Acoustic and Volumetric Properties of Mixture of ( N , N-Dimethylacetamide + Ethyl Acrylate ) with 1-Butanol or iso-Butanol or t-Butanol at 308 . 15

Densities, ρ, and ultrasonic speeds, u of mixtures of 1-butanol or iso-butanol or t-butanol with equimolar mixture of (N,Ndimethylacetamide + Ethyl acrylate) over the entire composition range have been measured at T = 308.15K. Using the experimental results, deviation in ultrasonic speed, Δu, deviation in isentropic compressibility, Δk s , excess molar volume, VE m , excess intermolecular free length, LE f , and excess acoustic impedance, Z, have been calculated. The variation of these properties with composition of the mixtures has been discussed in terms of molecular interactions in these mixtures. The deviation/excess properties have been fitted to Redlich-Kister type polynomial and the corresponding standard deviations have been calculated. Negative values ofV m , Δk s , and LE f and positive values of Δu, andZ are observed over the entire composition range.The observed negative and positive values of deviation/excess properties are attributed to the strong interactions between the unlike molecules of the mixtures. Further theoretical values of sound velocity in the mixtures have been evaluated using various theories and compared with experimental sound velocities to verify the applicability of such theories to the systems studied.Theoretical ultrasonic velocity data has been used to study molecular interactions in the systems investigated.


Introduction
The measurement of speed of sound in liquids enables for the determination of some useful acoustic and thermodynamic parameters that are found to be very sensitive to molecular interactions.Acrylic esters are important industrial chemicals that are widely used as precursors in the production of technically important special type polymers.Alkanol molecules are polar and self-associated through hydrogen bonding of their hydroxyl groups [1].N,Ndimethylacetamide is commonly used as a solvent for fibres or in the adhesive industry.Ethyl acrylate and N,N-dimethylacetamide molecules are polar having dipole moments 1.96 D [2] and 3.72 D [2] at 298.15 K, respectively.A survey of the literature indicates that Francesconi and Comelli [3], Gonzalez and Ortega [4], and Liau et al. [5] reported density and viscosity data for binary mixtures of esters with alkanols.Recently some researchers have reported the ultrasonic, volumetric, and viscometric studies of esters with alcohols [6][7][8].N,N-dimethylacetamide as one component and +2-propoxyethanol, +2-isopropoxyethanol [9] and +aliphatic alcohols [10,11], and +benzene, +toluene, +ethyl benzene [12] as other components.
The present work deals with the study of ultrasonic and volumetric properties to investigate the molecular interactions between the unlike molecules of the mixtures of 1butanol, iso-butanol, and t-butanol with equi molar mixture of (N,N-dimethylacetamide + Ethyl acrylate) over the entire composition range at  = 308.15K (see Table 2 for experimental values).

Experimental Section
Analytical Reagent grade (A.R) of EA (mass fraction purity 0.99) was obtained from KEMPHASOL Company, Mumbai, India.N,N-dimethylacetamide (mass fraction purity 0.99) and isobutyl alcohol (mass fraction purity 0.99) are of Graded Reagent (G.R) and 1-butanol (mass fraction purity 0.99) and t-butanol (mass fraction purity 0.99) of (AR grade) obtained from LOBA Chemicals, Mumbai, India, are used in the present investigation and are further purified by standard methods [25].Equimolar mixture of DMA and EA is prepared.This solution is in turn used to prepare the liquid mixtures with 1-butanol or iso-butanol or t-butanol so that the entire composition range is covered (i.e., 0-100% of the alkanols).Mixtures are prepared by mass in air tight bottles.The mass measurements are performed with a METTLER TOLEDO (Switzerland make) ABB5-S/FACT digital balance with an accuracy of ±0.01 mg.The uncertainty in the mole fraction is 10 −4 .The ultrasonic velocity of pure liquids and their mixtures has been measured by using a multifrequency ultrasonic interferometer (M-82 Model) supplied by Mittal enterprise, New Delhi, at a fixed frequency of 2 MHz with an accuracy of ±0.2%.In the present study, the constant temperature water bath (digital electronic) supplied by Concord Instruments Co. Ltd., Chennai (RAAGA type), has been used.The instrument can maintain temperature to ±0.01 K as per its specifications.
Densities of pure liquids and their mixtures have been determined by using a 5 cm 3 two stem double walled Parker & Parker type pyknometer [26].This pyknometer is calibrated with triply distilled water.The pyknometer filled with air bubble free experimental liquids was kept in a transparent walled constant temperature bath for 20 to 30 min to attain thermal equilibrium.The positions of the liquid levels in the two arms are recorded with the help of traveling microscope.At least three to four measurements are performed, from which an average value of density of the experimental liquid is

Results and Discussion
Using measured data of ultrasonic speed () and density (), acoustic parameters such as the isentropic compressibility (  ), acoustic impedance (), and the intermolecular free length (  ) have been determined from the following equations: where  is Jacobson temperature dependent constant and is equal to  = (93.875+ 0.375) × 10 −8 , where  is absolute temperature.
The deviation in ultrasonic speed in the mixtures has been calculated using the relation where "" is the mole fraction of the liquid mixture and the subscripts 1 and 2 stand for alkanols and equimolar mixture, respectively.Pertinent to the calculation of deviation and excess parameters, equimolar mixture is considered as one component of the liquid mixture [27].
The deviation in isentropic compressibility has been calculated from the following equation [28]: Since   is not additive on mole fraction, it is additive on volume fraction.Hence, such values are calculated using volume fraction The excess functions such as    ,    , and   have been calculated using The values of deviation in ultrasonic velocity, excess molar volume, excess free length, and excess acoustic impedance have been fitted to a Redlich-Kister [29] type polynomial equation where   is Δ,    ,    , and   .The subscript "" in the summation of the above equation takes values from 1 to 5.
The values of Δ  have been fitted to Redlich-Kister type polynomial with volume fraction instead of mole fraction in the polynomial: The values of coefficients   ( 1 ,  2 ,  3 ,  4 , and  5 ) in the above equations (( 5) and ( 6)) have been determined using the least square method and are compiled in Table 3 along  Figure 2: Variation of deviation in isentropic compressibility, Δ  , with volume fraction,  1 , of (e), 1-butanol/(◼), iso-butanol/(), and t-butanol with equimolar mixture of (DMA + EA).
with the standard deviations (  ) calculated using the expression where "" is the total number of experimental points (= 11) and "" is the number of coefficients (= 5) in (5).
The variations of these properties with mole fraction of 1-butanol/iso-butanol/t-butanol with equi molar mixture of (DMA + EA) are presented in Figures 1, 2, 3, 4, and 5. Negative values of    , Δ  , and    and positive values of Δ   have been observed in the present investigation mixtures.The factors that are mainly responsible for the expansion of molar volume, that is, positive values of    , are as follows [30,31].(i) Breaking one or both of the components in a solution, that is, loss of dipolar association between the molecules (dispersion Figure 5: Variation of excess acoustic impedance,   , with mole fraction,  1 , of (e), 1-butanol/(◼), iso-butanol/(), and t-butanol with equi molar mixture of (DMA + EA).

forces). (ii) The geometry of molecular structures which does not favor the fitting of molecules of one component into the voids created by the molecules of other component. (iii) Steric hindrance of the molecules. The negative values of 𝑉 𝐸
[32] are due to strong specific interactions such as (iv) association of molecules through the formation of hydrogen bond (or) association due to dipole-dipole interactions and (v) accommodation of molecules due to considerable differences in molar volumes.The variation of excess molar volume in the present investigation is negative over the entire mole fraction range [33].As we know, the molecules of alkanols are self-associated through hydrogen bonding in pure state [1].Mixing of (DMA + EA) with alkanols would induce mutual dissociation of hydrogen bonded structures present in the pure alkanols with subsequent formation of new hydrogen bonds (O⋅ ⋅ ⋅ H-O-) between carbonyl group (-C=O) of amide/acrylate molecules and hydroxyl group (-OH) of alcohol groups leading to a contraction in volume and decrease in isentropic compressibility of the mixtures.The magnitude of negative    , Δ  , and    values follows the order 1-butanol < iso-butanol < t-butanol which indicates the order of the interactions between the components of the mixtures.In general, the negative values of deviation in isentropic compressibility indicate strong and specific interactions such as H-O and -dipole interactions; on the other hand, the positive values of deviation in isentropic compressibility indicate weak interactions and dispersion forces operating between the molecules of the components of the mixtures [34,35].
Further, it is interesting to note that interaction is more in (DMA + EA) +t-butanol mixture than in (DMA + EA) +isobutanol mixture.This is due to the presence of three -CH 3 groups at the -carbon atom of t-butanol, which increase the electron density at oxygen atom to greater extent than that in iso-butanol, which has two -CH 3 groups at -carbon atom, resulting in the strong interaction in t-butanol mixture.Hence, the interaction between (DMA + EA) and alkanols increases when the -OH group is attached to more number of -CH 3 groups.The variation of Δ and   with composition of mixture is displayed in Figures 4 and 5, respectively.From these figures, Δ and   values are positive and become more positive with increasing of -CH 3 groups attached to -OH group of alkanols.It has been also observed that the strength of interaction in Δ and   is the same as that of    , Δ  , and    for all the systems.Furthermore, DMA and alkanol molecules having large dipole moments, causing dipole-dipole and dipole-induced dipole interactions, also exist between the liquid mixtures, which is also favorable to strong interactions between the liquid molecules.
In the present study, theoretical sound velocities have been evaluated by considering (DMA + EA) as one component and alkanols as the other component in the mixture.Such an evaluation of theoretical sound velocity is useful to verify the applicability of various postulates of the theories of liquid mixtures and to arrive at some useful inferences regarding the strength of molecular interactions between component liquids in some cases.The theoretical values of ultrasonic velocity obtained using various theories along with the experimental velocity are summarized in Table 4.
Nomoto [36] established the following relation with sound velocity based on the assumption of the linearity of the molecular sound velocity and the additivity of molar volume: where   is the mole fraction,   =  1/3    is the molar sound velocity,   is the molar volume, and   is the sound velocity of the th component.
Van Dael [37] obtained the ideal mixture relation where   is the molecular weight of th component in the liquid mixture.Impedance dependence relation used by Baluja and Parsania [38] is given as where   is the acoustic impedance and   is the density of the th component of the mixture.Junjie's [39] equation is given as Jacobson's [40] equation is given as where  is Jacobson temperature dependent constant and is equal to  = (93.875+ 0.375) × 10 −8 ,  is absolute temperature, and   is the ideal free length of the mixture given by   = ( 1  1 +  2  2 ).Rao's (specific sound velocity) [41] relation is given as where   =  1/3  /  is the Rao's specific sound velocity of the th component of the mixture.
The experimental data have been fitted to a polynomial; it describes the ultrasonic velocity data quantitatively as well as qualitatively even in the specific interaction predominant region where nonideal behavior of the system is noticed.
The polynomial equation is [42]  () =  () = ∑     , where  in the summation assumed values from 0 to 3,  is the mole fraction of the 1-butanol/iso-butanol/t-butanol, and   , is constant coefficient to be determined using numerical methods.The values of sound velocities (after determining the coefficients in the above polynomial equation by applying least squares method) have been compiled in Table 4.The root mean square deviation (RMSD) () corresponding to sound velocity values calculated using the polynomial equation ( 14) from their experimental values has been evaluated using the relation where   is the experimental sound velocity,   is the calculated sound velocity from the polynomial equation (), and  is the number of mole fractions at which experimental and theoretical velocities have been determined.These standard deviations which are small and coefficients obtained from ( 14) are presented in Table 5.
The percentage of deviations of theoretical velocities from the experimental ultrasonic velocity values are plotted in Figures 6, 7, and 8 for all the systems investigated.Data from Table 5 and from Figures 6, 7, and 8 reveal that sound speed computed from Jacobson's relation exhibits more satisfactory agreement with the experimental values.The interdependence of intermolecular free length and velocity is given by Jacobson relation.The small percentage deviation of Jacobson relation provides the better estimate of the ultrasonic velocity values.

Conclusions
(i) Ultrasonic velocities, , and densities, , of mixtures of 1-butanol or iso-butanol or t-butanol with equi molar mixture of (N,N-dimethylacetamide + Ethyl acrylate) over the entire composition range have been measured at  = 308.15K.
(ii) Using the experimental results, deviations in ultrasonic velocity, Δu, and isentropic compressibility, Δ  ,  excess molar volume,    , excess intermolecular free length,    , and excess acoustic impedance,   , have been calculated and these properties with composition of the mixtures have been discussed in terms of molecular interactions in these mixtures.
(iii) The deviation/excess properties have been fitted to Redlich-Kister type polynomial and the corresponding standard deviations have been calculated.
(iv) Negative values of    , Δ  , and    and positive values of Δ and   are observed over the entire composition range.The observed negative and positive values of deviation/excess properties are attributed to the strong interactions between the unlike molecules of the mixtures.
(vi) Further theoretical values of sound velocity in the mixtures have been evaluated using various theories and have been compared with experimental sound velocities to verify the applicability of such theories to the systems studied.Theoretical ultrasonic velocity data has been used to study molecular interactions in the systems investigated.

Table 1 :
Comparison of experimental values of ultrasonic speed, , and density, , of pure liquids with the corresponding literature values at 308.15 K.

Table 3 :
Coefficients   of Redlich-Kister type polynomial Equations (5) and (6) and the corresponding standard deviation, , of all the systems.
determined.The reproducibility in the measured parameter density is 3 in 10 5 parts.