
10.1
10.0 2.0 1.4
2
2.8
a0
1.8
3.5 3.4
, To
simplifj- this equation, i o can be asPunirtl to be negligible compared to il a n d is and can he dropped. I n order t o determine t h e conditions iinder which E, is a minimum, it, is necessary to make pome assriniptions concerning t h e relationships of So, SI,a n d Sz t o io, i l , and i r . Previous authors ( 2 , 3, 5 ) evidently assume, although t h e assumption is never made explicitly, t h a t SI and S? are independent of il and i? and conclude t h a t t h e ratio of if t o 2'1 should be about 2. This assumption attributes t h e error in il a n d i? to such factors as electroactive impurities and charging current, a n d neglects the appreciable contribution to the error from such factors as temperature and fluctuation of mercury height. Considering t h e latter factors of primarj- importance leads to the assumption t h a t not S , and S, but t h e relative errors, S1,'iI a n d S?/i,, are independent of il :tiid i 2 . This assiimption was made by 3leites. Both approaches c:tn be combined by assuming t h a t So,S1/il, and S2,'iz are independent of ioj il, a n d if. Because Sl/il and S?/iu are measures of the same quantity, affected in both cases by the same factors, they are indistinguishable and can be represented by a common symbol, E,. From these considerations the following simplification of Equation 3 rreults.
T h e analyst in t h e practical situation is probably inclined to accept il a t face value and to make his standard addition sufficient t o make i 2 = i,n. Whether the accuracy gained in the optimization of a outweighs t h e bother of the manipulations involved depends o n the specific case. T h e analyst can readily determine 010 from Equation 6 and its associated error from Equation 5 , Comparing this error t o t h a t obtained with t h r 01 of the ordinary procrdure should decide t h e question. LITERATURE CITED (1) Dai-ies, 0. L.. ed., "Statistical Methods in Research and I ' r o d i ~ p tion," p. 37, Oliver and Boyd, London, 1949. (2) Hohn. H . . "Chemische Analysen niit den1 Polarographen," p. 5 1 . Springer-Verlag, Berlin. 1937. (3) Kolthoff, I. lI.,Lingane, J. J., "Polarography," 2nd ed., vol. I, p. 377. Interscience, S e w P o r k . 1952. (4) hleites, L., ANAL.C H E x . , 28, 139 (19%). (5) Taylor, J. K . , I b i d . , 19, 368 (1947). \Vrrm.i>f
H. REIXMLTH
Department of Chemistry and Laboratory for Kuclear Science Massachusetts Institute of Technology Cambridge 39, hlass.
From this expression it is apparent t h a t the optimuni values of
ii and 'i depend o n t h e relative values of E , and Sa. There are two cases of practical interest. T h e first is the cape in which il is fixed: the second is t h a t in which iu is fixed. I n all cases t h e accuracy can be increased without bound by simply increasing iI a n d (i, - i l ) until one or both of these limits is encountered. Hence all cases reduce t o one of these tu-o. While in theory i t might be argued t h a t il can always be varied, in practice i t is often not feasible for a variety of reasons. If it is not feasible to v a r y il, then E, can be minimized onlj. by increasing i2. However, if iI can be adjusted, the optimum ratio of iz t o il can be estimated in the following manner. Obviously i? will be made as large as possible, in order to minimize t h e first t e r m in Equation 4. I n general, however, there is some natural limit t o the size of i,, due either t o deviations from t h e Ilkovi6 equation or to the limitations of the current detector. Designating this
MEETING REPORTS
Society for Analytical Chemistry HE
Scottish Section of t h e society met M a y 11 in Edinburgh
T t o hear a talk by R. E. Stuckey, British D r u g Houses, Ltd., London, o n recent developments in complexones. Following the introduction into analysis of a number of cornplexing agents by Schwarzenbach, ethylenediaminetetraacetic acid (EDTA) i n particular has become increasingly used. Some methods available for the determination of metal cations using E D T A were discussed and the methods of end point determination were reviewed.
ANALYTICAL CHEMISTRY
1358
reagents (color, adsorption, fluorescent, and precipitation indicat.ors) observed visually or photoelectrically, electrical methods such as potentiometry, amperometry, and lov and high frequency conductometry, and miscellaneous techniques based on properties of electrode systems. Such methods may be applied on any scale, but physical difficultiei of observation of color change, etc., or of accommodation of electrodes in the available solution volume, render the choice less wide as the operating scale is progressively reduced. Problems arising in small scale work were mentioned, and application of the differential electrolytic potentiometric technique to the ultramicro scale was briefly reported.
The use of a new complexing agent, 1,2-diaminocyclohexanetetraacetic acid, which forms more stable chelates than EDTA, has further extended the analytical applications of complexones, and new indicators such as pyrocatechol violet and metalphthalein have been introduced. End point determination i n E D T A titrations often presents difficulty and the applications of high frequency titration methods is of great value. The principles of high frequency methods were briefly described and simple types of apparatus were shown. Conditions necessary for EDTA titrations were described and results obtained by different methods were discussed.
At a joint meeting of t h e Food Group of the Society of Chemical Industry and t h e Soriety for Analytical Chemistry, held May 23 in London, two papers n-ere presented and discussed.
T h e Physical Methods Group met with the Photoelectric Spectrometry Group a t Oxford on M a y 25 to discuss nilclear and paramagnetic resonance.
Some New Factors in Pectin Gel Strength. MAMIEOLLIVER, P.~ T ~ D AND E ,KATHLEER P. DENT,Chivers & Sons, Ltd., Cambridge. Gels prepared from rapid setting powdered pectins by boiling in the presence of sugar and acid t o p H 3.1 and total soluble solids content of 70% have shown increased strength in the presence of small quantities of some surface-active agents, and larger quantities ot depectiniaed fruit juices The degree of strength increase appears to be related t o the setting temperature of the pectin, there being little change in strength with slow setting samples. I n the case of gels made from concentrated extract of pomace the pattern is not constant hut, i n general, no marked change in strength is found even with rapid setting extracts. These results have been used for a critical examination of the British (acid in boil) and American (acid in glass) methods for the strength grading of pectins. Various anomalies between the two prcrcedures have been resolved and a modified strength grading method was proposed which gives results more in line with practical jam manufarture.
Analytical Applications of Nuclear Resonance Spectroscopy. RICHARDS, Lincoln College, Oxford.
11.
A short description was given of what happens when a nuclear resonance spectrum is excited. Some of the factors which determine adsorption line shape, width, and intensity were discussed with particular reference to the analytical applications of the method. The nature of the “chemical shift and “multiplet interactions” which are observable under conditions of high resolution was described. The scope and limitations of the method for various t,ypes of analysis, as they appear at present, were discussed and illustrated with representative examples. Techniques of Magnetic Resonance Spectroscopy. E. E. SCHNEIKing’s College, University of Durham.
DER,
4
Binding of Ions and Detergents to Pectin, Protein, and Other Colloid Systems. B. A. PETHICA, Department of Colloid Science, University of Cambridge. The binding of ions t o lyophilic colloids has been studied by electrophoresis (particularly with the colloids adsorbed on microscopic particles), equilibrium dialysis, solubility, and viscosity methods, and calorimetry. The bulk of the data was for protein and polyelectrolyte systems, but sufficient, w s available for pectin colloids to allow interpretation of the gel properties of pectins in relation t o charge and ionic additives, including detergents. The relevance of hydrogen bonding and van der Waals’ interaction may also be suggested from work on these forces in related systems such as aluminum soap gels.
-4joint meeting of the Jlicrochemistry Group and t h e North of England Section of t h e Society for Analytical Chemistry and t h e Bradford Chemical Society was held May 25 a t Bradford, when three papers on microvolumetric analyses were presented and discussed. Apparatus and Technique. D. IT. WILSON,Department of Chemistry, Sir John Cass College, London. Some types of apparatus for the delivery and titration of small volumes of liquids were described. Their manipulation, accuracy, and the kinds of error to which they were subject were discussed. Primary Standards. R. BELCHER,Department of Chemistry, University of Birmingham. The requirements of primary standards for use in microanalysis were discussd. New observations were made concerning old-established standards with special reference to those used in standardizing solutions for completing determinations in organic microanalysis. A brief survey was given of new primary standards, which appear t o be of promise in both organic and inorganic microanalysis. End Point Location. E. BISHOP,Department of Chemistry, University of Exeter. Methods of locating the end point of a titrimetric process were enumerated and briefly examined: use of principal and ancillary
Electron spin magnetic resonance (usually described simply as “paramagnetic resonance”) is observed with paramagnetic atoms, ions, or molecules and is associated with unpaired electron spins. Nuclear magnetic resonance is observed in diamagnetic materials and is entirely due to the magnetism of the atomic nuclei. These phenomena can be understood most easily by considering the Larmor precession of classical magnetic gyroscopes in a constant magnetic field. A resonant absorption of magnetic energy occurs if a high frequency magnetic field applied normal to the constant field is in resonance with the precession frequency. Because of the different order of magnitude of the magnetic moments of electrons and nurlei, electron spin resonance at a constant magnetic field of some kilogauss occurs a t microwave frequencies, while nuclear rssonance frequencies lie in the radio-frequency range. The aspects of magnetic resonance studies which are of interest t o the chemist were surveyed and the relevant experimental techniques were desrribed. A number of special experimental problems were discussed in detail: observation of paramagnetic resonance in aqueous solutions, quantitative determination of the concentration of unpaired electron spins and magnetic nuclei from the intensity of paramagnetic and nuclear resonance absorption, respectively, and accurate measurement and analysis of complex paramagnetic resonance spectra. of organic radicals arising from the hyperfine interaction of the unpaired electrons with neigliboring nuclei.
.
Detection of Photochemically Formed Radicals by Magnetic Resonance. D. J. E. I N Q R University .~~, of Southampton. The technique of electron resonance has been employed for some time not only to observe the state and presence of normal paramagnetic atoms hut also t o study organic free radicals. Until recently the work on free radicals had been confined t o known stable compounds. Measurements were outlined which show that the technique can he extended t o cover many different types of radicals formed by breakage of bonds with ultraviolet irradiation. This method can he applied generally to any systein in which the r e d t a n t radicals can be trapped and observed after their produrtion, or alternatively can be observed during irradiation. In this way OH radicals trapped in frozen water-peroxide solutions have been studied, as well as several different organic radicals formed from ethyl iodide, benzyl chloride, and similar compounds. Trapped radicals can also be formed by x- and y-ray irradiation and in both this and the ultraviolet experiments, a marked hyperfine structure is often obtained. The occurrence of such a hyperfine structure is one of the powerful analytical tools of electron resonance, as it gives immediat.e identificatiw of the particular atoms involved, even if they are present in concentrations of only IO*.lf or lower.
