Correct determination of alcoholic strength in alcoholic products

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Introduction
The correct determination of alcoholic strength by volume in alcoholic products is critical for ensuring product quality, safety, and compliance with legal and regulatory requirements [1].The traditional method for determination of the alcoholic strength by volume is based on measuring of the density of the sample using a pycnometer, frequency oscillator, hydrostatic balance and the referencing it to the International Alcoholometric Tables [2].These tables provide the alcoholic strength by volume (ABV) corresponding to the measured density.The water-ethanol tabular method is based on the principle that the density of water-ethanol mixtures has an unambiguous dependence on the strength of the test sample.However, samples of distillates of alcoholic beverages obtained after distillation contain other volatile compounds besides ethanol, which can contribute to the density of the distillate.The presence of other volatile compounds in distilled beverages can affect the accuracy of alcoholic strength values.The use of data from waterethanol tables for such distillates can lead to incorrect values because these tables are based solely on the properties of water and ethanol.In order to obtain correct value of alcoholic strength for distilled beverage sample, it is necessary to use methods that take into account the presence of other volatile compounds.The developed GC-FID method is based on the use of ethanol as a reference substance, avoids the aforementioned disadvantages of the traditional internal standard method.There is no need to add any internal standard to the analysed sample, since ethyl alcohol is an essential component of any alcoholic beverage.This method was studied and validated for the determination of methanol in spirit drinks [3,4].
The aim of this study was to approbate the developed method on real samples of alcoholic beverages and compare obtained results with the results obtained using official method of analysis (Appendix I of Commission regulation EC) [1] The developed method was tested on 8 brandy samples.

Preparation of standard solutions
Four standard solutions with concentration levels of volatile compounds, ranging from 2 to 5000 mg/L of anhydrous alcohol (AA), were prepared by dilution of the stock solution with a hydroalcoholic mixture at 40% (ABV) ethanol.Ethyl alcohol itself is used as a reference substance and all data for the concentration of volatile compounds are calculated in relation to the content of ethanol.There is no need for any further internal standard addition.

Preparation of brandy samples
The 8 brandy samples were distillated according to the Appendix I of Commission regulation EC [1].The density and real alcoholic strength by volume of purchased samples was determined according to the Appendix II of Commission regulation EC [1] by Method A (pycnometry).Alcoholic beverage samples were prepared according to the procedure, described in the part III.2 item 8 of Commission regulation EC [1].

Instrumentation
A gas chromatograph model Crystal-5000.1,coupled with a flame ionization detector (Chromatec, Yoshkar-Ola, Mari El) was used for the chromatographic analyses.The separation was performed with a capillary column Rt-Wax, 50 m × 0.32 mm I.D. × 1.0 μm film thickness (Restek, Bellefonte, USA).The injector and detector temperatures were 200 °C and 280 °C, correspondingly.The GC oven was set as followed: 60 °C (6 min hold), and finally ramped to 190 °C at 12 °C/min (10 min hold).Nitrogen was used as the carrier gas and the injection was a splitless mode.The split ratio was 10:1, the injection volume was 1.0 μL.Data acquisition and processing were controlled by UniChrom software (New Analytical Systems Ltd, Minsk, Belarus).

Calculations
To calculate the concentration composition of the alcohol-containing sample being studied, it is assumed that the sample was prepared by mixing two separate solutions -pure water and the anhydrous part of the test sample, which consists of volatile compounds, including ethyl alcohol.The density of the solution after mixing water with the anhydrous part of the sample can be represented by the following formula where S  is the density of the sample, mg/L; The dependence of the factor on the volume fraction of water in the sample is a monotonic function without extremum.The analytical dependence of the value in the range of values F of the volume fraction of water C w in the test sample from 0.03 to 1.00 can be represented as an empirical formula   where the numerical values of the coefficients a, b, c, d, e, f, and g are calculated by approximating the function using water-alcohol tables [2].The graph of the function is shown in Fig.
1 The volume fractions of the ith volatile compounds, including ethanol, in the anhydrous part of the sample * i C can be represented by the following formula where i C is the concentration of the ith volatile compound in the anhydrous part of the sample, including ethanol, mg/L AA, determined from chromatographic data by direct determination of the concentrations of volatile compounds using ethanol as a reference substance [3,4] A are the areas of chromatographic peaks of the ith volatile compound and ethanol, obtained during measuring of the standard mixture, used for calibration, correspondingly, a.u.; st i C is the concentration of the ith volatile compound in the standard mixture for chromatograph calibration, mg/L AA.
After substituting (3) into (1), we find an expression for determining the volume fraction of water in the sample The volume fraction of the ith volatile compound, including ethanol, in the sample can be represented by the following formula * ( 1) .
The function

 
w F C is smooth and the system of equations ( 1)-( 6) can be solved by the method of successive approximations.In the zero approximation, we assume that the value (0) ( ) w F C = 1.Then expressions ( 6) and ( 7) can be presented in the following formulas In the jth approximation, the value of the function   w F C is calculated by formula (2) with the value of the argument ( 1) j W C  .The corresponding expressions for the concentrations of water and volatile compounds ( 6) and ( 7) can be presented in the following formulas 1 .
Solutions to the system of linear algebraic equations ( 2), ( 10), (11) can be found numerically by programming the algorithm of successive iterations, for example, in MS Excel.The number of iterations was 16.

Results and discussion
The results of the GC-FID analysis of brandy samples are presented in Table 1.The obtained chromatograms of brandy samples in logarithmic scale are shown in Figs. 2,  and 3.
Table 1.Results of the GC-FID analysis of brandy samples.

Compound Concentration, mg/L AA sample 1 sample 2 sample 3 sample 4 sample 5 sample 6 sample 7 sample 8
Acetaldehyde 182  The results of determining the strength of the samples according to the official [1] and developed methods are presented in the The sum of volume content of detected congeners in studied distillates ranged from 0.28 to 0.46%.The absolute difference between results for determination of alcoholic strength using only water-ethanol tables (traditional method) and combination of data from waterethanol tables and gas chromatography data (developed method) ranged from 0.22 to 0.40%.

Conclusions
The use of a computer calculation program that implements this method can help to automate and streamline the analysis of alcohol-containing products, and can help to reduce measurement uncertainty and improve the accuracy of results.The implementation of these proposals can help to improve the accuracy and reliability of measurements, promoting consistency and transparency in the alcoholic beverages industry.An example of performing calculations using the proposed method in MS Excel can be found at the link https://elab.bsu.by/article/747.Since during the analysis of alcoholic products it is necessary to establish the density of the sample and measure the chromatogram, there is no need to carry out any additional measurements, financial or labor costs to implement the proposed method.
High efficiency and wide international testing of the method using ethanol as a reference substance can serve as the basis for initiating, in the established manner, interlaboratory study under patronage of the International Organization of Vine and Wine (OIV) for the purpose of its subsequent approval as a standardized reference method on the international level.
the effective density of water in the mixture, mg/L; W  is the density of pure water at 20 °C, W  = 998230 mg/L;   w F C is the factor that takes into account the effect of "increasing the effective density of water"; i  is the density of ith volatile compound, mg/L; * i C -is the volume fraction of ith volatile compound in the anhydrous part of the sample; W C the volume fraction of the water in the sample.

Figure 1 .
Figure 1.Analytical function of the dependence of the factor F on the volume fraction of water in the test sample Cw.
, according to the following formulas