Terpene-Based Biofuel Additives (Citral, Limonene, and Linalool) with Chloroform: Experimental and Modeling Study of Volumetric and Transport Properties

Abstract

In this paper, the thermodynamic properties of terpene mixtures were investigated because they represent a promising group of compounds, usually extracted from biomass, with their most notable application as fuel performance enhancers. The densities, viscosities, refractive indices, and ultrasonic speeds of sound were measured for three binary mixtures, citral + chloroform, limonene + chloroform, and linalool + chloroform, across the full composition range at temperatures between 288.15 K and 323.15 K under atmospheric pressure. Using experimental data, excess molar volumes, viscosity deviations, refractive index deviations, and isentropic compressibility, deviations were calculated. Additionally, properties such as partial molar volumes, excess partial molar volumes, partial molar volumes at infinite dilution, and apparent molar volumes were derived. The excess and deviation properties were analyzed using the Redlich–Kister equation. A single mathematical model, the Heric–Brewer–Jouyban–Acree model, was used to represent densities, viscosities, refractive indices, and ultrasonic speeds of sound. The results obtained in this work suggest that dispersive interactions dominate in the limonene and linalool binary mixtures, while hydrogen bonding plays a significant role in the citral + chloroform system. In summary, dispersive interactions are dominant in nonpolar systems like limonene and linalool, while hydrogen bonding significantly affects the citral-chloroform mixture, where the polar groups in citral interact with chloroform molecules. These differences in intermolecular forces help explain the distinct behavior of each mixture. The modeling outcomes demonstrated that the Heric–Brewer–Jouyban–Acree model accurately correlated the experimental thermodynamic properties, with average percent deviations below 1% for all three systems.

1. Introduction

Terpenes can be valuable additives in biofuels due to their high energy density, low viscosity, and excellent combustion properties. As shown in previous research [1,2], terpenes used as additives in fuel mixtures can increase the fuel’s density, which may improve energy content and combustion efficiency. Adding a small amount of terpenes to diesel fuel or jet fuel was sufficient to decrease the cloud point of the fuel enhancing cold weather performance [1]. Additionally, they can enhance the volumetric net of combustion, boosting the overall energy release during the combustion process and improving fuel performance [2]. Their molecular structure makes them suitable for blending with conventional fuels and with biofuels like ethanol or biodiesel. Additionally, terpenes can be sustainably sourced, making them a promising alternative to petroleum-based fuel additives, further supporting the shift toward greener energy solutions. The extraction process of terpenes from plant material is crucial for their effective use as biofuel additives. The primary objective of this study was to obtain thermodynamic data that can significantly contribute to improving the use of biofuels in industrial applications, particularly by enhancing the performance and efficiency of modern engines. The detailed analysis of the binary mixtures of terpenes (citral, limonene, and linalool) with chloroform provides insights into the molecular interactions and excess properties that affect the fuel’s behavior under varying conditions. Understanding the ρ, η, and u allows for optimizing fuel formulations for better combustion performance, which can result in increased fuel efficiency and reduced engine wear. Citral is a naturally occurring monoterpene aldehyde [3] found in essential oils like lemongrass and lemon myrtle, known for its strong lemony aroma. It is also widely used in the flavor, fragrance, and pharmaceutical industries, serving as a precursor for compounds like vitamin A and exhibiting antimicrobial and antioxidant properties [4,5,6]. Limonene is a cyclic monoterpene commonly found in citrus peel oils, characterized by its pleasant, orange-like aroma. In addition to its applications, limonene exhibits antibacterial, antifungal, and anti-inflammatory properties [7,8,9,10]. Linalool is a naturally occurring terpene alcohol found in many flowers and spice plants [11,12,13,14], recognized for its soft, floral aroma. It has notable antimicrobial, anti-inflammatory, and sedative properties [15]. Chloroform is often utilized as a solvent in the extraction of terpenes from plant material due to its non-polar nature and high solubility for hydrophobic compounds. Its ability to dissolve a wide range of organic compounds, including terpenes, makes it effective for isolating these volatile constituents from complex plant matrices [16]. Among the various properties considered, chloroform was selected as a component in the binary mixtures examined in this study.

In this work, the densities (ρ), viscosities (η), refractive indices (n_D), and ultrasonic sound speeds (u) for three binary mixtures, citral + chloroform, limonene + chloroform, and linalool + chloroform, were measured across the entire composition range, at temperatures between T = 288.15 K and 323.15 K, under atmospheric pressure. Excess properties and deviations, such as excess molar volumes (V^E), viscosity deviations (Δη), refractive index deviations (Δn_D), and deviations in isentropic compressibility (Δκs), were calculated from the density, viscosity, refractive index, and sound speed data. Furthermore, partial molar volumes, excess partial molar volumes, partial molar volumes at infinite dilution, and apparent molar volumes were determined. The excess properties were fitted to the Redlich–Kister [17] equation as a function of mole fraction. The densities, viscosities, refractive indices, and ultrasonic sound speeds were modeled using the Heric–Brewer–Jouyban–Acree equation. The average percentage deviations, all less than 1% for all properties of the investigated mixtures, confirmed the accuracy and reliability of the model.

As mentioned earlier, the aim of this study was to obtain new experimental data, data that have not been measured and published previously—ρ, η, n_D, and u—of mixtures of terpenes and chloroform at different temperatures and pressures. This will help improve our understanding of their properties in liquid mixtures, as terpenes are a group of compounds that could serve as fuel additives, enhancing fuel characteristics.

2. Materials and Methods

2.1. Chemicals

Citral was supplied by Acros Organics (Dreieich, Germany), limonene was supplied by Acros Organics (Waltham, MA, USA), linalool was supplied by Acros Organics (Madrid, Spain) and chloroform was supplied by Fisher Scientific (Schwerte, Germany). The initial mass fraction purities are provided in

Table 1. Sample description.

Chemical Name	Supplier	CAS Registry n0	Molar Mass/g−1	Initial Mass Fraction Purity
Citral (mixture of geranial and neral)	Acros Organics	5392-40-5	152.24	0.95
(+)-limonene	Acros Organics	5989-27-5	136.24	0.96
Linalool	Acros Organics	78-70-6	154.25	0.97
Chloroform	Fisher Scientific	67-66-3	119.38	0.995

. Chemicals were kept in dark bottles under an inert nitrogen atmosphere and ultrasonically degassed just before sample preparation without further purification. The chemical structures of the reagents are presented in Figure 1.

2.2. Apparatus and Procedure

The experimental measurements of densities and the ultrasonic speed of sounds of the binary mixtures and corresponding pure substances were measured using the highly precise Anton Paar DSA 5000 M digital vibrating U-tube densimeter instrument. In this study, we measured the ultrasonic speed of sound to better understand the physical properties and molecular interactions of the liquid mixtures of terpenes and chloroform at different temperatures and pressures. Measuring the ultrasonic speed of sound in liquid mixtures provides a non-invasive, precise, and cost-effective way to gain insight into the behavior and characteristics of complex mixtures, which is crucial for various scientific and industrial applications. The speed of sound is highly sensitive to temperature and therefore it is controlled by a built-in solid-state thermostat. Viscosities and refractive index measurements were conducted using a Stabinger SVM 3000/G2 viscometer and an RXA-156, respectively. In this work ρ, η, n_D, and u were measured in the temperature range of T = (288.15–323.15) K with a 5 K increment. A detailed explanation of the characteristics of the apparatus and measurement methods used can be found in our previous work [18,19]. The mixtures were prepared gravimetrically using a Mettler AG 204 balance with a precision of 1·10⁻⁷ kg, and the procedure described previously was used. The uncertainty of the mole fraction calculation was less than ±1·10⁻⁴. All molar quantities were based on the IUPAC relative atomic mass table. The experimental uncertainties in the density, viscosity, refractive index, and speed of sound were estimated as 0.9 kg·m⁻³, 0.007 mPa·s, 5·10⁻⁴, and 0.6 ms⁻¹, respectively. When calculating the expanded uncertainty, all relative standard uncertainties were considered, including those from the apparatus, pressure, temperature, impurity of the sample, and measurement uncertainty. These factors contribute to the overall uncertainty by introducing potential variations or errors in the measurement process. By combining these sources, the expanded uncertainty provides a more comprehensive estimate of the possible deviation from the true value, typically expressed with a higher confidence level, such as 95%, to ensure the reliability of the results.

Table 2. Experimental and literature values of ρ, η, n_D, and u of the pure components at atmospheric pressure, 0.1 MPa ^a.

Component	T b/K	10−3 ρ c/kg·m−3		η d/mPa·s		nD e		u f/m·s
		Exp.	Lit.	Exp.	Lit.	Exp.	Lit.	Exp.	Lit.
Citral	293.15	0.88794	0.8884 [20]	2.2809	2.225 [20]	1.4879	1.48669 [20]
	298.15	0.88394	0.8847 [20]	2.0282	2.111 [20]	1.4854	1.48485 [20]
	303.15	0.87994	0.8804 [20]	1.8328	1.807 [20]	1.4829	1.48294 [20]
	313.15	0.87193	0.8723 [20]	1.5285	1.502 [20]	1.4781	1.47869 [20]
	323.15	0.86391	0.8643 [20]	1.2955	1.274 [20]	1.4732	1.47420 [20]
Limonene	293.15	0.84255	0.8448 [20] 0.8402 [21] 0.8457 [22]			1.4725	1.47274 [23]
	298.15	0.83864	0.8410 [20] 0.8386 [21] 0.8422 [22] 0.8373 [24] 0.8372 [25] 0.8424 [26]	0.8656	0.8599 [21] 0.8460 [27,28]	1.4700	1.47027 [25]
	303.15	0.83472	0.8370 [20] 0.8377 [22]
	308.15	0.83079	0.8343 [22]
	313.15	0.82683	0.8290 [20] 0.8303 [22]
	323.15	0.81893	0.8211 [20]
Linalool	293.15	0.86109	0.8618 [20]	5.4116	5.53 [20]	1.4615	1.46152 [20] 1.46272 [23]
	298.15	0.85687	0.8577 [20] 0.85809 [27] 0.85760 [28]	4.3329	4.47 [20] 4.3493 [21] 4.4640 [27] 4.3810 [28]	1.4590	1.45965 [20] 1.45970 [25] 1.4603 [27] 1.4605 [28]	1314.3	1313.1 [29]
	303.15	0.85263	0.8533 [20]	3.5570	3.63 [20]	1.4566	1.45665 [20]
	313.15	0.84412	0.8448 [20] 0.84543 [28]	2.4966	2.541 [20] 2.552 [27]	1.4516	1.45204 [20] 1.4535 [27]	1259.8	1260.8 [29]
	323.15	0.83548	0.8362 [20]	1.8367	1.868 [20]	1.4464	1.44738 [20]
Chloroform	288.15	1.49787	1.49808 [30]	0.6400	0.5962 [31]
	293.15	1.48840	1.48864 [30] 1.4884 [32]	0.6079	0.600 [33]	1.4455	1.44589 [32]
	298.15	1.47889	1.47915 [30]	0.5781	0.576 [33]			983.0	984.42 [34]
	303.15	1.46933	1.46961 [30] 1.4694 [32]	0.5520	0.552 [33]	1.4392	1.43987 [32]
	308.15	1.45971	1.46003 [30]	0.5268	0.533 [35]			948.9	950.45 [34]
	313.15	1.45003	1.45041 [30] 1.4500 [32]	0.5026	0.509 [33]	1.4330	1.43386 [32]
	318.15	1.44028		0.4818	0.491 [33]

^a u_c(p) = 0.005 MPa. ^b u_c(T) = 0.01 K and the combined expanded uncertainties U_c. ^c U_c(ρ) = 0.9 kg·m⁻³. ^d U_c(η) = 0.002 mPa s. ^e U_c(n_d) = 5·10⁻⁴ and ^f Uc(u) = 0.6 m·s⁻¹ with a 0.95 level of confidence (k = 2).

lists the measured ρ, η, n_D, and u of pure components along with the corresponding literature values. The agreement between experimental and literature data was good.

3. Results and Discussion

3.1. Volumetric and Transport Properties

The experimental values for ρ, η, n_D, and u for three binary mixtures, citral + chloroform, limonene + chloroform, and linalool + chloroform, were measured at a temperature range of T = (288.15–323.15) K and at atmospheric pressure. Experimental data were used for the calculation of additional thermodynamic properties, e.g., the excess molar volume (V^E), viscosity deviation (Δη), deviation in refractive index (Δn_D), and deviation in isentropic compressibility (Δκ_s) of the selected binary mixtures at each temperature. All the data are listed in Table S1.

Excess molar volumes (V^E) were calculated using the following equation:

$$V^{\mathrm{E}}={\displaystyle \frac{x_1{M}_1+x_2{M}_2}{\rho }}-\left({\displaystyle \frac{x_1{M}_1}{{\rho }_1}}+{\displaystyle \frac{x_2{M}_2}{{\rho }_2}}\right)$$

(1)

where ρ [kg·m⁻³] is the density of the binary mixture, ρ₁ and ρ₂ are densities of pure components 1 and 2, and M₁ and M₂ are the molar masses of component 1 and 2, respectively.

The deviations in viscosity, Δη, were calculated as follows:

$$\Delta \eta =\eta -{\displaystyle \sum _{i=1}^2{x}_i{\eta }_i}$$

(2)

where η [mPa·s] is the viscosity of the binary mixture, η_i is the viscosity of pure component i, and x_i is the mole fraction of component i.

The deviations in the refractive index, Δn_D, were calculated using the following equation:

$$\Delta n_D=n_D-{\displaystyle \sum _{i=1}^2{x}_i{n}_{D,i}}$$

(3)

where n_D is the refractive index of the binary mixture, n_D,i is the refractive index of the pure component i, and x_i is the mole fraction of component i.

Isentropic compressibility (κ_s) was calculated from measured densities and the speed of sound using Equation (4):

$${\kappa }_s={\displaystyle \frac{1}{\rho u^2}}$$

(4)

The deviations in isentropic compressibility (Δκ_s) were calculated using the following relation:

$$\Delta {\kappa }_s={\kappa }_s-{\displaystyle \sum _{i=1}^2{\kappa }_{s,i}{x}_i}$$

(5)

where κ_s is the isentropic compressibility of the binary mixture, κ_s,i is the isentropic compressibility of pure component i, and x_i is the mole fraction of component i.

The results for V^E, Δη, Δn_D, and Δκ_s were correlated using the Redlich–Kister equation [17]:

$$Y=x_i{x}_j{{\displaystyle \sum _{\mathrm{p}=0}^k{A}_p\left(2x_i-1\right)}}^p$$

(6)

where A_p are the adjustable parameters of the related property Y (V^E, Δη, Δn_D or Δκ_s).

The corresponding standard deviation is defined by the following equation:

$$\sigma ={\left({{\displaystyle \sum _{\mathrm{i}=1}^m\left(Y_i^{\exp }-Y_i^{cal}\right)}}^2/\left(n-m\right)\right)}^{1/2}$$

(7)

where Y^exp and Y^cal are the experimental and calculated values for the related property (V^E, Δη, Δn_D, or Δκ_s), n is the number of experimental data points, and m is the number of fitting parameters of the Redlich–Kister equation.

The fitting parameters A_p of Equation (6) and the corresponding standard deviations σ for the analyzed binary mixtures are listed in Table S2.

The experimental and correlated values of excess molar volume V^E calculated by Equation (1) as a function of molar fraction x₁ for the three binary systems at all temperatures are shown in Figure 2. A graphical representation of Δη, Δn_D, and Δκ_s together with the Redlich–Kister polynomial fit are shown in Figure 3, Figure 4 and Figure 5.

The partial molar volume of the binary solution [36] is defined as follows:

$${\overline{V}}_1=V_1+{(1-x_1)}^2{\displaystyle \sum _{i=0}^n{A}_i{(2x_1-1)}^i+2x_1{(1-x_1)}^2{\displaystyle \sum _{i=1}^n(i)}}{A}_i{(2x_1-1)}^{i-1}$$

(8)

$${\overline{V}}_2=V_2+x_1^2{\displaystyle \sum _{i=0}^n{A}_i{(2x_1-1)}^i+2x_1^2(1-x_1){\displaystyle \sum _{i=1}^n(i)}}{A}_i{(2x_1-1)}^{i-1}$$

(9)

where A_i is the fitting parameters of the Redlich–Kister equation.

For a further analysis of the deviation of the mixed solution from the ideal solution, the excess partial molar volume could be used. It can be calculated as follows:

$${\overline{V}}_1^E={\overline{V}}_1-V_1$$

(10)

The values of partial molar volume ${\overline{V}}_{\mathrm{i}}$ and the values of excess partial molar volume ${\overline{V}}_{\mathrm{i}}^{\mathrm{E}}$ for binary mixtures measured in this work are given in Table S3. A graphical representation is shown in Figure 6.

The behavior of real liquid solutions is primarily influenced by chemical and structural interactions between the pure components in the mixture. These non-ideal behaviors arise from various contributions [37], including specific interactions such as hydrogen bonding, dipole–dipole interactions, and dispersion forces between unlike components. Structural effects, like molecular packing and steric hindrance due to differences in the size and shape of the compounds, also play a significant role. The combination of these interactions between molecules affects the excess molar volume, leading to either the expansion or contraction of the mixture’s volume, which can be positive or negative compared to the ideal volume.

In order to better understand the non-ideal behavior of the analyzed systems, a molecule structure of each compound is shown in Figure 1. Limonene is a hydrocarbon having a cyclic molecule structure, while citral and linalool have an acyclic molecule structure (see Figure 1). Linalool is an alcohol having both hydrogen donor and acceptor abilities while citral as an aldehyde acting as a hydrogen acceptor [38], so only linalool is capable of forming hydrogen bonding in a mixture with chloroform. Because of this dual behavior, linalool in its pure state tends to form clusters, or aggregates, held together by intermolecular hydrogen bonds. When mixed with other compounds, the equilibrium of these bonds is disrupted. This disruption has a twofold effect: breaking the bonds between terpene molecules leads to an expansion in the mixture’s volume, while the formation and strength of new bonds between different compounds determine whether the overall volume of the mixture will expand or contract. On the other hand, citral molecules are capable of forming dipole–dipole interactions due to a high polarity of 4.39 D, while hydrocarbons mainly interact through weaker dispersion forces (the dipole moment for limonene is 1.570 D and for chloroform 1.1 D) [37].

As shown in Table S1 and Figure 2 and Figure 5, the V^E and Δκ_s showed the same trend, i.e., negative for the citral + chloroform mixture and positive for the limonene + chloroform and linalool + chloroform systems. The same behavior was evident for the excess partial molar volumes, i.e., ${\overline{V}}_1^{\mathrm{E}}$ and ${\overline{V}}_2^{\mathrm{E}}$ (Table S3 and Figure 6). Negative values in excess partial molar volumes indicate that the volume of a compound is lower in a mixture than in the pure state, due to the occurrence of solute–solvent interactions, while positive values are typical for the mixtures where solute–solute, solvent–solvent, or weak solute–solvent interactions occur. Having in mind the compounds’ structure explained above, it seems that hydrogen bonding between neat linalool molecules predominates the interactions between linalool and chloroform molecules, causing the expansion in volume and positive excess volumes. Also, the linear structure of linalool molecules prevents better packing when mixed with chloroform molecules. Contrarily, both citral and chloroform exhibited negative ${\overline{V}}_1^{\mathrm{E}}$ and ${\overline{V}}_2^{\mathrm{E}}$ values at infinite dilution, which refers to a decrease in volume upon mixing. This can be attributed to dipole–dipole interactions and/or more efficient packing in a mixture resulting in volume compression. As the limonene molecule is not capable of forming strong interactions with chloroform, both ${\overline{V}}_1^{\mathrm{E}}$ and ${\overline{V}}_2^{\mathrm{E}}$ were close to zero, which means that the volumes of both molecules in mixtures remained close to their volumes in pure states.

The values of Δη and Δn_D were mainly positive (Figure 3 and Figure 4), except for the system linalool + chloroform that showed negative deviations in viscosities. Positive viscosity deviations for the citral + chloroform mixture due to the increase in viscosity upon mixing indicated the existence of specific interactions between unlike compounds. Contrarily, large negative viscosity deviations for the linalool + chloroform system were due to a loss in associations existing in the pure compounds and a lack of new interactions between unlike compounds [39]. These behaviors support the conclusions drawn from the V^E and Δκ_s results.

Two properties, the apparent molar volume and the partial molar volume at infinite dilution, are also important for describing the behavior of the solution.

The apparent molar volume is calculated as follows:

$$V_{\phi ,1}=V_1+\left(V^E/x_1\right)$$

(11)

$$V_{\phi ,2}=V_2+\left(V^E/x_2\right)=V_2+V^E/\left(1-x_1\right)$$

(12)

The partial molar volume is calculated as follows:

$${\overline{V}}_1^{\infty }=V_1+{\displaystyle \sum _{i=0}^n{A}_i{\left(-1\right)}^i}$$

(13)

$${\overline{V}}_2^{\infty }=V_2+{\displaystyle \sum _{i=0}^n{A}_i}$$

(14)

The apparent molar volume and the partial molar volume at infinite dilution for all investigated binary mixtures are shown in Tables S4 and S5 in Supplementary Materials, and the comparison of the apparent molar volume at T = 298.15 K is graphically represented in Figure 7.

3.2. Volumetric and Transport Properties Correlation by Heric–Brewer–Jouyban–Acree Model

The experimentally measured properties, ρ, η, n_D, and u of the binary mixtures of terpenes with chloroform, can be mathematically represented using the Heric–Brewer–Jouyban–Acree model [40,41]. This model has previously demonstrated excellent results in correlating the thermodynamic properties of binary liquid mixtures and was applied in this study. The suggested three-parameter model describes the ρ, η, n_D, and u of mixtures as a function of composition and temperature. In this work, the model’s unique set of parameters was determined for the entire temperature range. The Heric–Brewer–Jouyban–Acree model is expressed as follows:

$$\ln Y_{m,T}=x_1\ln Y_{1,T}+x_2\ln Y_{2,T}+J_0\left[{\displaystyle \frac{x_1{x}_2}{T}}\right]+J_1\left[{\displaystyle \frac{x_1{x}_2\left(x_1-x_2\right)}{T}}\right]+J_2\left[{\displaystyle \frac{x_1{x}_2{\left(x_1-x_2\right)}^2}{T}}\right]$$

(15)

where Y_m,T, Y_1,T, and Y_2,T are the values of the related property (ρ, η, n_D, and u) for the mixture, component 1 (terpenes) and component 2 (chloroform) at temperature T, and x₁ and x₂ are the mole fractions of the terpenes or chloroform in the binary mixture, respectively. J_i is the model parameters obtained using the least-squares method. The suitability and applicability of the tested three-parameter model were evaluated by the average percent deviation D:

$$D/\%={\displaystyle \frac{100}{N}}{\displaystyle \sum \left(\frac{Y_{cal}-Y_{\exp }}{Y_{\exp }}\right)}$$

(16)

where N is the number of data points in each set.

The Heric–Brewer–Jouyban–Acree model parameters together with standard deviation σ and the average percent deviation D are shown in

Table 3. Heric–Brewer–Jouyban–Acree model parameters for density ρ, viscosity η, refractive indices n_D, speed of sound u, standard deviations σ, and the average percent deviation (D%).

Function	T/K	A0	A1	A2	σ	D/%
Citral (1) + chloroform (2)
10−3 ρ/kg·m−3	288.15–323.15	−67.0604	17.4571	−8.4024	0.0006	0.0416
η/mPa·s	288.15–323.15	362.2231	−162.6951	52.0481	0.0137	0.8713
nD	288.15–323.15	8.2593	−3.4111	0.8729	0.0008	0.0409
u/m·s−1	288.15–323.15	49.9569	−7.6477	−0.4393	4.4611	0.3033
Limonene (1) + chloroform (2)
10−3 ρ/kg·m−3	288.15–323.15	−71.6699	17.1021	−4.5862	0.0012	0.0926
η/mPa·s	288.15–323.15	105.6325	−42.3770	−1.1663	0.0062	0.6984
nD	288.15–323.15	4.3198	−1.3223	0.9099	0.0005	0.0256
u/m·s−1	288.15–323.15	23.3360	−0.1104	−5.0613	0.6580	0.0445
Linalool (1) + chloroform (2)
10−3 ρ/kg·m−3	288.15–323.15	−88.2525	28.1124	−9.7100	0.0017	0.1254
η/mPa·s	288.15–323.15	76.2210	15.4006	−44.9597	0.0287	0.9696
nD	288.15–323.15	2.5822	0.0489	0.2538	0.0004	0.0240
u/m·s−1	288.15–323.15	28.2242	7.4589	−11.1498	0.4510	0.0319

. From Table 3, it can be concluded that the Heric–Brewer–Jouyban–Acree correlation model showed satisfactory results for all three binary systems.

The binary mixture with linalool showed a maximum average percent deviation for the ρ and η measurements of 0.12% and 1%, respectively. On the other hand, the binary mixture with citral showed the maximum average percent deviation for the n_D and u measurements of 0.04% and 0.3%, respectively.

4. Conclusions

In this paper, ρ, η, n_D, and u were measured for three binary mixtures: citral + chloroform, limonene + chloroform, and linalool + chloroform, across the entire composition range and at temperatures ranging from 288.15 to 323.15 K, under atmospheric pressure. Excess molar volume V^E and deviation properties (Δη, Δn_D, and Δκ_s) were calculated from the experimental data, along with partial and excess partial molar volumes and partial molar volumes at infinite dilution. The Redlich–Kister equation was employed to fit the excess molar volumes and deviation properties. Among the analyzed systems, only the binary system of citral and chloroform exhibited negative V^E and Δκ_s, as well as excess partial molar volumes. This behavior suggests a decrease in volume upon mixing due to stronger solute–solvent interactions compared to solute–solute or solvent–solvent interactions. Conversely, the results obtained for the linalool and chloroform binary mixture indicate that hydrogen bonding between neat linalool molecules predominated the interactions between the linalool and chloroform molecules, resulting in volume expansion and positive excess volumes and excess partial volumes. Additionally, the very small deviation from the ideal behavior observed in the mixture of limonene and chloroform suggests that the linear structure of limonene molecules hinders efficient packing when mixed with chloroform molecules. Deviations in viscosity and refractive indices further support the conclusions drawn from the V^E and Δκ_s results. Moreover, the Heric–Brewer–Jouyban–Acree model successfully correlated the experimental values of thermodynamic properties with the unique set of parameters for the entire temperature range with a maximum average percent deviation of less than 1% for all the investigated properties and systems.

The results of this study provide valuable thermodynamic data for the design and optimization of biofuels. Understanding the molecular interactions and excess properties of binary mixtures containing terpenes, such as citral, limonene, and linalool, is crucial for enhancing biofuel formulations. The observed deviations in volume, viscosity, and refractive indices can provide valuable information for the selection of optimal additives that improve fuel performance, such as increasing fuel stability, enhancing combustion efficiency, and reducing emissions. Additionally, the successful application of the Heric–Brewer–Jouyban–Acree model demonstrates its potential as a predictive tool for further investigation into the thermodynamic behavior of more complex biofuel mixtures.