C3H5(OCO)3(CH2)M(CH=CH)D(CH3)3

The integral of a resonance being the area under the resonance curve, in the next chemometric equations the following suggestive notations were adopted for the integral values of the corresponding resonances: A(A+B), AC, AD, AE, AF, AG, AH, and A(I+J), respectively.

The average number of methylene groups (M) and the average number of double bonds (D) in the alkyl chain can then be calculated as:

$$\mathbf{M} = \frac{3}{2} \cdot \frac{\mathbf{A}\_{\mathbf{C}} + \mathbf{A}\_{\mathbf{D}} + \mathbf{A}\_{\mathbf{E}} + \mathbf{A}\_{\mathbf{F}} + \mathbf{A}\_{\mathbf{G}}}{\mathbf{A}\_{(\mathbf{A} + \mathbf{B})}} \tag{1}$$

$$\mathbf{D} = \frac{\mathbf{3}}{2} \cdot \frac{\mathbf{A\_{(I+J)}} - \mathbf{A\_{H}}/4}{\mathbf{A\_{(A+B)}}} \tag{2}$$

(i) The normalization factor 3/2 appeared as a consequence of the different number of protons that generated the resonances involved in Equations (1) and (2), i.e., two protons in the case of the resonances at the numerator and three in the case of the resonances at the denominator;


The mean number of carbon atoms in the hydrocarbon chain (nC) and the average number of hydrogen atoms in the hydrocarbon chain (nH) can be computed as:

$$
\mathbf{n}\_{\mathbb{C}} = \mathbf{M} + 2\mathbf{D} + 1 \tag{3}
$$

$$\mathbf{n}\_{\rm H} = 2\mathbf{M} + 2\mathbf{D} + 3\tag{4}$$

leading to the mean formulae of the hydrocarbon chain (CM+2D+1H2M+2D+3) and of the triacylglycerol, i.e., C6+3 (M+2D+1) H5+3(2M+2D+3) O6.

As a consequence, the average molecular weight of TAGs becomes:

$$\mathbf{M\_{TAG}} = 12 \times \left[ 6 + 3(\mathbf{M} + 2\mathbf{D} + 1) \right] + 1 \times \left[ 5 + 3(2\mathbf{M} + 2\mathbf{D} + 3) \right] + 16 \times 6 \tag{5}$$

The SV represents the amount of KOH (in mg) required for the saponification of 1 g of fat [15]. Therefore, SV can be computed as:

$$\text{SV } (\text{mg KOH/g fat}) = 3 \times \text{v} \times 56 \times 10^3 \tag{6}$$

where ν represents the number of TAG moles *per* gram of fat (ν = 1/MTAG), while (3 × ν) is the number of moles of ester groups *per* gram of oil.

An example of SV calculation from 1H-NMR data is shown in the Supplementary Materials (Table S2).

The SV values for the SO-TB and RO-TB series (both determined by the method based on the 1H-NMR data and determined experimentally by the conventional ISO 3657:2013 method taken as reference) are presented in Table 2.

**Table 2.** SVs determined from the 1H-NMR data and through the standard (i.e., ISO 3657:2013) method for the SO-TB and RO-TB series (95% confidence level).


a–x Means with different letters within a column are significantly different (*p* < 0.05). A, B Means with different letters within a row are significantly different (*p* < 0.05). \* Determined in triplicate (NMR method) and in duplicate (ISO method); values are reported as the mean ± sd.

As reflected in Table 2, the values obtained based on the 1H-NMR data were close to the values determined by the conventional method, which reflects the accuracy of the calculation algorithm.

The accuracy of the new method was assessed by calculating for each sample the SV (NMR) deviation from the SV (ISO), taken as a reference and expressed as percentages relative to the SV (ISO) (see details in Table S3). The mean percent deviation of SV (NMR) from SV (ISO) was found to be 2%, which stands for a robust NMR algorithm. The accuracy of the proposed method was also reflected by the SV (NMR) plotted against the SV (ISO) in Figure 3. The concordance between the values obtained by the NMR method and the

titration values is reflected by values close to 1 for both the slope of the trendline (in the case of perfect concordance, tg α = 1, corresponding to an angle of 45◦) and for the coefficient of correlation *R*2. As reflected from Figure 3, values close to 1 were obtained for the two parameters, indicating a good correlation between the two methods.

.

#### *3.3. Determination of the SV for Edible Oils and Fats*

Subsequently, the algorithm for determining the saponification value was applied to a series of commercial samples of vegetable oils and fats, butter, cheeses and spreadable fat mixtures (margarine type). The results are presented in Table 3.

**Table 3.** SVs determined from 1H-NMR data and through the standard (ISO 3657:2013) method for a series of edible fats and oils (95% confidence level).



**Table 3.** *Cont.*

a–c Means with different letters within a column are significantly different (*p* < 0.05). A, B Means with different letters within a row are significantly different (*p* < 0.05). \* Determined in triplicate (NMR method) and in duplicate (ISO method), respectively; values reported as the mean ± sd. \*\* Variable composition (various amounts of butter and different vegetable oils).

As reflected from Table 3, there was agreemen<sup>t</sup> between the SVs calculated from the 1H-NMR data and the SVs determined through the wet (ISO 3657:2013) method. However, in the case of the oil and fat samples, the mean percent deviation of SV (NMR) from SV (ISO) was 3%, higher than in the case of the oil–TB series (2%), which may be due to the fact of their more complex composition compared to the binary mixtures.

Edible fats have variable SVs, depending on the species. As expected, vegetable oils, such as sunflower, soybean and rapeseed, had similar SVs, ranging from 194 to 196 mg KOH/g oil (as determined from the 1H-NMR data). These values are in agreemen<sup>t</sup> with the fatty acid composition consisting of C18 fatty acids (i.e., linoleic C18:2 and oleic C18:1 as the main constituents, various amounts of stearic C18:0 and linolenic acid C18:3 in small amounts) and modest amounts of C16:0 (palmitic) acid [21–23]. They are also in agreemen<sup>t</sup> with similar SVs reported in the literature [21]. On the other hand, lauric fats, such as coconut oil and palm fat, showed significantly higher SVs (mean values of 248.5 and 236.5 mg KOH/g oil, respectively) due to the fact of their specific fatty acid profiles rich in lauric (C12:0), myristic (C14:0) and myristoleic (C14:1) fatty acids. In the case of the coconut oil, its fatty acid profile is dominated by medium chain length fatty acids, with lauric acid ranging between 30 and 50% [24–26], while myristic was also reported in high levels (accounting for more than 20%) [24–26]. Palm fats are abundant in palmitic (C16:0) acid [25,27], with large amounts of lauric and myristic acids (especially palm kernel oil [3]). The high levels of C12 and C14 explain the marked increase in the SVs of coconut and palm fats compared to the rest of the vegetable oils.

In the case of dairy products (i.e., butter and cheese fats), the average saponification values were approximately 242 mg KOH/g fat in both cases. The SV results correlated with their particular fatty acid profile, containing mainly long chain (C14–C18) as well as important amounts of short (butyric, caproic) and medium (C8–C14) chain fatty acids [19,28]. It is worth mentioning that milk fats contain high amounts (up to 32.4% [29]) of palmitic acid (C16:0), whereas myristic (C14:0) and myristoleic (C14:1) acids occur in important amounts, accounting for more than 10–12% altogether [30,31]. Consequently—although belonging to the long chain fatty acids category—C14 fatty acids contributed to the global lowering of the average molecular weight of the triacylglycerols of milk fats compared to vegetable oils (mainly consisting of C16–C18 fatty acids). Altogether, the short and medium chain fatty acids, myristic and palmitic acid levels explain the high SV in the case of dairy products.

On the other hand, spreadable fat mixtures, the analyzed samples consisted of mixtures of butter with various amounts of vegetable fats. Given the variable composition of these samples (depending on the producers' recipes), an average SV cannot be calculated. The spreadable fat mixtures have SV lower than those of butters and cheeses, due to the higher amounts of C16 and C18 fatty acids from the oils and fat ingredients of vegetal origin.
