The NIST SRM 2900 ethanol solution of certified value: 95.6% ± 1.9%was used for calibration. Isopropanol (HPLC Grade > 99% from Merck) served as the internal standard and ultrapure water was obtained from a Millipore Milli-Q RG system (USA).

Six calibration solutions were prepared for the HS-GC-FID by gravimetric dilution from a stock solution of the NIST SRM. These calibration solutions were: 100, 300, 600, 900, 1200, and 1500 mg/kg, each prepared in a 100 mL volumetric flask. An internal standard solution was gravimetrically prepared at a concentration of 1000 mg/kg and added to each calibration solution. The detailed preparation procedure is described elsewhere [27] .

Analysis of ethanol samples was performed using a Thermo Scientific Trace GC Ultra GC equipped with FID, dual S/SL inlets, and AS2000 autosampler. A WAXMS capillary column (30 m × 0.25 mm × 0.25 µm) was used for the chromatographic separation. The test sample was kept in the headspace oven at 70˚C for 10 minutes and 350 µL of the sample was injected in a split ratio of 20:1. The oven temperature program began with an initial hold at 50˚C for 2 minutes, followed by a ramp to 220˚C at a rate of 20 ˚C/min. The final temperature of 220˚C was held for an additional 2.5 minutes. The GC inlet and detector temperatures were 250˚C and 300˚C, respectively. The carrier gas (helium) flow rate was 35 mL/min, while the hydrogen and air flow rates were 45 mL/min and 450 mL/min, respectively.

The limit of detection, LOD is defined as the lowest concentration that can be detected with statistical significance by means of a given analytical procedure. Meanwhile, the LOQ is the smallest concentration of an analyte that can be reliably measured [26] . For the determination of both characteristics, a blank sample was injected, but it did not produce any area values. Therefore, a low concentration of ethanol (100 ppm) was prepared and an IS of 1000 mg/kg was added to it. This sample was injected into the HS-GC-FID using the developed method three times and the obtained area ratio was recorded in Table 1.

The standard deviation (SD) of the average area ratio was found 0.0006. The LOD was calculated as 1.27 mg/kg using equation 1 and the LOQ was calculated as 3.86 mg/kg using equation 2 where n is the number of measurements.

L O D     =     3.3   × S D n (1)

L O D = 10 × S D n (2)

A key characteristic of an analytical procedure is its linearity. This refers to the method ability to produce results that are directly proportional to the concentration of the analyte within a specific range [25] . In this study, we evaluated linearity within the range of 100 - 1500 mg/kg in which six calibration solutions of 100, 300, 600, 900, 1200, and 1500 mg/kg were used. Each solution was spiked with 1000 mg/kg of internal standard (IS). The area ratio (A_Et/A_IS) of the analyte peak to the IS peak was plotted against the concentration ratio (C_Et/C_IS) to generate the calibration curve shown in Figure 1. The linear equation for the calibration curve was determined to be y = 0.4723x + 0.0017. The near-zero intercept indicates good linearity within the chosen range. Additionally, the R² value of 0.9994, which is very close to 1 signifies a strong fit of the calibration points to the line supporting linearity of the method.

Furthermore, we calculated the residuals (y_i − ŷ) for each calibration point and analyzed their distribution around zero. As recommended by IUPAC guidelines (1998), residuals should be randomly distributed around zero for a linear method [28] [29] . From Table 2, it can be seen that the observed residuals are indeed randomly distributed around zero, providing additional evidence for the linearity of the method.

Selectivity refers to the extent to which a particular method can be used to determine analytes under given conditions in the presence of other components of similar behavior [30] . In or study, a blank water sample spiked with 1 mg of ethanol and 1 mg of the internal standard (1-propanol) was analyzed using the HS-GC-FID. The resulting chromatogram shown in Figure 2 confirms excellent selectivity for ethanol because no interfering peaks from the water matrix were observed near the ethanol peak, which elutes at a retention time (RT) of 4.875 min.

Precision refers to the closeness of repeated measurements of the same sample [31] . In this study, precision of the method was investigated in the range of 100 - 1500 ppm and we investigated how well the method can reproduce results for low, middle, and high mass fraction levels. Thus, three ethanol samples were prepared as 99.72, 867.35 and 1403.67 mg/kg and three IS mass fraction, 953.33, 934.94 and 856.79 mg/kg were added respectively to them. Each sample was measured by HS-DC-FID three times and the results are given in Table 3. The precision was evaluated as RSD% by equation 3, which expresses the variability of the measurements as a percentage of the mean value.

R S D   %     =     S D x ¯     × 100 (3)

A lower RSD% indicates higher precision, meaning that the repeated measurements are more consistent. If the RSD% increases or decreases significantly at a specific mass fraction (low, middle, or high), it might indicate limitations in the method precision at that particular mass fraction. The factors outlined the precision of the method can be the stable carrier gas flow, detector response, and column performance throughout the GC analysis minimize random fluctuations. Also, the use of NIST SRM calibration standards with known ethanol concentrations allows for precise quantification. In addition, employing a consistent integration method for the ethanol peak on the chromatogram reduces errors in measurement

Analysis of the RSD% values in Table 3 reveals that the middle and high ethanol mass fractions exhibit consistent RSD% values below 0.5%. However, the RSD% for the low mass fraction is about three times larger (1.26%). This indicates that the method precision is lower when determining smaller ethanol mass fractions. Nevertheless, the overall precision across the three ethanol levels remains acceptable well below the 5% threshold. This demonstrates that the method is suitable for its intended purpose of reference material characterization.

This analytical method is simpler because it does not involve extraction or cleanup steps that can lead to analyte loss. Consequently, to evaluate how well the method recovers the target analyte, a spike of a blank approach was used. A specific mass fraction (1035.29 mg/kg) from the ethanol NIST SRM was used for spiking and was measured 9 times by HS-GC-FID. The average and standard deviation were calculated and presented in Table 4. Equation 4 was then used to calculate the percentage recovery, which was found to be 98.14% [26] [32] .

R ( % ) = x ¯ C C R M × 100 (4)

where,

x ¯ —average mass fraction of ethanol (mg/kg);

C_CRM—mass fraction of the CRM sample (mg/kg).

This near 100% recovery indicates that the method captures almost all of the spiked ethanol and is reliable to quantify ethanol in water within an acceptable error range.

The method bias was calculated by subtracting the average of measurements from the reference value, as described by equation 5 and was reported in Table 4 as −19.29 mg/kg.

b     =   x ¯     −     x C R M (5)

The calculated bias was tested if significant using the criterion in equation 6. If the bias falls within the range established by this criterion, the method is considered unbiased.

− 2 σ     ≤     b     ≤     + 2 σ (6)

The standard deviation (σ) was calculated using equation 7, which considers uncertainties from both the repeatability of measurements and the standard uncertainty of the NIST SRM (1.9%/2) [32] .

σ =     ( S D n ) 2     +       ( u C R M ) 2 (7)

Notably, the reference material uncertainty was expressed as a percentage, while the repeatability uncertainty was given in mg/kg. To address this unit inconsistency, an uncertainty ratio was employed to eliminate units and then the resulting number was multiplied by the average mole fraction of ethanol to obtain σ, which was found to be 10.16. Thus, it can be observed that the bias of −19.29 mg/kg falls within the range of −2σ (−20.32) and +2σ (+20.32). This confirms that the method exhibits no significant bias.

An ethanol sample of concentration 1028.85 mg/kg was analyzed 10 times using HS-GC-FID calibrated by the NIST SRM, and the mole fraction (x) was calculated using the calibration function 8.

x =     ( A U n A I S −   b )   × C I S a (8)

where

x—mass fraction of unknown (mg/kg)

A_Un—area of unknown

A_IS—area of IS

b—intercept

C_IS—concentration of IS added to the sample

a—slope.

From this mathematical model, it is clear that the explicit sources of uncertainty are: area of unknown, area of IS, intercept, slope and concentration of the IS added to the unknown sample. In addition, the NIST SRM calibration solutions and the mass of the ethanol sample are two implicit sources of uncertainty. They were combined into the uncertainty of the concentration of IS (C_IS) to fit the model equation 8. This means that these two implicit sources of uncertainty are not explicitly accounted for in the model calculations, but their contribution is assumed to be reflected in the overall uncertainty of the IS concentration [27] . The calculation of the uncertainty contributions was carried out according to the ISO GUM [33] . The combined standard uncertainty, u_c was calculated according to equation 9 in which the dx/dy_i were the sensitivity coefficients obtained by differentiation of equation 8.

u c = ( ∂ x ∂ A u n ⋅ u A u n ) 2 + ( ∂ x ∂ A I S ⋅ u A I S ) 2 + ( ∂ x ∂ a ⋅ u a ) 2 + ( ∂ x ∂ b ⋅ u b ) 2 + ( ∂ x ∂ C I S ⋅ u C I S ) 2 (9)

The expanded uncertainty U_exp, was then calculated at a 95% confidence level using a coverage factor k = 2 as in equation 9.

U exp = k × u c (10)

The resulting uncertainty budget is presented in Table 5 that shows value (x_i) of each source, and the corresponding uncertainty, u (x_i), the probability distribution,

the sensitivity coefficient, c_i and the uncertainty contribution, c i . u ( x i ) . From this table it is clear that the expanded uncertainty, U_exp%, produced by the method reached 2%. Thus, by identifying and quantifying these uncertainties, we can get a better understanding of the limitations of the ethanol measurements by HS-GC-FID and express the results with more confidence.