Scientific paper
Densities and Viscosities of Alkylethanoates +Cyclohexane, +Benzene, +1,4-dimethylbenzene, and +1,3.5-trimethylbenzene at 308.15 K
S. S.Yadava,1* Y. Singh2 and Neetu Kushwaha1
1 Department of Chemistry, D.D.U.Gorakhpur University, Gorakhpur-273009 (U.P.) 2 Department of Chemistry, U.P.Autonomous College, Varanasi, (U.P.), India * Corresponding author: E-mail: ssyadava1@rediffmail.com
Received: 25-12-2009
Abstract
Densities (p12) and viscosities (tf12) of binary mixtures of alkylethanoates, + cyclohexane, benzene, 1,4-dimethylbenze-ne and 1,3,5-trimethylbenzene have been measured over the whole mole fractions range at atmospheric pressure and temperature 308.15 K. Deviations of experimental viscosities from the linear mixing rule (An) for binary mixtures of the esters and cyclohexane are large and negative. At] values are less and negative for binary mixtures of esters and aromatic hydrocarbons except binary mixtures of n-propylethanoate and benzene which show less positive At] values. At] values for binary mixtures of ethylethanoate + 1,4-dimethylbenzene, +1,3,5-trimethylbenzene and n-propylethanoate + 1,4-dimethylbenzene are both less negative and less positive. At] values are fitted into Redlich-Kister polynomial equation and standard deviations, o of At] for all the binary mixtures are reported. Several viscosity equations are critically analysed. The strengths of molecular interactions are discussed on the basis of Grunberg-Nissan interaction parameters.
Keywords: Density, viscosity, binary mixture, esters, hydrocarbons, molecular interactions.
1. Introduction
Recently much attentions have been given on the studies of viscosities1-5 for binary mixtures containing one component as either aliphatic or aromatic esters. Viscosities of binary mixtures of some alkanoates and bromoalka-noates with n-hexane at 303.15 K have been measured and the data have been analyzed6 in terms of dipole-dipole interaction in alkanoates and intramolecular Br...O interaction in bromoalkanoate. Binary mixtures of several alky-lalkanoate with several glycols7 have been studied at several temperatures employing measurements of viscosities together with other physical properties and qualitative analysis of deviation and excess functions have been made to ascertain the nature and type of bulk state interactions. In wine distillation processes the main components are water and ethanol and several other minor components called as congeners are higher alcohols, aldehydes and esters8. Esters are important class of compound used in pharmaceutical aid, artificial fruit essences, manufacturing of artificial
leather and perfumes. Ethylethanoate is also used in protein sequencing. A very few investigations for the binary mixtures of alkanoate with aromatic hydrocarbons 911 have been reported either by viscosity or by some other methods. In our laboratory binary mixtures of several polar aliphatic molecules with non-polar aromatic molecules have been studied by viscosities1215 measurements.
In view of the several industrial importances of the esters and limited studies on binary mixtures of esters with aromatic hydrocarbon solvents it is intended to perform viscosity measurements on binary mixtures containing aliphatic esters viz. methylethanoate, ethylethanoate and n-propylethanoate and aromatic hydrocarbon solvents viz. benzene, 1,4-dimethylbenzene and 1,3,5-trimethylbenzene at 308.15 K. Binary mixtures of these esters with inert solvent cyclohexane are also studied to have a reference point for assessing the interactions. Moreover, successive alkylated ethanoates and aromatic hydrocarbon solvents are deliberately chosen to have an idea of the effect of substituents on either of the interacting components over molecular interactions. The chosen esters suc-
cessively differ in their dipole moments and the aromatic hydrocarbons also successively differ in their polarisabili-ties. Thus the present investigation is also intended to throw light on the effects of dipole moments and polarisa-bilities over such interactions.
2. Experimental
All Chemicals in this study methylethanoate (mass fraction purity 0.99), ethylethanoate (mass fraction purity 0.995 ), n-propylethanoate (mass fraction purity 0.98), benzene (mass fraction purity 99.7), 1,4-dimethylbenzene (mass fraction purity 0.99) and 1,3,5-trimethylbenzene (mass fraction purity 0.98) were obtained from Merck and purified by fractional distillation over one meter long column and collecting only the middle fractions for the study. Cyclohexane (mass fraction purity 0.997) was used without further purification. The purities of the liquids were further verified by density measurements.
Tabela 1:
v = n/p = at-b/t
(1)
Compound	Density x 10-	3 at 308.15 K
	experimental	literature
	(kg m-3)	(kg m-3)
Cyclohexane	0.76477	0.7645a
Benzene	0.86302	0.86300b
		0.86290c
1,4-dimethylbenzene	0.84878	0.84791d
		0.84787e
1,3,5-trimethylbenzene	0.85447	0.85315f
Methylethanoate	0.91561	0.91522g
Ethylethanoate	0.88252	0.88250h
n-propylethanoate	0.87105	0.8718i
a: Ref.16; b: Ref.17; c: Ref.18; d: Ref.19; e: Ref.20; f: Ref.15; g: Ref.21; h: Ref.7; i: Ref.22.
Binary liquid mixtures of esters and hydrocarbon solvents were prepared by weight covering whole mole fractions range employing a single pan analytical balance (Model K-15 Deluxe, K. Roy Instruments Pvt. Ltd., Vara-nasi) with an uncertainty of ±0.00001 x 10-3 kg. Liquids were injected into sealed glass vials by means of syringe in order to minimize evaporation losses during sample preparation. Densities of samples were measured by single stem pyknometer within ±0.00001 x 103 kg m-3 uncertainty. Times of flow (t) with ±0.01Sec uncertainty and dynamic viscosities (n12) with an uncertainty of ±0.0001 mPa.s for liquids and their binary mixtures were measured employing Tuan and Fuoss viscometer as described elsewhere15. All measurements were carried out at constant temperature at 308.15 ± 0.03 K employing water thermostat with toluene regulator.
Dynamic viscosities (n12) of either component liquids or their binary mixtures were determined by equation
where v and p are the kinematic viscosity and density respectively. a and b are characteristic constants of visco-meter determined by method of least squares using kown viscosities of several liquids viz. cyclohexane, benzene, methylbenzene and propanone at experimental temperature. The constants 'a' and 'b' were 0.004320 and 0.331602 respectively.
3. Results and Discussion
Experimental values of densities (p12) and viscosities (n12) at temperature 308.15 K with mole fractions of non-polar hydrocarbon solvents (x1) for all the binary mixtures studied are recorded in table 3. Deviations of experimental viscosities from the binary mixing rule, An for the binary mixtures are evaluated from equation
An = n,2 - x,n, - x2n
(2)
and also recorded in table 3. n1, n2 and x1, x2 are the viscosities and mole fractions in the mixtures respectively of the components 1 and 2.
Variations of An values with mole fractions of the hydrocarbon solvents for the binary mixtures of methylet-hanoate, ethylethanoate and n-propylethanoate with all the four non-polar hydrocarbon solvents are shown in figs. 1, 2 and 3 respectively.
Figure 1: Deviations in viscosities (An) of binary mixtures of methylethanoate + hydrocarbons (4-cyclohexane, H-benzene, A-1,4-dimethylbenzene, x-1,3,5-trimethylbenzene)versus mole fractions of hydrocarbon (xj) at 308.15 K.
0.06 -i 0.04 -
0.02 -
0.14
Figure 2: Deviations in viscosities (An) of binary mixtures of ethy-lethanoate + hydrocarbons (♦-cyclohexane, H-benzene, A-1,4-di-methylbenzene, x-1,3,5-trimethylbenzene) versus mole fractions of hydrocarbon (x1) at 308.15 K.
0.08 -I-
0.06 -0.04 -
0.02 -
0.12
Figure 3: Deviations in viscosities (Ar]) of binary mixtures of n-propylethanoate + hydrocarbons (♦-cyclohexane, H-benzene, A-1,4-dimethylbenzene, x-1,3,5-trimethylbenzene) versus mole fractions of hydrocarbon (x1) at 308.15 K.
An values for binary mixtures of all the esters with cyclohexane are large and negative. It decreases at lower side of the mole fractions of cyclohexane come to a minimum at around 0.6 mole fraction of cyclohexane in the binary mixture and then increases. Similar observations i.e. large and negative An values are reported for binary mixtures of bromoalkane + cyclohexane15 at 308.15 K and 2-butanone + cyclohexane 23 at 303.15 K. An values for binary mixtures of methylethanoate with three aromatic hydrocarbon solvents viz. benzene, 1,4-dimethylbenzene
and 1,3,5-trimethylbenzene are also negative at all composition and follow the order :
cyclohexane < benzene < 1,3,5-trimethylbenzene <
1,4-dimethylbenzene
In binary mixtures of ethylethanoate with aromatic hydrocarbon solvent, benzene, An values are negative at all composition. However, for binary mixtures of ethylethanoate with either 1,4-dimethylbenzene or 1,3,5-trimethylbenzene, An values are both positive and negative, and both types of values are lesser in magnitude for ethy-lethanoate + 1,4-dimethylbenzene than that for the mixtures of ester + 1,3,5- trimethylbenzene.When n-propyletha-noate is taken as a component for binary mixtures of ester + aromatic hydrocarbon solvents, An values are positive and small at all composition for n-propylethanoate + benzene and negative at all composition except one positive value at lower mole fraction of the hydrocarbon solvents for binary mixtures of n-propylethanoate + 1,3,5-trimethylbenzene, An values for n-propylethanoate + 1,4-di-methylbenzene binary mixture are vanishingly small in magnitude and negative at lower and positive at higher mole fractions of the hydrocarbon.
The smallest values of An for the binary mixtures of all the esters + cyclohexane suggest the presence of weakest unlike interactions between the components. The enhanced values of An in case of the binary mixtures of ester + aromatic hydrocarbon solvents show the presence of strong specific interactions between the components of such mixtures. On the basis of measurements of excess volume and excess Gibb's energy of activation of flow, presence of specific molecular interactions between unlike molecules in binary mixtures of ester + benzene9 is suggested. It is pointed out that specific interaction in mixtures of esters with benzene may be due to the formation of n-n complex between the free electrons of the car-boxylic group and n-electrons of the aromatic ring. Earp and Glasstone24 have observed greater values of molar polarization for binary mixtures of ester + benzene than that for mixtures of ester + cyclohexane and suggested the formation of coordinate link where oxygen atom of the ester acts as a donor and benzene as acceptor. Rastogi et al.25 have suggested that observed excess property is a combination of an interaction and a non-interaction part. Thus,
Ye (observed) = YE (interaction) + YE (size effect)
where YE refers to the excess or deviation in the property. The non-interaction part in the form of the size effect can be comparable to the interaction part and may be sufficient to reverse the trend set by the latter. In the present investigation, importance of size effect is evident in binary mixtures of all the esters with 1, 3, 5-trimethylbenzene where An values are lesser than the binary mixtures of esters with 1,4-dimethylbenzene,although polarisability26 of
the former hydrocarbon is higher than the latter which requires higher interactions in the former case and subsequently An values would have been larger for the former case than for the latter.
The values of An are fitted into second degree Red-lich-Kister polynomial of the type
Ar}IXjX2 = A + B(xrx2) + C(x,-x2)2
(3)
where ,%2 are the mole fractions of the hydrocarbons and ester respectively in the binary mixtures and A, B and C are the constants of the polynomial. The values of these constants and the standard deviations, o for all the mixtures studied in present investigation are recorded in table 2.
for methylethanoate + 1,4-dimethybenzene. The order of d values for methylethanoate + hydrocarbons is similar to that observed for An values.This is quite in line with the suggestion made by Fort et al.28 that d and An values have similar variation with the strength of interactions. Large negative d values for methylethanoate + cyclohexane show the existence of dispersion forces. Higher (lesser negative) d values for methylethanoate + benzene suggest the stronger interactions and still higher (least negative) values for methylethanoate + 1,3,5-trimethybenzene are due to further stronger interactions between the components of the mixture. The d values are positive for mixtures of methylethanoate + 1,4-dimethylbenzene at experimental temperature. This shows that interactions between
Table 2: Values of constants A, B and C of Redlich-Kister equation and standard deviations of deviation in viscosity, ofor different systems at 308.15 K.
System	A	B	C	O m Pa.s
Cyclohexane + Methylethanoate	-0.4421	-0.3454	-0.3537	±0.0220
Benzene + Methylethanoate	-0.1258	+0.0145	+0.0541	±0.0015
1,4-dimethylbenzene+Methylethanoate	-0.0174	+0.0171	-0.0194	±0.0013
1,3,5-trimethylbenzene+Methylethanoate	-0.0785	-0.0101	-0.0513	±0.0009
Cyclohexane + Ethylethanoate	-0.4973	-0.2690	-0.1587	±0.0032
Benzene + Ethylethanoate	-0.1106	-0.0260	-0.0077	±0.0011
1,4-dimethylbenzene+Ethylethanoate	+0.0002	+0.0130	+0.0146	±0.0018
1,3,5-trimethylbenzene+Ethylethanoate	-0.0065	-0.0141	+0.0445	±0.0082
Cyclohexane + n-propylethanoate	-0.4211	-0.2113	+0.0985	±0.0104
Benzene + n-propylethanoate	+0.0088	-0.0127	+0.0222	±0.0016
1,4-dimethylbenzene+n-propylethanoate	-0.0017	+0.0184	+0.0239	±0.0004
1,3,5-trimethylbenzene+n-propylethanoate	-0.0426	-0.0395	+0.0011	±0.0032
Several viscosity equations are critically analyzed with a view to select a suitable equation for the mixtures undertaken in the present investigation. Grunberg and Nissan27 equation for viscosities of liquid mixtures is
In n12 = x. In n, + x2 In n2X,x2 d
(4)
where n12 , n1 & n2 and x1 & x2 are the viscosity of the mixture, viscosities and mole fractions of the components 1 & 2 respectively. d is the interaction parameter which is proportional to WIRT, W being the interchange energy. d may be regarded as an approximate measure of the strength of interaction between the components. It has been suggested28 that variations of d and An are similar with strength of interaction at any given composition. Both are negative for systems in which dispersion forces are dominant. They become less negative and then increasingly positive as the strengths of interactions increase.
Values of d evaluated for all the systems in the present investigation at 308.15 K are recorded in table 3. Perusal of table 3 shows that the d values are large negative for mixtures of methylethanoate + cyclohexane, lesser negative for methylethanoate + benzene, least negative for methylethanoate + 1,3,5-trimethylbenzene and positive
components are strongest in this system amongst the studied binary mixtures with methylethanoate. The lesser d values for mixture of methylethanoate + 1,3,5-trimethylbenzene than that for methylethanoate + 1,4-dimethylben-zene once again show the dominance of size effect over interaction in the former mixture. In binary mixtures of ethylethanoate with cyclohexane, d values are large negative, lesser negative for ethylethanoate + benzene system and positive for mixtures of ethylethanoate with 1,4-dimethylbenzene or 1,3,5-trimethylbenzene systems. For binary mixtures of n-propylethanoate with several hydrocarbon solvents, d values are again large negative for mixtures with cyclohexane, positive for mixtures with benzene,and both, positive and negative values for mixtures with 1, 4-dimethylbenzene and negative for those with 1,3,5-trimethylbenzene. These variations also follow the trend similar to those of An values for the systems.
Hind-McLaughlin-Ubbelohde29 equation for mixture viscosity is
ni2 = xi ni + x2 n2 + 21 x2 H12
(5)
where H12 is the interaction parameter. x1,x2 and n1, n2 are the mole fractions of the components in the mixture and
Table 3: Mole fraction (x1), of hydrocarbons, densities (p12), Viscosities (n12), deviations in viscosities (Ar)), interaction parameters (d), (H12) and (K12), interaction energy (wvis) are excess free energies of activation for viscous flow (G*E) for binary mixtures of different esters + hydrocarbon solvents at 308.15K.
x1	P12 * 103 kg m3	^12 mPa s	ATJ mPa s	d	H12 mPa s	K12	wvis J mol1	G*e J mol1
			Cyclohexane (1) + Methylethanoate (2)					
0.00000	0.91561	0.3470	-	-	-	-	-	-
0.10176	0.88989	0.3470	-0.0423	-0.8758	0.3236	-0.7566	-1938.42	-1.77
0.19971	0.86793	0.3554	-0.0745	-0.8328	0.3217	-0.7153	-1832.54	-2.93
0.30251	0.84792	0.3711	-0.1016	-0.8107	0.3140	-0.6970	-1785.68	-3.77
0.40017	0.83067	0.3913	-0.1219	-0.8114	0.3008	-0.6982	-1788.90	-4.29
0.49683	0.81571	0.4176	-0.1359	-0.8237	0.2831	-0.7117	-1823.41	-4.56
0.60098	0.80211	0.4536	-0.1431	-0.8556	0.2564	-0.7473	-1914.52	-4.59
0.70000	0.79075	0.4986	-0.1393	-0.8987	0.2230	-0.7932	-2032.11	-4.27
0.79112	0.78142	0.5537	-0.1221	-0.9415	0.1854	-0.8370	-2144.31	-3.54
0.89061	0.77293	0.6359	-0.0812	-0.9808	0.1379	-0.8803	-2255.41	-2.20
1.00000	0.76477	0.7626	-	-	-	-	-	-
%Ad = ±0.0003 %AH = ±0.0013 %AK = ±0.0001
Benzene (1) + Methylethanoate (2)
0.00000	0.91561	0.3470	-	-	-	-	-	-
0.10333	0.90885	0.3553	-0.0101	-0.2064	0.3818	-0.1911	-489.67	-0.45
0.20217	0.90220	0.3647	-0.0184	-0.2122	0.3793	-0.1936	-495.89	-0.80
0.30174	0.89597	0.3760	-0.0249	-0.2137	0.3773	-0.1942	-497.63	-1.05
0.40155	0.89124	0.3899	-0.0289	-0.2088	0.3764	-0.1941	-497.32	-1.20
0.49845	0.88577	0.4050	-0.0311	-0.2098	0.3742	-0.1939	-496.87	-1.24
0.59729	0.88135	0.4247	-0.0291	-0.1919	0.3759	-0.1789	-458.42	-1.10
0.69852	0.87656	0.4472	-0.0248	-0.1744	0.3776	-0.1624	-415.10	-0.88
0.79661	0.87279	0.4709	-0.0186	-0.1591	0.3791	-0.1531	-392.20	-0.64
0.89755	0.87093	0.5014	-0.0061	-0.0532	0.4034	-0.0852	-218.36	-0.20
1.00000	0.86302	0.5258	-	-	-	-	-	-
			%Ad = ±0.0001	%AH =	±0.1975 %AK =	±0.0000		
1,4dimethylbenzene (1) + Methylethanoate (2)
0.00000	0.91561	0.3470	-	-	-	-	-	-
0.10315	0.90577	0.3628	-0.0041	-0.0118	0.4213	0.0918	235.09	0.22
0.20182	0.89724	0.3818	-0.0041	0.0400	0.4308	0.1403	359.55	0.58
0.30094	0.88904	0.3980	-0.0071	0.0197	0.4268	0.1189	304.62	0.64
0.39561	0.88195	0.4163	-0.0071	0.0298	0.4287	0.1271	325.69	0.78
0.49725	0.87508	0.4385	-0.0045	0.0564	0.4345	0.1512	387.46	0.97
0.60002	0.86957	0.4605	-0.0023	0.0736	0.4387	0.1621	415.29	0.99
0.69291	0.86425	0.4787	-0.0021	0.0712	0.4385	0.1574	403.15	0.86
0.79307	0.85988	0.4981	-0.0020	0.0648	0.4373	0.1415	362.46	0.59
0.89376	0.85537	0.5177	-0.0019	0.0487	0.4335	0.1110	284.44	0.27
1.00000	0.84878	0.5401	-	-	-	-	-	-
%Ad = ±0.0003% AH = ±0.0001 %AK = ±0.0003
1, 3,5trimethylbenzene (1) + Methylethanoate (2)
0.00000	0.91561	0.3470	-	-	-	-	-	-
0.10375	0.90463	0.3631	-0.0097	-0.1146	0.4196	0.0711	182.25	0.17
0.20201	0.89499	0.3829	-0.0145	-0.0675	0.4269	0.1156	296.14	0.48
0.30079	0.88732	0.4053	-0.0168	-0.0368	0.4319	0.1377	352.68	0.74
0.39898	0.88039	0.4274	-0.0192	-0.0325	0.4318	0.1361	348.60	0.84
0.49755	0.87450	0.4529	-0.0184	-0.0138	0.4351	0.1487	380.90	0.95
0.59872	0.86997	0.4756	-0.0209	-0.0385	0.4284	0.1147	293.81	0.71
0.69588	0.86539	0.5008	-0.0200	-0.0493	0.4246	0.0993	254.46	0.54
0.79113	0.86241	0.5284	-0.0162	-0.0511	0.4228	0.0866	221.93	0.37
0.88838	0.85960	0.5573	-0.0116	-0.0798	0.4134	0.0411	105.22	0.10
1.00000	0.85447	0.5968	-	-	-	-	-	-
			%Ad = ±0.0000	%AH =	±0.0001 %AK =	±0.0004		
x1	p12 x 103 kg m3	mPa s	AT] mPa s	d	H12 mPa s		K12	wvs J mol1	G*e J mol1
0.00000	0.88252	0.3950	Cyclohexane (1) + Ethylethanoate (2)						
0.10463	0.86615	0.3993	-0.0341	-0.6164	0.3970		-0.5759	-1475.41	-1.38
0.20008	0.85151	0.4036	-0.0649	-0.6873	0.3759		-0.6422	-1645.40	-2.63
0.30369	0.83660	0.4144	-0.0922	-0.7170	0.3609		-0.6694	-1715.11	-3.63
0.40048	0.82399	0.4321	-0.1100	-0.7223	0.3497		-0.6748	-1728.87	-4.15
0.49957	0.81191	0.4544	-0.1242	-0.7541	0.3303		-0.7061	-1809.09	-4.52
0.59675	0.80098	0.4862	-0.1281	-0.7675	0.3126		-0.7192	-1842.49	-4.43
0.69868	0.78942	0.5208	-0.1310	-0.8700	0.2675		-0.8152	-2088.50	-4.40
0.79949	0.78061	0.5746	-0.1143	-0.9428	0.2223		-0.8911	-2283.05	-3.66
0.89495	0.77284	0.6468	-0.0772	-1.0166	0.1683		-0.9678	-2479.52	-2.33
1.00000	0.76477	0.7626	-	-	-		-	-	-
			%Ad = ±0.0003	%AH =	±0.0001 %AK =	±0.0000			
0.00000	0.88252	0.3950	Benzene (1) + Ethylethanoate (2)						
0.10020	0.88116	0.3979	-0.0102	-0.2370	0.4037		-0.2379	-609.45	-0.55
0.19794	0.87827	0.4061	-0.0148	-0.1808	0.4140		-0.1713	-438.80	-0.70
0.29588	0.87606	0.4118	-0.0219	-0.2055	0.4080		-0.1949	-499.38	-1.04
0.39660	0.87417	0.4218	-0.0251	-0.1991	0.4081		-0.1893	-485.07	-1.16
0.50010	0.87183	0.4319	-0.0285	-0.2145	0.4034		-0.2033	-520.82	-1.30
0.59110	0.87029	0.4440	-0.0283	-0.2153	0.4019		-0.2050	-525.27	-1.27
0.70227	0.86811	0.4603	-0.0266	-0.2286	0.3969		-0.2177	-557.83	-1.17
0.79038	0.86624	0.4762	-0.0222	-0.2358	0.3935		-0.2228	-570.72	-0.95
0.89202	0.86459	0.4978	-0.0139	-0.2472	0.3884		-0.2337	-598.70	-0.58
1.00000	0.86302	0.5258	-	-	-		-	-	-
			%Ad = ±0.0001	%AH =	±0.0001 %AK =	±0.0001			
0.00000	0.88252	0.3950	1, 4dimethylbenzene (1) + Ethylethanoate (2)						
0.10408	0.87904	0.4106	0.0006	0.0686	0.4707		0.0858	219.74	0.21
0.20239	0.87493	0.4223	-0.0020	0.0230	0.4614		0.0457	116.98	0.19
0.30413	0.87128	0.4373	-0.0018	0.0319	0.4633		0.0543	139.09	0.29
0.40065	0.86821	0.4538	0.0007	0.0565	0.4690		0.0772	197.71	0.47
0.49394	0.86393	0.4672	0.0006	0.0539	0.4687		0.0794	203.44	0.51
0.60558	0.86080	0.4864	0.0036	0.0786	0.4750		0.1013	259.54	0.62
0.69676	0.85818	0.4967	0.0006	0.0529	0.4690		0.0737	188.89	0.40
0.79593	0.85477	0.5105	0.0001	0.0464	0.4676		0.0689	176.39	0.29
0.88762	0.85228	0.5264	0.0026	0.0952	0.4806		0.1145	293.32	0.29
1.00000	0.84878	0.5401	-	-	-		-	-	-
			%Ad = ±0.0004	%AH =	±0.0001 %AK =	±0.0001			
0.00000	0.88252	0.3950	1, 3, 5trimethylbenzene (1) + Ethylethanoate (2)						
0.10355	0.87881	0.4245	0.0086	0.3182	0.5427		0.3802	973.96	0.90
0.19815	0.87434	0.4287	-0.0062	0.0021	0.4763		0.0717	183.73	0.29
0.30053	0.87069	0.4534	-0.0022	0.0670	0.4907		0.1352	346.49	0.73
0.39593	0.86842	0.4685	-0.0064	0.0312	0.4826		0.0943	241.50	0.58
0.49361	0.86525	0.4888	-0.0058	0.0383	0.4844		0.1017	260.62	0.66
0.60022	0.86256	0.5210	0.0049	0.1224	0.5062		0.1841	471.62	1.13
0.69472	0.86064	0.5451	0.0099	0.1677	0.5194		0.2266	580.63	1.23
0.79823	0.85872	0.5613	0.0053	0.1374	0.5123		0.1925	493.08	0.79
0.88565	0.85681	0.5689	-0.0048	0.0050	0.4725		0.0490	125.58	0.13
1.00000	0.85447	0.5968	-	-	-		-	-	-
			%Ad = ±0.0003	%AH =	±0.0001 %AK =	±0.0002			
0.00000	0.87105	0.4958	Cyclohexane (1) + n		i-Propylethanoate (2)				
0.10248	0.86001	0.4950	-0.0281	-0.4973	0.4762		-0.4861	-1245.35	-1.15
0.19888	0.84916	0.4956	-0.0533	-0.5400	0.4621		-0.5250	-1345.03	-2.14
0.29761	0.83625	0.5003	-0.0750	-0.5697	0.4501		-0.5421	-1388.86	-2.90
0.39914	0.82460	0.5086	-0.0937	-0.6103	0.4339		-0.5803	-1486.62	-3.57
x1	p12 x 103 kg m3	mPa s	An mPa s	d	H12 mPa s	K12	wvis J mol1	G*e J mol1
0.49975	0.81585	0.5236	-0.1056	-0.6424	0.4181	-0.6224	-1594.58	-3.99
0.59907	0.80517	0.5453	-0.1104	-0.6776	0.3995	-0.6563	-1681.35	-4.04
0.70004	0.79233	0.5763	-0.1062	-0.7188	0.3762	-0.6828	-1749.32	-3.67
0.79722	0.78512	0.6138	-0.0947	-0.8030	0.3364	-0.7828	-2005.63	-3.24
0.89387	0.77614	0.6722	-0.0621	-0.8489	0.3021	-0.8390	-2149.50	-2.04
1.00000	0.76477	0.7626	-	-	-	-	-	-
			%Ad = ±0.0007	%AH =	±0.0004 %AK =	±0.0000		
Benzene (1) + n-Propylethanoate (2)
0.00000	0.87105	0.4958	-	-	-	-	-	-
0.10878	0.87809	0.5033	0.0042	0.0890	0.5327	0.0292	74.77	0.07
0.20393	0.87682	0.5044	0.0025	0.0321	0.5185	0.0139	35.60	0.06
0.30294	0.87626	0.5070	0.0021	0.0215	0.5158	0.0146	37.45	0.08
0.40286	0.87552	0.5099	0.0019	0.0182	0.5150	0.0166	42.63	0.10
0.50159	0.87475	0.5132	0.0023	0.0201	0.5155	0.0204	52.34	0.13
0.60094	0.87396	0.5180	0.0041	0.0354	0.5195	0.0348	89.27	0.21
0.70145	0.87307	0.5197	0.0029	0.0280	0.5176	0.0231	59.29	0.12
0.80146	0.86530	0.5208	0.0008	0.0133	0.5138	0.0462	118.23	0.19
0.89719	0.86448	0.5236	0.0009	0.0200	0.5156	0.0507	129.77	0.12
1.00000	0.86302	0.5258	-	-	-	-	-	-
			%Ad = ±0.0130	%AH =	±0.0001 %AK =	±0.0012		
1,4dimethylbenzene (1) + n-Propylethanoate (2)
0.00000	0.87105	0.4958	-	-	-	-	-	-
0.10242	0.87012	0.5001	-0.0003	-0.0014	0.5167	-0.0179	-45.87	-0.04
0.20099	0.86810	0.5046	-0.0002	-0.0024	0.5176	-0.0081	-20.75	-0.03
0.30236	0.86523	0.5078	-0.0014	-0.0093	0.5146	-0.0139	-35.61	-0.08
0.40210	0.86305	0.5122	0.0014	-0.0078	0.5150	-0.0120	-30.68	-0.07
0.49886	0.86100	0.5174	0.0006	-0.0002	0.5170	-0.0047	-12.08	0.00
0.60032	0.85882	0.5234	0.0010	0.0117	0.5201	0.0065	16.76	0.04
0.69962	0.85607	0.5288	0.0020	0.0217	0.5227	0.0188	48.15	0.10
0.79703	0.85394	0.5335	0.0024	0.0314	0.5253	0.0272	69.60	0.11
0.89420	0.85169	0.5381	0.0027	0.0565	0.5322	0.0501	128.25	0.12
1.00000	0.84878	0.5401	-	-	-	-	-	-
			%Ad = ±0.0038	%AH =	±0.0000 %AK =	±0.0021		
1, 3,5trimethylbenzene (1) + npropylethanoate (2)
0.00000	0.87105	0.4958	-	-	-	-	-	-
0.10218	0.86930	0.5078	0.0016	0.0542	0.5555	0.0686	175.74	0.16
0.19832	0.86660	0.5086	-0.0073	-0.0710	0.5236	-0.0490	-125.64	-0.20
0.30194	0.86437	0.5175	-0.0089	-0.0624	0.5254	-0.0399	-102.11	-0.22
0.39689	0.86259	0.5265	-0.0094	-0.0564	0.5267	-0.0341	-87.48	-0.21
0.49766	0.86090	0.5363	-0.0098	-0.0550	0.5268	-0.0331	-84.90	-0.21
0.59783	0.85951	0.5462	-0.0100	-0.0584	0.5255	-0.0376	-96.29	-0.23
0.69925	0.85810	0.5581	-0.0083	-0.0537	0.5265	-0.0334	-85.49	-0.18
0.79367	0.85631	0.5661	-0.0098	-0.0889	0.5162	-0.0650	-166.55	-0.27
0.89187	0.85505	0.5772	-0.0087	-0.1384	0.5013	-0.1112	-284.97	-0.28
1.00000	0.85447	0.5968	-	-	-	-	-	-
			%Ad = ±0.0017	%AH =	±0.0000 %AK =	±0.0012		
viscosities of the pure components respectively. The experimental n12 values in the present investigation are used to evaluate values of H12 for all the systems and are reported in table 3. H12 values are positive for all the binary mixtures studied. The H12 values at any composition for mixtures of methylethanoate + hydrocarbon solvents follow the order:
cyclohexane < benzene < 1,3,5-trimethylbenzene < 1,4-dimethylbenzene
which is again similar to those of An and d values. For binary mixtures of ethylethanoate + hydrocarbons and n-propylethanoate + hydrocarbons H12 values also follow the trend of their d and An values. For a common hydrocarbon solvent, H12 values for binary mixtures with different esters follow the trend:
methylethanoate < ethylethanoate < n-propylethanoate
which is the order of the gas phase dipole moments30 of the esters.
Katti and Chaudhri 31 equation for mixture viscosities is
In n12V12 = x1 In tfjVj + x2 In n2V2 + x1 x2 K12
(6)
where K12 = wvisc/RT, wvisc is the interaction energy term. R and T are gas constant and temperature respectively. V1,V2 are the molar volume of the components 1 and 2 and V12 is the molar volume of the mixture given by
V12 = (XjM1 + X2M2 )pi2
(7)
M1 & M2 and p12 are molecular weights of the components 1 & 2 respectively and density of the mixture. The interaction parameter, K12 and interaction energy wvisc evaluated by equation (6) for all the systems are recorded in table 3. Table 3 shows that K12 values are negative for binary mixtures of methylethanoate and ethylethanoate with either cyclohexane or benzene and positive with 1,4-dimethyl-benzene and 1,3,5-trimethylbenzene at all composition. K12 values for binary mixtures of n-propylethanoate + cyclohexane are negative and of n-propylethanoate + benzene are positive at all compositions. These values are positive as well as negative for the mixtures of n-propyletha-noate + 1,4-dimethylbenzene and n-propylethanoate + 1,3,5-trimethylbenzene at experimental temperature. The values of wvisc have the similar sign as that of K12 for the binary systems. For a common ester wvisc values for binary mixtures with several hydrocarbon solvents have trend similar to d values. This is expected due to logarithmic nature of equations for both d and wvisc.
Excess free energies of activation for viscous flow G*E are evaluated by equation
G*e = RT [In n12V12 -x1 In n1V1 - x2 In n2V2] (8)
and the values are reported in table 3. The magnitude and sign of G*E for each system have similar order as those of wvis. The values of G*E are negative for binary mixtures of all the ethanoates with cyclohexane for whole mole fraction range. The G*E values increase when cyclohexane is replaced with benzene in the binary mixture. These values are less negative for mixtures of methyl and ethylethanoa-tes with benzene and are positive for the mixtures of n-propylethanoate + benzene for the whole mole fraction range. Binary mixtures of methyl and ethylethanoates with 1,4-dimethylbenzene and 1,3,5-trimethylbenzene have positive G*E values for the whole mole fraction range while mixtures of n-propylethanoate with 1,4-dimethyl-benzene and 1,3,5-trimethylbenzene have positive except one negative for the former and negative except one positive G*E values for the latter hydrocarbon.It has been suggested32 that values of G*E may be attributed to large size and cohesive energy difference between the two unlike
components. Palepu et al. have suggested that positive values of G*E may be considered as a reliable guide to the presence of interaction between the molecules. It may be noted that all the interaction parameters viz. d, H12 and K12 vary with composition of the mixture.
In order to test the suitability of several viscosity equations, percentages of deviation of the interaction parameters evaluated on the basis of equations (4), (5) and (6) for each binary mixtures are evaluated and reported in table 3 below the column of the parameter. The viscosity equation, which gives least value of average percentage of deviation of interaction parameter, will be the most suitable equation for these binary mixtures. Table 3 reveals that none of the equations gives least values of percentage average deviation for all the systems studied. Grunberg-Nis-san equation, Katti-Chaudhri equation and Hind-Mc-Laughlin-Ubbelhode viscosity equation give least values of percentage average deviations for two, five and six systems respectively. Thus it may be concluded that the latter equation is most suitable for the viscosities of binary mixtures between alkylethanoates and hydrocarbon solvents.
4. Conclusions
Viscosity measurements on binary mixtures of esters + benzene, + 1,4-dimethylbenzene and 1,3,5-trimethylbenzene is suitable for molecular interactions studies. An values are large and negative for binary mixture of ester + cyclohexane and negative values reduce (An values increase) for binary mixture of esters + aromatic hydrocarbons. Hind-McLaughlin-Ubbelohde viscosity equation is most suitable for the study of binary mixtures.
5. Acknowledgements
The authors are thankful to the Head, Department of Chemistry, D. D. U. Gorakhpur University for providing laboratory facilities and to the U.G.C., New Delhi for the financial assistance.
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Povzetek
Dvanajstim binarnim mešanicam z metiletanoatom, etiletanoatom in ra-propiletanoatom z nepolarnimi topili (ciklohek-san, benzen, 1,4-dimetilbenzen and 1,3,5-trimetilbenzen) smo pri 308.15 K izmerili viskoznost s (n12) in gostoto (p12) v celotnem koncentracijskem območju. Viskoznost mešanic narašča z naraščajočim molskim deležem nepolarnega topila, odstopanja od idealnih vrednosti, An, pa so negativna za vse preiskovane mešanice, kar kaže na močne medmolekulske sile, ki smo jih obravnavali s pomočjo Grunberg-Nissanovega inetrakcijskega parametra.