Viscosity and Excess Viscosity for Associated Binary ... · Viscosity and Excess Viscosity for Associated Binary Mixtures at T= (298.15, 308.15 and 318.15) Arun K.Singh, ... Viscosities
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Viscosity and Excess Viscosity for Associated Binary Mixtures at T= (298.15,
308.15 and 318.15)
Arun K.Singh, Brajesh Kumar and Rajeev K.Shukla*
Associate Professor, Department of Chemistry, V.S.S.D.College, Kanpur-208002., India.
Association properties are usually evaluated using the deviation from the result that would be expected if the properties of the
components were treated in an additive manner. The RA model, which assumes linearity of acoustic impedance with the amount-of-
substance fraction of components, was used to derive a model that was corrected [9] and tested [21] to predict the behavior of each mixture with association between the components. The calculations were performed using a computer program, and the parameters
were adjusted either automatically or manually. The association constant (Kas) and ηA,B were used as the fitted parameters, where ηA,B
is the acoustic velocity in a hypothetical pure liquid with only the species AB formed by association of the components A and B.
When the parameters are changed, the equilibrium concentrations of the species [A], [B], and [AB] will change and this could affect
the viscosity. The differences between experimental and theoretical viscosity values were used to obtain sum of squares for the
deviation. It was assumed that three species (A, B, and AB) were present in solution instead of only two (A and B) because of
formation of the AB species by association after mixing. The acoustic velocity in the pure associate could be treated as a fitted one
with a value of Kas.
Thermal expansion coefficient () and isothermal compressibility (βT) values for the Flory model were obtained using an established
equation, which has been tested on many mixtures [22]. The mixing function () can be represented mathematically by the Redlich-
Kister polynomial [13] for correlating experimental data:
i
i
p
ii xAxxy )12()1( 1
01
(24)
where y is the change in viscosity (∆η ), xi is the amount-of-substance fraction, and Ai is the coefficient. The values of the coefficients
are summarized along with the standard deviations between the experimental and fitted values of the respective function (Table 1). For
the dynamic viscosity, the range was 0.005-0.011.
Table 1 Coefficients of Redlich- Kister Polynomial and Standard Deviation (σ) for Viscosity of Binary Liquid Mixtures at Various
Temperatures
2-Propenol+2-Phenylethnol
T/K A0 A1 A2 A3
Std dev.
(σ)
298.15 -5.35 0.81 -0.44 -0.81 0.008
308.15 -3.49 0.34 0.02 -0.19 0.009
318.15 -2.00 0.09 0.17 -0.19 0.011
McAllister coefficients a, b and c were calculated and standard deviations between the calculated and experimental values were
determined (Table 2)
Table 2 Parameters of McAllister three body and four Body Interaction Models and Standard Deviation (δ) for Viscosity of Binary
Figure 1 Changes in the excess viscosity (ηE) with the amount-of-substance fraction (x1) for 2-propanol + (1–x) 2-phenylethanol at
298.15, 308.15 and 318.15 K. Results were obtained using the following models: black diamond, Flory model, black square,
Ramaswamy and Anbananthan model, and black triangle, model suggested by Glinski
In all the cases, the association models showed lower changes in the excess viscosity than the non-association model (i.e. Flory
model). The RA model gave better results than the model suggested by Glinski. The trends observed in all the figures were similar and
showed negative changes with increasing temperature, which indicates stronger interactions between the liquid molecules at higher
temperatures. Excess viscosity, E values are negative over the entire mole fraction range for all three binary mixtures. The results of
excess viscosity at other temperatures follow the same trends. The values of E increases from T= 298.15K to T=318.15K for all these
binary systems.
Conclusion:
Models assuming association give more reliable results than those assuming non-association. Association models can be helpful for
determining how components in a mixture associate. This can be achieved using the viscosity in a hypothetical pure component and
the observed dependence of concentration on the composition of a mixture.
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Table 4 Experimental Density, Experimental Viscosity, Theoretical Viscosity from Flory Model, Ramaswami and Anbananthan Model (RS),Model Devised by Glinski,
McAllister 3 body (McA-3) and McAllister 4 body (McA-4) models and their Percent deviations for Binary Liquid Systems at various temperatures