Abstract:
The invention relates to a process for determining the composition of binary liquid mixtures. This process is characterized in that a solvatochromic compound is added to the sample to be analyzed, the solvatochromism band λ max  is determined in the UV-spectrum, the E T  -value (molar stimulation energy) of the solvatochromic substance is calculated and the concentration of the more polar component is determined in accordance with the following equation 
     
       c.sub.P =c*exp(E.sub.T /E.sub.D -E.sub.T °/E.sub.D)-c* (1) 
     
     in which 
     c P  represents the concentration of the more polar component, the component having the greater E T  30-value being defined as the more polar component, 
     E T  represents the molar excitation energy of the solvatochromic compound, 
     E T  ° represents the E T  -value of the pure, more apolar component, 
     E T  30 is the E T  -value using pyridinium phenol betaine and 
     c* and E D  are empirical parameters which may be taken from Tables or empirically determined.

Description:
This application is a continuation, of application Ser. No. 322,636, filed Nov. 18, 1981, now abandoned. 
    
    
     BACKGROUND OF THE INVENTION 
     This invention relates to a process for determining the composition of binary liquid mixtures by which the concentrations of the individual components may readily be determined. 
     PRIOR ART 
     K. Dimroth and C. Reichardt [Z. Analyt. Chem. 215, 344 (1966)] report on studies of binary solvent mixtures using solvatochromic dyes. These authors observed that the position of the longest-wave band in the UV-spectrum of solvatochromic substances is greatly influenced by the solvent used. This property has proved to be particularly useful for characterising the polarity of solvents. In apolar solvents, such as dioxane for example, pyridinium-N-phenol betaines for example absorb in the long-wave region, whilst in polar solvents, such as methanol for example, they absorb in the short-wave region. The maximum of this solvatochromic absorption is termed λ max . The molar excitation energy E T  may be calculated from the absorption wavelength λ max  in accordance with the following equation: 
     
         E.sub.T =28,590(kcal·nm·mol.sup.-1)/λ.sub.max. 
    
     The authors drew up calibration curves for nine mixtures of organic solvents with water. These calibration curves enable the water content of a mixture of unknown composition to be determined. However, this known process is attended by the disadvantage that calibration curves first have to be drawn up and that it is time-consuming and laborious. 
     The E T  -values used in the above process are generally suitable for characterising the polarity of organic solvents and the E T  -scale is now the most frequently used polarity scale [cf. K. Dimroth and C. Reichardt &#34;Angewandte Chemie&#34; 91, 119 (1979); K. Dimroth and C. Reichardt &#34;Fortschritte der chemischen Forschung&#34;, Vol. 11/1, page 1 (1968)]. 
     OBJECT OF THE INVENTION 
     The object of the present invention is to provide a simple and accurate rapid test for determining the composition of binary liquid mixtures. 
     SUMMARY OF THE INVENTION 
     The present invention relates to a process for determining the composition of binary liquid mixtures which is characterised in that a solvatochromic compound is added to the sample to be analysed, the solvatochromism band λ max  in the UV-spectrum is determined, the E T  -value (molar excitation energy) of the solvatochromic substance is calculated and the concentration of the more polar component is determined in accordance with the following equation 
     
         c.sub.p =c* exp (E.sub.T /E.sub.D -E.sub.T °/E.sub.D)-c* (1) 
    
     in which 
     c p  represents the concentration of the more polar component, the component having the greater E T  30-value being defined as the more polar component, 
     E T  30 represents the molar excitation energy of pyridinium phenol betaine in the particular solvent, 
     E T  represents the molar excitation energy of the dye used and 
     E T  ° represents the E T  -value of the pure, more apolar component, 
     c* and E D  are empirical parameters which may be taken from Tables or empirically determined. 
    
    
     BRIEF DESCRIPTION OF THE FIGURES 
     FIG. 1 contains a plot of E T  30 against in c p  for a methanol-acetone mixture. 
     FIG. 2 contains a plot of E T  30 against ln(c p  /c*+1) for a methanol-acetone mixture. 
     FIG. 3 contains a plot of E T  30 against ln c p  for an ethanol-acetone mixture. 
     FIG. 4 contains a plot of E T  30 against ln(c p  /c*+1) for an ethanol-acetone mixture. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The Applicant has surprisingly found that, for all the binary systems studied, there is a connection between the E T  -values of solvatochromic substances and c p  according to equation (1) above. 
     The E T  -values may be calculated from λ max  of the solvatochromism band of the solvatochromic substances in accordance with the following equation 
     
         E.sub.T =28,590 kcal·nm.·mol.sup.-1 /λ.sub.max (2) 
    
     To determine the E T  -values, the solvatochromic substance is dissolved in the sample to be analysed and λ max  is measured in known manner. The concentrations are preferably selected in such a way that the extinctions at λ max  lie in the extinction range from 0.4 to 1.2, preferably in the extinction range from 0.5 to 1.0 and, more preferably, in the extinction range from 0.7 to 1.0. Any suitable UV-spectrometer may be used for determining the λ max  -values. 
     Equation (1) is a two-parameter equation in which c* and E D  may be determined for each binary solvent mixture by a simple procedure in which mixtures of the two samples to be analysed in known concentrations are prepared, a solvatochromic compound is added to the solutions and the E T  -values of these solutions are determined. The respective contents of the two components in the solutions are then converted into concentrations and, in a graph, the E T  -values obtained are plotted against ln c p . The slope E D  and the ordinate section b of the linear part are determined and c* is calculated in accordance with the following equation 
     
         c*=exp [(E.sub.T °-b)/E.sub.D ]                     (3) 
    
     The concentrations may be converted into percent by weight in accordance with the following equation 
     
         % by weight=c.sub.p [mol/1]·Mw.sub.p /(ρsolution[g/ml]·10)                        (4) 
    
     in which 
     Mw p  is the molecular weight of the more polar component and 
     ρ is the density of the solution. 
     For frequently used solvents, the values E D , c* are shown in Table I below. E T  ° is the value of the pure, more apolar component. 
     DETERMINATION OF THE VALUES OF TABLE I 
     The E T  -value is determined by a simple procedure. The pyridinium phenol betaine corresponding to the following formula ##STR1## is dissolved in a small quantity (&lt;5 mg) in the solvents to be studied. λ max  of (I) in this solution is determined and the E T  -value is calculated with the aid of equation (2). 
     The solvatochromic substances used in accordance with the invention are the above-mentioned pyridinium phenol betaine corresponding to formula (I) or so-called Kosower&#39;s dye which corresponds to the following formula ##STR2## [E. M. Kosower, J. Am. Chem. Soc. 80, 3253 (1953)] or the solvatochromic substances which are described in C. Reichardt&#39;s book &#34;Solvent Effects in Organic Chemistry&#34;, 1st Edition, Verlag Chemie Weinheim 1979, pages 193 and 194. It is particularly preferred to use the pyridinium phenol betained of formula (I). 
     Preferred components for binary mixtures are, in particular, the compounds described in Table (2) by C. Reichardt, &#34;Angewandte Chemie&#34; 91, pages 119 to 131 (1979), cf. in particular pages 124, 125. 
     The Applicant has studied numerous binary liquid mixtures and has found that, without exception, they may all be described by the equation observed. 
     The results obtained from 38 binary liquid mixtures are shown in Table I below. The E D  - and c*-values are quoted. Many different solvents were used in varying combinations. 
     
                                           TABLE I__________________________________________________________________________Determination of E.sub.D and c* with the pyridinium phenol betaine offormula (I) inaccordance with equation (1) for various solvent mixturesComponents.sup.(a)          c.sub.P.sup.(b,c)                E.sub.T.sup.o(d,e)                    c*.sup.(c,f)                        E.sub.D.sup.(d,f)                            E.sub.D.sup.(g)                               r.sup.(h)                                   n.sup.(i)__________________________________________________________________________1 1-butanol/acetone          0.01-10.9                42.2                    0.14                        1.99                            0.013                               0.99952                                   312 ethanol/acetone          0.02-17.1                42.2                    0.14                        2.27                            0.019                               0.99939                                   283 methanol/acetone          0.03-24.7                42.2                    0.10                        2.53                            0.019                               0.99973                                   294 water/acetone          0.06-55.4                42.2                    0.31                        2.83                            0.022                               0.99963                                   295 N--tert.-butyl form-          0.01-9.0                46.0                    0.27                        1.87                            0.013                               0.99948                                   31  amide/acetone6 ethanol/acetonitrile          0.01-17.1                46.0                    0.10                        1.83                            0.012                               0.99972                                   307 1-hexanol/acetonitrile          0.01-8.0                46.0                    0.08                        1.08                            0.019                               0.99786                                   298 methanol/acetonitrile          0.03-24.7                46.0                    0.06                        1.83                            0.033                               0.99877                                   319 water/acetonitrile          0.06-49.8                46.0                    0.15                        2.07                            0.024                               0.99877                                   2710  N--tert.-butylform-          0.01-9.0                34.5                    0.01                        2.27                            0.031                               0.99851                                   31  amide/benzene11  water/tert.-butyl          0.06-33.2                43.9                    1.01                        2.82                            0.050                               0.99666                                   26  alcohol12  water/tert.-butyl          0.4-7.4                49.7                    0.312                        1.40                            0.021                               0.99922                                   12  hydroperoxide13  water/dimethyl          0.06- 38.8                43.8                    11.43                        9.24                            0.18                               0.99527                                   27  formamide14  acetonitrile/1,4-dioxane          0.02-19.1                36.0                    0.77                        3.23                            0.031                               0.99909                                   2915  1-butanol/1,4-dioxane          0.01-10.1                36.0                    0.90                        5.39                            0.026                               0.99973                                   3016  ethanol/1,4-dioxane          0.02-17.1                36.0                    0.72                        4.99                            0.030                               0.99975                                   3017  methanol/1,4-dioxane          0.03-24.7                36.0                    0.35                        4.55                            0.037                               0.99922                                   3018  nitromethane/1,4-dioxane          0.02-18.6                36.0                    1.01                        3.49                            0.026                               0.99929                                   3119  pinacolone/1,4-dioxane          0.2-8.0                36.0                    3.43                        3.33                            0.16                               0.98025                                   1920  propionitrile/1,4-          0.01-14.1                36.0                    1.41                        3.33                            0.038                               0.99834                                   30  dioxane21  water/1,4-dioxane           0.6-55.4                36.0                    0.58                        4.34                            0.054                               0.99922                                   2222  1-butanol/nitromethane          0.01-10.9                46.3                    0.06                        1.43                            0.015                               0.99914                                   3123  ethanol/nitromethane          0.02-17.1                46.3                    0.03                        1.41                            0.030                               0.99704                                   3024  methanol/nitromethane          0.03-22.2                46.3                    0.01                        1.66                            0.018                               0.99947                                   2925  acetone/pyridine          0.03-12.2                40.2                    32.06                        4.01                            0.13                               0.98710                                   2826  1-dodecanol/pyridine          0.004-4.5                40.2                    0.89                        2.90                            0.03                               0.99901                                   3027  ethanol/pyridine          0.02-17.1                40.2                    12.75                        9.64                            0.17                               0.99554                                   3128  1-hexanol/pyridine          0.01-8.0                40.2                    1.11                        2.90                            0.047                               0.99763                                   3029  methanol/pyridine          0.03-24.7                40.2                    5.84                        6.92                            0.081                               0.99802                                   3130  nitromethane/pyridine          0.02-18.6                40.2                    13.62                        6.46                            0.14                               0.99384                                   3031  tert.-pentyl alcohol/          0.005-8.3                40.2                    0.95                        1.02                            0.025                               0.99341                                   29  pyridine32  water/pyridine          0.06-49.8                40.2                    5.48                        7.09                            0.12                               0.99599                                   2933  1-butanol/CS.sub.2          0.01-10.9                32.6                    0.03                        2.42                            0.028                               0.99906                                   3634  1,4-dioxane/CS.sub.2          0.01-11.7                32.6                    1.96                        1.21                            0.049                               0.98083                                   3135  1-octanol/CS.sub.2          0.01-6.4                32.6                    0.06                        2.83                            0.055                               0.99676                                   3036  pinacolone/CS.sub.2          0.3-8.0                32.6                    7.89                        9.30                            0.26                               0.99459                                   1637  methanol/acetone.sup.(m)          0.03-24.7                66.3.sup.(m)                    0.65                        4.66                            0.014                               0.99993                                   1138  methanol/1,4-dioxane.sup.(m)          0.03-24.7                63.0.sup.(m)                    2.66                        8.52                            0.18                               0.99384                                   31__________________________________________________________________________ .sup.(a) The more polar solvent is named first. .sup.(b) Concentration range studied. .sup.(c) In mol · 1.sup.-1 .sup.(d) In kcal · mol.sup. -1 .sup.(e) E.sub.T 30value of the more apolar solvent (cf. also lit.) .sup.(f) See text. .sup.(g) Variance of E.sub.D .sup.(h) Correlation coefficient where equation (3) is applied. .sup.(i) Number of measuring points. .sup.(m) Using Kosower&#39;s dye. 
    
     The new analysis process may be carried out with all kinds of binary systems. The samples to be analysed may be mixtures of aliphatic, cycloaliphatic and aromatic hydrocarbons, alcohols, ketones, nitriles, aldehydes, sulfur compounds such as, for example, sulfoxides, sulfones and mercaptans, of esters such as, for example, carboxylic acid esters, lactones and sulfonic acid esters, ethers, acetals and ketals, oximes, heterocyclic compounds, nitrogen compounds such as, for example, amines, amides, hydrazines and lactams, phosphorus compounds such as, for example, phosphines, phosphine oxides, phosphorous acids esters and phosphoric acid esters and substituted derivatives thereof. There are virtually no limitations in regard to the nature of the binary mixtures to be analysed. It is also possible to analyse mixtures of water and the above-mentioned solvents, as described in the applicant&#39;s copending application Ser. No. 322,571, filed simultaneously with the present application on Nov. 18, 1981 now abandoned and titled &#34;A Process for Determining Water in Samples Containing Water. 
     The new analysis process may be used for example in studies of the composition of monomer mixtures in copolymerisation reactions, in studies of the composition of solvent mixtures in the manufacture of dyes, lacquers and pharmaceutical products and--generally--in the analysis of mixtures of the type used in chemical syntheses and in the working up of extractants and flotation agents. Because it is highly specific, it may be used as a process for testing purity. 
     The sole limitation exists in cases where binary mixtures containing components of very similar polarity are used. In that case, the change in the measured value (λ max  or E T ) accompanying any change in the composition of the solvent is so small that exact content determination is no longer possible. 
     Another remarkable feature is that the two components of the binary mixture do not have to be liquid. The equation that has been found even applies to the liquid component of a mixture of a solid with a liquid or of two solids. 
     Accordingly, the composition of numerous samples to be analysed may be determined by the process according to the invention. For example, the solvent content of liquid, gaseous and solid samples may be determined by the process according to the invention. In the case of liquid samples, the solvent content is directly determined in accordance with equation (1) using a solvatochromic dye. 
     Gaseous samples may also be analysed. In order for example to determine the solvent content (LM1) of a gas, a specific volume of the gas is passed through a second high-boiling solvent (LM2) which washes out the first solvent. The solvent content of the gas may be determined by calculating the content of LM1 in LM2 in accordance with (1). 
     It is also possible to analyse solid samples. For example, the water content or the content of a certain solvent in polymeric naturally occurring materials, such as for example starch, cellulose, in synthetic polymers, in pharmaceutical preparations and solvent-binding substances, such as for example salts, etc., may be determined in accordance with the invention. 
     If dispersions or suspensions are analysed by the process according to the invention, it is important to ensure that some of the light transmitted through is scattered. Although this phenomenon does not in any way change the position of λ max , it can complicate the measurement. In a case such as this, it may be necessary to use a sensitive spectrometer for determining λ max . 
     The process according to the invention may be carried out at room temperature. For determining the Table values and in cases where highly accurate analytical results are required, it is preferred to carry out the process according to the invention at a constant temperature. However, this is not absolutely necessary because the effect of temperature on the process according to the invention remains within very narrow limits. 
     The process according to the invention may be carried out at any temperatures at which the dye used is heat-stable. At very high temperatures above the boiling point of the mixture, the process becomes complicated. 
     In one particularly preferred simplified embodiment of the invention, analysis in accordance with equation (1) is carried out by visual colour comparison with a colour scale. To this end, the absorption colour of the solution or dispersion is visually compared with a colour scale (absorption colour as a function of λ max  of the absorption) and λ max  absorption is determined on the basis of this comparison. 
     The process according to the invention may also be carried out by absorbing the solvatochromic dyes onto solids, for example paper, so that test strips are obtained. These test strips are dipped into the solution to be analysed. The test strips change colour according to the content of the individual components. λ max  is determined by a colour comparison with a colour scale (λ as a function of the absorption colour) and c p  is calculated in accordance with equation (1). 
     It is of particular importance to the result that there is a logarithmic relationship between the E T  -values and c p  according to equation (1). Accordingly, the relative accuracy of the determination of c p  is constant over a wide concentration range. c p  may even be determined with great accuracy where the more polar component is present in low concentrations 
     The invention is illustrated by the following Examples. 
     In the Examples, the UV-spectra are recorded by means of a Zeiss DMR21 UV-spectrophotometer. Visual comparison of the solution with a colour scale is sufficient for an approximate determination of concentration. 
     EXAMPLE 1 
     General procedure for determining the composition of binary liquid mixtures 
     Quantities of 0.1, 1, 2 . . . ml of the more polar component of the binary mixture are introduced into a 10 ml measuring flask. The measuring flask is made up to 10 ml with the other component. A small quantity (&lt;5 mg) of the phenol betaine of formula (I) is added to the solvent mixture and the position of the solvatochromism band λ max  is determined in the UV-spectrum at 25° C. The concentrations are intended to be selected in such a way that λ max  lies in the extinction range of 0.7 . . . 1.0. For accurately locating λ max , the point at which the line connecting the radii intersects the absorption curve may be determined in accordance with the Mathias rule. 
     λ max  is converted in accordance with equation (2) into the E T  -value which is subsequently introduced into equation (1) with the values E T  °, c* and E D  of Table I and c p  calculated. 
     In a graph, E T  is plotted against ln c p  and the slope E D  and the ordinate section b of the linear part are determined. c* is calculated in accordance with equation (3), as indicated in the specification. 
     The POLAR computer program is available for this procedure; this program also takes into account measured values in the non-linear part of the graph. 
     EXAMPLE 2 
     Special procedure for determining the parameters E D  and c* of the &#34;methanol-acetone&#34; system 
     Following the procedure described in Example 1, the milliliters of methanol indicated in Table 2 below are pipetted into a 10 ml measuring flask. The flask is then made up to 10 ml with acetone. The phenol betaine of formula (I) is dissolved in a small quantity (&lt;5 mg) in the solutions obtained, after which λ max  is measured. The milliliters introduced are converted into the concentration in mol·1 -1  c p  of methanol and the λ max  -values are converted into E T  30. ln c p  is then calculated. The results obtained are shown in Table 2. 
     
                       TABLE II______________________________________ml methanol      λ.sub.max             c.sub.p (mol/l)                          E.sub.T 30                               ln c.sub.p______________________________________0.00       677.0  0.000        42.2 -11.510.01       666.0  0.025        42.9 -3.700.02       662.0  0.049        43.2 -3.010.03       657.0  0.074        43.5 -2.600.04       650.0  0.099        44.0 -2.310.05       648.0  0.123        44.1 -2.090.06       643.0  0.148        44.5 -1.910.07       641.0  0.173        44.6 -1.760.08       638.0  0.198        44.8 -1.620.09       636.0  0.222        45.0 -1.500.10       628.0  0.247        45.5 -1.400.20       610.0  0.494        46.9 -0.710.30       598.0  0.741        47.8 -0.300.40       590.0  0.988        48.5 -0.010.51       586.0  1.260        48.8 0.230.61       580.0  1.507        49.3 0.410.71       573.0  1.754        49.9 0.560.80       567.0  1.976        50.4 0.680.90       563.0  2.223        50.8 0.801.00       562.0  2.470        50.9 0.902.00       543.0  4.940        52.7 1.603.00       533.0  7.410        53.6 2.004.00       530.0  9.880        53.9 2.295.00       523.0  12.350       54.7 2.516.00       522.0  14.820       54.8 2.707.00       519.0  17.290       55.1 2.858.00       516.0  19.760       55.4 2.989.00       512.0  22.230       55.8 3.1010.00      511.0  24.700       55.9 3.21______________________________________ The measurements were carried out at a temperature of 298.00° K. and the starting conditions were as follows: Concentration factor: 2.470 Energy factor: 28590 c*: 0.1 Number of measured values: 29 
    
     In FIG. 1, E T  30 is plotted against ln c p  and a straight line drawn through the linear part of the curve. The slope E D  of the straight line amounts to 2.53. 
     The ordinate section b has a value of 48.1, as reported in FIG. 1. 
     According to C. Reichardt &#34;Angewandte Chemie&#34; 91, 119 (1979), 42.2 kcal·mol -1  is the E T  °-value. 
     c* is calculated in accordance with formula (3): 
     
         c*=exp [(E.sub.T °-b)/E.sub.D ]→c*=0.097 mol·1.sup.-1 
    
     The more exact value for c* is calculated using the POLAR computer program: 
     
         c*=0.099 mol·1.sup.-1 
    
     It is now possible to analyse any mixtures with the aid of the calculated values c* and E D  for the methanol-acetone mixture. 
     The results obtained are shown in Table III. 
     The results of the machine evaluation of the methanol-acetone system are shown in FIG. 2. 
     
                       TABLE III______________________________________c(Mol/l) E.sub.T 30 ln (c.sup.+  c*)                         ln (c/c* + 1)______________________________________0.000    42.2       -2.31     0.000.025    42.9       -2.09     0.220.049    43.2       -1.91     0.400.074    43.5       -1.75     0.560.099    44.0       -1.62     0.690.123    44.1       -1.50     0.810.148    44.5       -1.40     0.920.173    44.6       -1.30     1.010.198    44.8       -1.22     1.100.222    45.0       -1.14     1.180.247    45.5       -1.06     1.250.494    46.9       -0.52     1.790.741    47.8       -0.17     2.140.988    48.5       0.08      2.401.260    48.8       0.31      2.621.507    49.3       0.47      2.791.754    49.9       0.62      2.931.976    50.4       0.73      3.042.223    50.8       0.84      3.162.470    50.9       0.94      3.264.940    52.7       1.62      3.937.410    53.6       2.02      4.339.880    53.9       2.30      4.6112.350   54.7       2.52      4.8314.820   54.8       2.70      5.0217.290   55.1       2.86      5.1719.760   55.4       2.99      5.3022.230   55.8       3.11      5.4224.700   55.9       3.21      5.52______________________________________ Correlation coefficient: 0.99973 Sigma E.sub.D : 0.018693 
    
     EXAMPLE 3 
     Procedure for determining the content of methanol in a mixture of methanol and acetone of unknown concentration 
     The phenol betaine of formula (I) is dissolved in a mixture of methanol and acetone and λ max  is determined. 
     λ max  amounts to 610 nm. 
     
         →E.sub.T 30=46.9 kcal·mol.sup.-1 
    
     The following values are calculated in accordance with equation (1): 
     
         c.sub.p =c* exp (E.sub.T /E.sub.D -E.sub.T °/E.sub.D)-c* 
    
     
         c.sub.p =0.535 mol·1 
    
     
         E.sub.D =2.53 kcal·mol.sup.-1 
    
     
         c*=0.099 mol·1.sup.-1 
    
     
         E.sub.T °=42.2 kcal·mol.sup.-1 
    
     Accordingly, the mixture to be studied contained 0.54 mol·1 -1  of methanol; the set value of c p  was 0.494. The rest was acetone. The accuracy with which c p  is determined may be further increased by using a better spectrometer. 
     EXAMPLE 4 
     A mixture of ethanol and acetone is studied by the process described in Example 2. 
     E D , b and c* are determined in the same way as described above. 
     Ethanol is the more polar component. 
     
         E.sub.D =2.27 kcal·mol.sup.-1 
    
     
         C*=0.137 mol·1.sup.-1 
    
     
         b=46.8 kcal·mol.sup.-1 
    
     
         E.sub.T °=42.2 kcal·mol.sup.-1 
    
     (E T  30-value of acetone according to C. Reichardt &#34;Angewandte Chemie&#34; 91, 119, (1979)). 
     The results obtained are shown in Tables IV and V and in FIG. 3 (manual evaluation) and in FIG. 4 (machine evaluation). 
     
                       TABLE IV______________________________________ml ethanol   λ.sub.max (nm)               c.sub.p (Mol/l)                         E.sub.T 30                                 ln c.sub.p______________________________________0.00    677.5       0.000     42.2    -∞0.01    670.0       0.017     42.7    -4.070.02    668.0       0.034     42.8    -3.370.03    664.0       0.051     43.1    -2.970.04    662.0       0.069     43.2    -2.680.05    660.0       0.086     43.3    -2.460.06    658.0       0.103     43.4    -2.270.07    656.0       0.120     43.6    -2.120.08    656.0       0.137     43.6    -1.990.09    654.0       0.154     43.7    -1.870.10    650.0       0.171     44.0    -1.760.20    624.0       0.343     45.8    -1.070.30    625.0       0.514     45.7    -0.670.40    620.0       0.685     46.1    -0.380.50    613.0       0.857     46.6    -0.150.60    607.0       1.028     47.1    0.030.70    600.0       1.199     47.6    0.180.90    597.0       1.542     47.9    0.431.00    592.0       1.713     48.3    0.542.00    572.0       3.427     50.0    1.233.00    562.0       5.140     50.9    1.644.00    556.0       6.853     51.4    1.925.00    551.0       8.566     51.9    2.156.00    551.0       10.280    51.9    2.337.00    548.0       11.993    52.2    2.488.00    541.0       13.706    52.8    2.629.00    542.0       15.420    52.7    2.7410.00   540.0       17.133    52.9    2.84______________________________________ Starting conditions: Concentration factor: 1.713 Energy factor: 28590 c*: 0.1 Number of measured values: 28 
    
     
                       TABLE V______________________________________c.sub.p (Mol/l)     E.sub.T 30 ln (c.sup.+  c*)                          ln (c/c* + 1)______________________________________0.000     42.2       -1.99     0.000.017     42.7       -1.87     0.120.034     42.8       -1.77     0.220.051     43.1       -1.67     0.320.069     43.2       -1.58     0.410.086     43.3       -1.50     0.490.103     43.4       -1.43     0.560.120     43.6       -1.36     0.630.137     43.6       -1.29     0.690.154     43.7       -1.23     0.750.171     44.0       -1.18     0.810.343     45.8       -0.73     1.250.514     45.7       -0.43     1.560.685     46.1       -0.20     1.790.857     46.6       -0.01     1.981.028     47.1       0.15      2.141.199     47.6       0.29      2.281.542     47.9       0.52      2.511.713     48.3       0.62      2.603.427     50.0       1.27      3.265.140     50.9       1.66      3.656.853     51.4       1.94      3.938.566     51.9       2.16      4.1510.280    51.9       2.34      4.3311.993    52.2       2.50      4.4813.706    52.8       2.63      4.6215.420    52.7       2.74      4.7317.133    52.9       2.85      4.84______________________________________ Correlation coefficient: 0.99939 Sigma E.sub.D : 0.019 
    
     EXAMPLE 5 
     Analysis of a mixture of ethanol and acetone of unknown concentration 
     A mixture of ethanol and acetone of unknown concentration is studied by the process described in Example 3. 
     
         λ.sub.max =650 nm→E.sub.T +=44.0→cp=0.166 mol·1.sup.-1 ; 
    
     the set value was 0.171 mol·1 -1   
     The mixture to be studied contains 0.166 mol·1 -1  of ethanol. The rest is acetone.