Effect of Boric Acid on the Ionization Equilibrium of α-Hydroxy Carboxylic Acids and the Study of Its Applications

To investigate the synergistic catalytic effects of boric acid and α-hydroxycarboxylic acids (HCAs), we analyzed and measured the effects of the complexation reactions between boric acid and HCAs on the ionization equilibrium of the HCAs. Eight HCAs, glycolic acid, D-(−)-lactic acid, (R)-(−)-mandelic acid, D-gluconic acid, L-(−)-malic acid, L-(+)-tartaric acid, D-(−)-tartaric acid, and citric acid, were selected to measure the pH changes in aqueous HCA solutions after adding boric acid. The results showed that the pH values of the aqueous HCA solutions gradually decreased with an increase in the boric acid molar ratio, and the acidity coefficients when boric acid formed double-ligand complexes with HCAs were smaller than those of the single-ligand complexes. The more hydroxyl groups the HCA contained, the more types of complexes could be formed, and the greater the rate of change in the pH. The total rates of change in the pH of the HCA solutions were in the following order: citric acid > L-(−)-tartaric acid = D-(−)-tartaric acid > D-gluconic acid > (R)-(−)-mandelic acid > L-(−)-malic acid > D-(−)-lactic acid > glycolic acid. The composite catalyst of boric acid and tartaric acid had a high catalytic activity—the yield of methyl palmitate was 98%. After the reaction, the catalyst and methanol could be separated by standing stratification.


Introduction
α-Hydroxy carboxylic acids (HCAs), such as citric acid and malic acid, play an important role in life activities. The mentioned acids are involved in tricarboxylic acid cycle reactions. Boron is widely distributed on the earth and is an indispensable trace element for animals and plants [1,2]. Due to the electrical absorption of boron atoms, boric acid can form complex complexes with hydroxy-containing compounds as well as 1:1 and 1:2 complexes with HCAs [3]. The structure, reaction equilibrium, reaction kinetics, and thermodynamics of the complexes formed by boric acid and HCA have been extensively investigated by researchers [4][5][6][7]. Activation of acid by boric acid has been successfully applied in synthetic organic chemistry [8]. L-(+)-tartaric acid is a chiral polyhydroxyl compound which can form L-(+)-tartrate-boric acid with a ring structure through a complexation acid with boric acid in methanol solutions when the ratio of L-(+)-tartrate to boric acid is 2:1. This ratio increases the difference between the chiral complexation acid and the two enantiomers in terms of spatial matching and improves the chiral recognition [9]. In addition, the electrical conductivity and rotation of the complex formed by tartaric acid and boric acid are increased [10,11]. The hydration reaction of α-pinene catalyzed by HCA and boric acid can increase the conversion rate of α-pinene [12]. In the synthesis of isobornyl acetate and isoborneol catalyzed by HCA and boric acid composite catalysts from camphene, HCA and boric acid show significant synergistic catalytic effects [13]. Because the composite catalyst Boric acid has an effect on the ability of HCAs to ionize protons through the reaction of boric acid with HCA hydroxyl groups to form various complexes, thus promoting a positive shift in the ionization equilibrium. The determination of the pH for different molar ratios of boric acid to HCA provides insight into the effects of the complexation reactions on the ionization equilibria and informs the design of catalysts. We used HCAs, including glycolic acid ( The pKa1 of boric acid (9.24) is much larger than those of HCAs (3.04-3.86). If the influence of the self-ionization of boric acid on the pH is ignored, the influence of boric acid on the ionization equilibrium of different HCAs can be investigated by measuring the pH after adding boric acid for a certain HCA concentration, as shown in Figures 1-3. 2.1.2. Rates of pH Change after Addition of Boric Acid to Aqueous HCA Solution (a) By fitting the experimental data in Figure 1, Equations (S1)-(S8) (see Supplementary Materials) for the change in the pH with the addition of boric acid for HCA concentrations of 0.1 mol/kg were obtained.
The derivatives of Equations (S1)-(S8) provide Equations (S9)-(S16) (see Supplementary Materials) for the rates of change of the pH with the addition of boric acid for HCA concentrations of 0.1 mol/kg.
As can be seen from Figure 1 and Equations (S1)-(S8), with the increase in the boric acid addition, the pH of the HCA aqueous solution decreased, that is [H + ] in the solution increased. From Equations (S9)-(S16), it can be seen that the pH rates of change in the HCA solutions were negative, and with the increase in the boric acid dosage, the absolute value gradually decreased and then increased. Figure 4 shows the pH rate of change curves of the HCA with the change in the boric acid dosage. The absolute values of the pH rates of change in the HCA solutions had minimum values, which occurred when the molar ratio of boric acid to HCA was about 2. The actual ratios for glycolic acid, lactic acid, mandelic acid, gluconic acid, malic acid, L-tartaric acid, d-tartaric acid, and citric acid were 2.3, 2.0, 2.1, 1.9, 2.5, 2.1, 2.1, and 2.0, respectively.          HCA solutions were negative, and with the increase in the boric acid dosage, the absolute value gradually decreased and then increased. Figure 4 shows the pH rate of change curves of the HCA with the change in the boric acid dosage. The absolute values of the pH rates of change in the HCA solutions had minimum values, which occurred when the molar ratio of boric acid to HCA was about 2. The actual ratios for glycolic acid, lactic acid, mandelic acid, gluconic acid, malic acid, L-tartaric acid, d-tartaric acid, and citric acid were 2.3, 2.0, 2.1, 1.9, 2.5, 2.1, 2.1, and 2.0, respectively. (b) By fitting the experimental data in Figure 2, Equations (S17)-(S24) (see Supplementary Materials) for the change in the pH with the addition of boric acid for HCA concentrations of 0.2 mol/kg were obtained.
The derivatives of Equations (S17)-(S24) provide Equations (S25)-(S32) (see Supplementary Materials) for the rates of change of the pH with the addition of boric acid for HCA concentrations of 0.2 mol/kg.
As can be seen from Figure 2 and Equations (S17)-(S24), with the increase in the boric acid addition, the pH values of the HCA aqueous solutions decreased, that is, [H + ] in the solution increased. From Equations (S25)-(S32), it can be seen that the absolute values of the pH rates of change in the HCA solutions gradually decreased and then increased. Figure 5 shows the pH rate of change curves of the HCA solutions with the amount of boric acid. The absolute values of the pH rates of change in the HCA solutions had minimum values, and the molar ratios of boric acid to HCA corresponding to the minimum values for the glycolic acid, lactic acid, mandelic acid, gluconic acid, malic acid, and D-tartaric acid were 3.5, 2.0, 2.0, 2.0, 2.1, and 2.2, respectively. The minimum rates of change in the pH for L-tartaric acid and citric acid were 0. When the rate of change in the pH for L- The derivatives of Equations (S17)-(S24) provide Equations (S25)-(S32) (see Supplementary Materials) for the rates of change of the pH with the addition of boric acid for HCA concentrations of 0.2 mol/kg.
As can be seen from Figure 2 and Equations (S17)-(S24), with the increase in the boric acid addition, the pH values of the HCA aqueous solutions decreased, that is, [H + ] in the solution increased. From Equations (S25)-(S32), it can be seen that the absolute values of the pH rates of change in the HCA solutions gradually decreased and then increased. Figure 5 shows the pH rate of change curves of the HCA solutions with the amount of boric acid. The absolute values of the pH rates of change in the HCA solutions had minimum values, and the molar ratios of boric acid to HCA corresponding to the minimum values for the glycolic acid, lactic acid, mandelic acid, gluconic acid, malic acid, and D-tartaric acid were 3.5, 2.0, 2.0, 2.0, 2.1, and 2.2, respectively. The minimum rates of change in the pH for L-tartaric acid and citric acid were 0. When the rate of change in the pH for L-tartaric acid was 0, the molar ratios of boric acid to tartaric acid were 1.75 and 2.23, respectively. When the rate of change in the pH for citric acid was 0, the molar ratios of boric acid to citric acid were 1.46 and 2.37, respectively.
Molecules 2023, 28, x FOR PEER REVIEW 5 of 17 tartaric acid was 0, the molar ratios of boric acid to tartaric acid were 1.75 and 2.23, respectively. When the rate of change in the pH for citric acid was 0, the molar ratios of boric acid to citric acid were 1.46 and 2.37, respectively.  As can be seen from Figure 3 and Equations (S33)-(S40), with the increase in the boric acid addition, the pH of the HCA aqueous solution decreased, that is, [H + ] in the solution increased. From Equations (S41)-(S48), it can be seen that the absolute values of the rates of change in the pH values of the HCAs decreased and then increased. Figure 6 shows the rates of change in the pH values of the HCAs with the amount of boric acid. The absolute values of the pH rates of change in the HCAs had minimum values, and the molar ratios of boric acid to HCA corresponding to the minimum values for the glycolic acid, lactic acid, mandelic acid, gluconic acid, malic acid, L-tartaric acid, and D-tartaric acid were 1.34, 0.75, 0.71, 0.68, 0.71, 0.69, and 0.68, respectively. The minimum pH rate of change for citric acid was 0, and the corresponding molar ratios of boric acid to citric acid were 0.62 and 0.94, respectively.  As can be seen from Figure 3 and Equations (S33)-(S40), with the increase in the boric acid addition, the pH of the HCA aqueous solution decreased, that is, [H + ] in the solution increased. From Equations (S41)-(S48), it can be seen that the absolute values of the rates of change in the pH values of the HCAs decreased and then increased. Figure 6 shows the rates of change in the pH values of the HCAs with the amount of boric acid. The absolute values of the pH rates of change in the HCAs had minimum values, and the molar ratios of boric acid to HCA corresponding to the minimum values for the glycolic acid, lactic acid, mandelic acid, gluconic acid, malic acid, L-tartaric acid, and D-tartaric acid were 1.34, 0.75, 0.71, 0.68, 0.71, 0.69, and 0.68, respectively. The minimum pH rate of change for citric acid was 0, and the corresponding molar ratios of boric acid to citric acid were 0.62 and 0.94, respectively.

Comparative Experiments with Different Substituent Carboxylic Acids
For comparison, carboxylic acids with different structures such as glycine, benzoic acid, salicylic acid, and oxalic acid were also investigated ( Figure 7). The results showed that the pH of the boric acid-benzoic acid mixture did not change with an increase in the concentration of boric acid, while the pH of the reaction mixture for the other three carboxylic acids decreased slightly. Under the experimental conditions, the total pH rates of change in the reaction mixture after the addition of boric acid decreased in the order of glycine (9.7%) > salicylic acid (5.7%) > oxalic acid (2.3%) > benzoic acid (0). Because the pKa of boric acid was similar to that of glycine, the pH change in the boric acid-glycine mixture with the addition of boric acid did not necessarily suggest the formation of a strong complex between glycine and boric acid. Benzoic acid did not contain a hydroxyl group that could form an annular complex with boric acid, which explained the absence of an observable effect of boric acid addition on the pH of the boric acid-benzoic acid mixture. The hydroxyl and carboxyl groups of salicylic acid were at the ortho positions to each other on the benzene ring. Due to the influence of the benzene ring, the boric acid-salicylic acid mixture exhibited a greater rate of pH change compared to boric acid-oxalic acid. strong complex between glycine and boric acid. Benzoic acid did not contain a hydroxyl group that could form an annular complex with boric acid, which explained the absence of an observable effect of boric acid addition on the pH of the boric acid-benzoic acid mixture. The hydroxyl and carboxyl groups of salicylic acid were at the ortho positions to each other on the benzene ring. Due to the influence of the benzene ring, the boric acidsalicylic acid mixture exhibited a greater rate of pH change compared to boric acid-oxalic acid.   Figures 1-3, the effect of boric acid on the pH of boric acid-HCA mixture increased with increasing HCA concentration, where the total pH rates of change showed a similar trend among the seven HCAs, except for gluconic acid.
As shown by the above ranking of the total pH rates of change, the more hydroxyl groups in the HCA molecule, the greater the total pH rates of change. Specifically, the total pH rates of change of polycarboxylic acids such as citric acid and tartaric acid was greater than those of monobasic acids such as lactic acid and glycolic acid. The total pH rates of change in gluconic acid with multiple hydroxyl groups was greater than those of monobasic acids such as mandelic acid, lactic acid, and glycolic acid. Gluconic acid has five hydroxyl groups on its alkyl chain, which were prone to hydrogen bonding and could react with multiple boronic acids to form complexes. Consequently, the total pH rates of change increased significantly with an increasing concentration of gluconic acid, with the total pH rates of change at 0.5 mol/kg being similar to that of citric acid.
However, due to the strong electronegativity of the boron atom, HCAs with groups exhibiting strong electron-donating abilities could form stable complexes; thus, they would more readily undergo proton dissociation in aqueous solutions. Mandelic acid contains one benzene ring linked to the α-carbon atom, leading to a high electron cloud density on the benzene ring, causing the complexes formed by mandelic acid with boric acid to be highly stable. With the exception of gluconic acid, the reaction mixture containing mandelic acid showed the highest rate of pH change among the monobasic acids, which even surpassed that of malic acid, a dibasic carboxylic acid. By contrast, the reaction mixture containing lactic acid had a greater rate of pH change than glycolic acid because lactic acid contained a methyl group, which was a stronger electron-donating group.
Two chiral enantiomers, L-(+)-tartaric acid and D-(−)-tartaric acid, were selected for comparison. Boric acid was found to have the same deprotonation capacity for each tartaric acid enantiomer. Except for gluconic acid, the order of acidity of the boric acid and HCA mixtures was the same as the order of the total pH rate of change. The order from strong to weak was citric acid > tartaric acid > mandelic acid > malic acid > gluconic acid > lactic acid > glycolic acid.

Complexation Reaction of Boric Acid with HCA
The addition of boric acid could significantly improve the ionization ability of an HCA in an aqueous solution. It can be seen from Figures 4-6 that with the increase in the molar ratio of boric acid to HCA, the absolute values of the pH rates of change in the HCAs gradually decreased and then slightly increased. The minimum values corresponded to molar ratios of boric acid to HCA of about 2 at HCA concentrations of 0.1 and 0.2 mol/kg and about 0.7 at HCA concentrations of 0.5 mol/kg. There should be some equilibrium at the absolute minimum of the pH rate of change. Boric acid and HCA can form 1:1 and 1:2 complexes, and large excesses of HCA are often required to facilitate the formation of 1:2 complexes. However, the results for both 1:1 and 1:2 complexes promote the ionization of HCA − in aqueous solutions. If H n CA (n = 1, 2, 3) represents one, two, and three carboxylic alpha-hydroxyl carboxylic acids, respectively, (HO) 2 BCA − and B(CA) − 2 represent the 1:1 and 1:2 complexes formed by boric acid and HCA, respectively. I: For HCAs containing carboxyl groups, the ionization process of the HCA aqueous solution after adding boric acid is as follows: where k 0 is the ionization constant of HCA, k 1 generates the equilibrium constant of the 1:1 monoligand complex (HO) 2 BCA − , and k 2 generates the equilibrium constant of the 1:2 biligand complex B(CA) − 2 . Assuming half of the HCA is fully ionized, the pH values corresponding to 0.1, 0.2, and 0.5 mol/kg concentrations were calculated to be about 1.3, 1.0, and 0.6, respectively. As can be seen from Figures 1-3, the pH values of the HCA after the addition of boric acid were greater than the pH values calculated using the above assumptions. Therefore, the solution contained HCA, CA − , H 3 BO 3 , (HO) 2 BCA − , and B(CA) − 2 . Even if the molar ratio of boric acid to HCA reached 3, the solution still contained more un-ionized HCA.
(1) If we assume k 2 << k 1 , then is ignored. Assuming that k 0 << k 1 , the total reaction equation can be obtained from Formulas (2) and (3) as follows: According to Formula (4), the equation for calculating the equilibrium constant K 2 when the complexation product of boric acid and HCA is a single ligand is as follows: Molecules 2023, 28, 4723 8 of 16 By taking the logarithm of Formula (5), the following can be obtained: where K 2 is the total ionization equilibrium constant, k 0 is the ionization equilibrium constant of the HCA, and k 1 is the equilibrium constant of the complex reaction of boric acid and CA − to form a single ligand. From the data given in Figures 1-3, we know the specified concentration of HCA (C 0 ), the pH without the addition of boric acid (y 0 ), and the quantity with the addition of boric acid (x 1 ). As long as the value of the pH (y 1 ) after adding boric acid is measured, [H + ] = 10 −y 1 , [HCA] = C 0 − 10 −y 1 , [(HO) 2 BCA − ] = 10 −y 1 , and [H 3 BO 3 ] = x 1 − 10 −y 1 can be obtained using the formula pH = − log[H + ]. Then, the total ionization equilibrium constant K 2 and logK 2 can be calculated. According to the formula pKa = − log K 2 , the acidity coefficient of the HCA after adding boric acid can be obtained: By measuring the pH (y 1 ) value corresponding to a certain amount of boric acid (x 1 ), Equation (7) can be used to obtain the acidity coefficient pKa when the complex product is a single ligand. Formula (7) is applicable for the case where the molar ratio of boric acid to HCA is large when the concentration of [H + ] is large. Ragnar et al. studied the infrared spectra of complexes in an aqueous solution of lactic acid and boric acid, and they found that the molar ratios of boric acid and lactic acid were 0.4, 1.5, and 2. Through analysis, they found that boric acid and lactic acid formed a 1:1 complex when pH was 2 [4].
(2) If we assume that k 1 << k 2 , then k 1 that is, the generated single ligand is quickly converted to a double ligand. Then, Formulas (2) and (3) can be combined into the following: Assuming that k 0 << k 1 , [CA − ] → 0 , the total reaction equation can be obtained from (1) and (8) as follows: According to Formula (9), the equation for calculating the equilibrium constant K 1 when the complexation product of boric acid and HCA is a double ligand is as follows: where K 1 is the total ionization equilibrium constant, k 0 is the ionization equilibrium constant of HCA, and k 1 is the equilibrium constant of boric acid combining with CA − to form a double ligand. By taking the logarithm of Formula (10), the following can be obtained: From the data shown in Figures 1-3, we know the specified concentration of HCA (C 0 ), the pH (y 0 ) without the addition of boric acid, and the quantity with the addition of boric acid (x 1 ). As long as the pH (y 1 ) after adding boric acid is measured, [H + ] = 10 −y 1 , [HCA] = C 0 − 2 × 10 −y 1 , [B(CA) 2 − ] = 10 −y 1 , and [H 3 BO 3 ] = x 1 − 10 −y 1 can be obtained using the formula pH = − log[H + ], and then the total ionization equilibrium constant K 1 and logK 1 can be calculated. According to the formula pKa = − log K 1 , the acidity coefficient of the HCA after adding boric acid can be obtained as follows: pKa = − log K 1 = 2y 1 + 2 log(C 0 − 2 × 10 −y 1 ) + log(x 1 − 10 −y 1 ). (12) By measuring the pH (y 1 ) corresponding to a certain amount of boric acid (x 1 ), Equation (12) can be used to obtain the acidity coefficient pKa when the complex product is a double ligand. Formula (12) is applicable when the concentration of [H + ] is large, the ionization equilibrium constant of HCA is small, and the molar ratio of HCA to boric acid is large. Maseda et al. used a concentration of 1.0 mol/dm 3 of lactic acid and a concentration of 0.02 mol/dm 3 of boric acid to adjust the pH of the aqueous solution to ≤2.5 and determined the formed diligand through 11B NMR analysis [6].
For a certain concentration of HCA, with the increase in the molar ratio of boric acid to HCA, the concentration of boric acid increases, which promotes the equilibrium given by Equation (2) to move in the positive direction, that is, the content of a singleligand complex increases. At the same time, the equilibrium of Equation (1) moves in the positive direction, that is, the relative content of the HCA decreases. Since the amount of increase in the single-ligand complex is the same as the amount of decrease in the HCA, the effect of this on the equilibrium of Equation (3) is bidirectional. Therefore, when the concentration of boric acid is low, two-ligand-dominated complexes are formed, whereas when the concentration of boric acid is increased, the relative content of the single-ligand complex increases faster. From Figures 4-6, it can be seen that the molar ratio of boric acid to HCA corresponding to the minimum value of the pH rate of change was about 2 for HCA concentrations of 0.1 and 0.2 mol/kg. When the concentration of HCA was increased to 0.5 mol/kg, the molar ratio of boric acid to HCA decreased to about 0.7, corresponding to the minimum pH rate of change. With increasing HCA concentrations, the association between HCA molecules was enhanced, and the complexation reaction between boric acid and HCA was more sensitive to the effect of pH change rate. At the same time, as the boric acid concentration increased, the molar ratio of boric acid to HCA corresponding to the minimum pH change rate decreased correspondingly.
For gluconic acid containing more than one hydroxyl group, the pH rate of change was larger than those of malic acid and tartaric acid. The complex reaction with boric acid was more complex than those of glycolic acid and lactic acid. In addition to the carboxyl group and α hydroxyl group, the other four hydroxyl groups could also form complexes with boric acid. With the increase in the number of types of complexes formed by gluconic acid and boric acid, the ionization equilibrium of gluconic acid moves further in the forward direction, and the concentration of [H + ] is much higher than that without boric acid. II: For an H 2 CA, such as tartaric acid and malic acid, the ionization and possible complexation reactions of the H 2 CA aqueous solution after adding boric acid are as follows: where k 0 and k 1 are the ionization equilibrium constants for the aqueous H 2 CA, and k 2 -k 8 are the complexation reaction equilibrium constants. Equations (18) and (21) are possible complexation reactions following the ionization of tartaric acid. As can be seen from Equations (13)- (21), when boric acid was added to the H 2 CA aqueous solution, the number of complex species that could be formed was much higher than those of the HCAs containing one carboxyl group, which means that more anions ionized by H 2 CA could be consumed. Thus, the pH rate of change was greater than those of the HCAs containing one carboxyl group.
III: Citric acid contains three carboxyl groups. After adding boric acid, the ionization and possible complexation reactions of the citric acid solution are as follows: where k 0 -k 3 are the ionization equilibrium constants for aqueous citric acid solutions, and k 4 -k 13 are the complexation reaction equilibrium constants. As can be seen from Equations (22)-(35), complex complexation reactions can occur after the addition of boric acid in a citric acid solution, and more-complex species can be formed compared with those for HCAs containing two carboxyl groups, which means that more H 3 CA can be consumed. Thus, the pH rate of change was greater than those of the HCAs containing two carboxyl groups. Since the ionization constants of citric acid are pK 1 = 3.13, pK 2 = 4.76, and pK 3 = 6.40, the content of CA 3− in an aqueous solution of citric acid would be very low. The concentration of the complexation product [BCA 3− ] of Equation (32) was estimated to be very low under an acidic environment, and the concentrations of complexation products of Equations (33)-(35) were likely to be even lower.
When an HCA containing multiple carboxyl groups, such as tartaric acid, malic acid, and citric acid, is ionized in an aqueous solution, if only first-order ionization is taken into account and it is assumed that only single-or double-ligand complex products with negative charges are formed with boric acid, then its ionization equilibrium constant can be obtained from Formulas (5) and (10). The acidity coefficient of HCA after adding boric acid was calculated by Formulas (7) and (12), and the corresponding acidity coefficients at the apexes of the curves in Figures 4-6 are shown in Table 1. When boric acid was added to the HCA aqueous solutions, the acidity coefficients of the solutions with monoligand and diligand complexes are shown as pKa values.   Note: Values computed where the pH rates of change were the smallest; pKa (1:1) is the acidity system assuming that only single ligands were formed; pKa (1:2) is the acidity coefficient assuming that only double ligands were formed.
From Formulas (7) and (12), it can be seen that the acidity coefficient of HCA after adding boric acid is a function of three variables: the HCA concentration (C 0 ), the molar ratio of boric acid to HCA (x), and the measured value of the solution pH (y). As can be seen from Table 1, when C 0 , x, and y were the same, the pKa (1:1) calculated by the single-ligand formula was greater than that calculated by the double-ligand formula (1:2). There were various complexation reactions in the HCA aqueous solution after the addition of boric acid. Usually, monoligands and diligands coexist, and the actual pKa value should be between the two, that is, pKa (1:2) < pKa < pKa (1:1).
According to Formulas (1)-(35), as the molar ratio of boric acid to HCA (x) increased, the composition of the complex in the aqueous solution also changed. Combined with the analysis in Table 1, it can be seen that when x was very small, boric acid and HCA formed a 1:2 double-ligand complex, and the corresponding pH rate of change was large. When x increased, the content of the 1:1 monoligand complex formed by boric acid and HCA increased, the pH of the solution decreased, as did the pH rate of change. When x was increased to the minimum pH rate of change, the rate of increase in the 1:2 complex amount in the aqueous solution was close to 0. As x continued to increase, the content of the monoligand complex continued to increase, which was represented by a slight increase in the pH rate of change. However, as boric acid approached saturation, the pH did not change with x or showed only small fluctuations (measurement error).

Fatty Acid Esterification Catalyzed by Boric Acid-HCA Complexes
Concentrated sulfuric acid has often been used as a catalyst for esterification of fatty acids to prepare fatty acid esters. However, the use of concentrated sulfuric acid could result in the corrosion of equipment and formation of a large amount of wastewater. Moreover, its strong oxidizing ability may lead to darkening of the products. By contrast, the mixture of boric acid and HCAs could catalyze the esterification of fatty acids with high product selectivity and without product darkening.
The effect of the composition of the boric acid-HCA mixture as a catalyst system for the synthesis of methyl palmitate is shown in Figure 8. When boric acid was used alone as the catalyst, the conversion of palmitic acid after 8 h of reaction was only 7.2%; however, the conversion of palmitic acid increased to 85% after the addition of tartaric acid ( Figure 8a). As indicated by Figure 8b, the 20 h conversion of palmitic acid was 44.5% when using tartaric acid alone as the catalyst, but the addition of boric acid increased the yield of methyl ester to 98%. Hence, the mixture of boric acid and tartaric acid had better catalytic performance than boric acid or tartaric acid alone, which was mainly due to the enhanced deprotonation of tartaric acid in the presence of boric acid.
Because the esterification reaction produced water, it was advantageous to use B 2 O 3 instead of boric acid as the catalyst. Excess alcohol also favored the formation of esters and, in addition to affecting the reaction equilibrium, more importantly, promoted the dissolution of the catalyst in the system. A notable advantage of such a reaction system was that when the methyl esterification reaction was complete, the reaction mixture could be left to settle into two distinct layers, with the catalyst being predominantly present in the methanol layer and the main product (fatty acid methyl ester) being neutral in polarity.
This was advantageous for both the recycling of the catalyst and the refining of the product, making such a reaction system suitable for large-scale industrial applications.
Because the esterification reaction produced water, it was advantageous to use B2O3 instead of boric acid as the catalyst. Excess alcohol also favored the formation of esters and, in addition to affecting the reaction equilibrium, more importantly, promoted the dissolution of the catalyst in the system. A notable advantage of such a reaction system was that when the methyl esterification reaction was complete, the reaction mixture could be left to settle into two distinct layers, with the catalyst being predominantly present in the methanol layer and the main product (fatty acid methyl ester) being neutral in polarity. This was advantageous for both the recycling of the catalyst and the refining of the product, making such a reaction system suitable for large-scale industrial applications. The mass spectrum of methyl palmitate is shown in the Supplementary Materials ( Figure  S1). The infrared spectrum of methyl palmitate is shown in the Supplementary Materials ( Figure S2). It can be seen from Figure S2 that 2923.60 cm -1 was the antisymmetric stretching vibration peak of C-H in -CH2-. 2852.25 cm -1 was the symmetric stretching vibration peak of -CH2-. 1743.36 cm -1 was the stretching vibration peak of ester >C=O. 1465.91 cm -1 and 1436.05 cm -1 were the superimposed peaks of -CH3 asymmetric deformation vibration The mass spectrum of methyl palmitate is shown in the Supplementary Materials ( Figure S1). The infrared spectrum of methyl palmitate is shown in the Supplementary Materials ( Figure S2). It can be seen from Figure S2 that 2923.60 cm −1 was the antisymmetric stretching vibration peak of C-H in -CH 2 -. 2852.25 cm −1 was the symmetric stretching vibration peak of -CH 2 -. 1743.36 cm −1 was the stretching vibration peak of ester > C=O. 1465.91 cm −1 and 1436.05 cm −1 were the superimposed peaks of -CH 3 asymmetric deformation vibration and -CH 2 shear vibration. 1363.04 cm −1 was the bending vibration absorption peak of CH 3 . 1196.3 cm −1 , 1170.60 cm −1 was the antisymmetric stretching vibration peak of ester C-O-C.

Determination of the pH of Boric Acid/HCA Mixtures
The HCAs were prepared at three different concentrations of 0.1, 0.2, and 0.5 mol/kg with distilled water. Then, boric acid was added at different proportions to three replicate HCA solutions of each given concentration, followed by measuring the pH values of the three replicate solutions. The total pH rates of change in the HCA solutions were calculated by (pH 0 − pH 1 )/pH 0 , where pH 0 is the initial pH of the HCAs at the given concentration, and pH 1 is the pH after the addition of boric acid.

Fatty Acid Ester Synthesis
In a reaction flask, 10 g of fatty acid, 20 g of methanol, 0-0.5 g of boric acid, and 0-2.5 g of tartaric acid were added and stirred magnetically (500 rpm). The reaction temperature was controlled at 65 • C, and the reaction time was 8-20 h. After the reaction, the product was poured into a separatory funnel and allowed to settle into two distinct layers. The layer of fatty acid ester was separated, washed with water, dried with anhydrous sodium sulfate, and then sampled for analysis.

Analytical Methods
For infrared spectral data acquisition, the sample was placed on an infrared spectrometer slide with air as the background, and the spectrum was acquired in the wave number range of 400-4000 cm −1 , where the number of sample scans was 24, the number of background scans was 24, the sample gain was 1.0, the mirror velocity was 0.6329, and the aperture was 95.00.
For H-NMR data acquisition, the sample was placed into a measuring sample tube, CDCl 3 was added, and the sample was measured by a 600 MHz NMR instrument (frequency: 600.18 MHz), where the temperature was 296.9 K, the number of scans was 64, and the pulse width was 12.6 µs. The spectral width was 12,315.27 and the data point size was 32,768. The NMR spectra were processed by Mestrenova software, and integrated after calibration, phase, and baseline calibration.
For GC analysis, high-purity nitrogen was used as the carrier gas, and the temperature program was as follows. The initial temperature was 70 • C (held for 2 min), with the first ramp of 5 • C/min to 150 • C (held for 3 min), followed by a second ramp of 10 • C/min to 230 • C (held for 10 min). The inlet temperature was set to 250 • C, and the total flow rate was set to 130.5 mL/min, with a split ratio of 50:1 and a septum purge rate of 3 mL/min. The analytes were detected using a flame ionization detector (FID), with a detection port temperature of 250 • C, a hydrogen flow rate of 40 mL/min, an air flow rate of 450 mL/min, and a nitrogen purge rate of 25 mL/min. The injection volume was 0.2 µL.
For GC-MS analysis, high-purity helium was used as the carrier gas, and the temperature program was as follows. The initial temperature was 50 • C (held for 3 min), with a first ramp of 20 • C/min to 120 • C, followed by a second ramp of 2 • C/min to 180 • C (held for 2 min), and a third ramp of 50 • C/min to 250 • C (held for 5 min). The inlet temperature was set to 230 • C, and the interface temperature was set to 250 • C.
For mass spectrometry, electron ionization (EI) was used as the ionization source, with an ionization voltage of 70 eV, where full-scan mode was used with a scan range of 45-350 amu. In addition, a solvent delay time of 5 min was set, where the injection volume was set to 0.5 µL (the sample was dissolved in ethanol with a mass fraction of 1%).

Conclusions
(1) The effect of boric acid on the ionization balance of HCA was studied by analyzing and measuring the pH values of aqueous solutions of eight HCAs-glycolic acid, D-(−)-lactic acid, (R)-(−)-mandelic acid, D-gluconic acid, L-(−)-malic acid, L-(+) -tartaric acid, D-(−)-tartaric acid, and citric acid-after adding boric acid. The functions for the pH variations of the HCAs with the amount of boric acid at specified concentrations were obtained by polynomial fitting. By differentiating the fitted pH functions, the functions of the pH rate of change with the change in the boric acid dosage at specified concentrations were obtained. The complexation reactions of boric acid and HCAs were analyzed, and the formulas for calculating the ionization equilibrium constants of monoligand complexes and diligand complexes were deduced. The effects of these two complexes on the ionization equilibrium were compared. (2) Boric acid can react with the hydroxyl groups of HCA to form complexes, which promotes the ionization equilibrium of HCA to move in the positive direction. HCA molecules contain strong electron donor groups, and the boric acid complex became more stable with a greater proton donating ability. The acidities of the combination of boric acid and HCAs were in the following order: citric acid > tartaric acid > mandelic acid > malic acid > grape acid > lactic acid > glycolic acid. (3) The compound catalyst composed of tartaric acid and boric acid was used to catalyze the esterification of palmitic acid and methanol, and the yield of methyl ester was up to 98%. The short-chain alcohol was favorable to promote the dissolution of the complex catalyst. The catalyst was mainly present in the alcohol after the esterification reaction was finished, and the product ester was neutral. This facilitated the recovery of catalyst and excess alcohol, which was beneficial to environmentally friendly production.
Author Contributions: R.Q.: conceptualization, supervision, methodology, validation, formal analysis, investigation, data curation, writing-original draft preparation, writing-review and editing, project administration, and funding acquisition; H.C.: data curation, formal analysis and investigation, writing-review and editing; R.W.: investigation and resources; G.L.: writing-review and editing; Z.M.: conceptualization, supervision, methodology, project administration, writing-original draft preparation, writing-review and editing, and funding acquisition. All authors contributed equally to this work. All authors have read and agreed to the published version of the manuscript. Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.