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## Brazilian Journal of Chemical Engineering

##
*Print version* ISSN 0104-6632*On-line version* ISSN 1678-4383

### Braz. J. Chem. Eng. vol.17 n.4-7 São Paulo Dec. 2000

#### http://dx.doi.org/10.1590/S0104-66322000000400011

**VISCOSITIES AND EXCESS ENERGY OF ACTIVATION FOR VISCOUS FLOW FOR BINARY MIXTURES OF TETRAHYDROFURAN WITH 1-BUTANOL, 2-BUTANOL AND 1-CHLOROBUTANE AT 283.15, 298.15 AND 313.15 K**

**A.Mariano ^{2+}, A.Camacho^{2}, M.Postigo^{2*}, A.Valen^{1}, **

H.Artigas^{1}, F.M.Royo^{1} and J.S.Urieta^{1}

^{ }

^{1}Departamento de Química Orgánica y Química Física, Facultad de Ciencias,

Universidad de Zaragoza, Ciudad Universitaria, Zaragoza 50009, España.

E-mail: urieta@posta.unizar.es

^{*}CONICET member,

^{ +}CONICET scholarship,

^{ 2}Cátedra de Fisicoquímica, Dpto.

de Química, Facultad de Ingeniería, Universidad Nacional del Comahue,

Tel.: 54 299 449 0340, Fax: 54 299 448 8306, Buenos Aires 1400,

Neuquén 8300, Argentina.

E-mail: postigo@uncoma.edu.ar

*(Received: October 10, 1999 ; Accepted: April 6, 2000)*

Abstract- Kinematic viscosities of binary mixtures composed of tetrahydrofuran with 1-butanol, 2-butanol and 1-chlorobutane have been measured at 283.15, 298.15 and 313.15 K and atmospheric pressure for the whole range of compositions. The dynamic viscosity, the excess viscosity and the excess energy of activation for viscous flow were also calculated. The excess viscosity shows negative deviations from ideal behavior for the mixtures tetrahydrofuran with 1-butanol and 2-butanol and a small positive deviation for the binary tetrahydrofuran + 1-chlorobutane system. The experimental results have also been used to test some empirical and semiempirical equations adopted previously to correlate viscosity – composition data.

Keywords: viscosities, excess viscosities, tetrahydrofuran, 1-butanol, 2-butanol, 1-chlorobutane.

**INTRODUCTION**

Experimental viscosities provide information on the structure of liquids and are required in the design of processes which involve mass transfer, fluid flow, etc. This has motivated the development of an extensive and varied range of empirical and semiempirical equations to represent the viscosity – composition data of liquid mixtures. A large portion of these equations has been revised and classified by Monnery et al. (1995). Different approaches have been suggested for the problem of predicting viscosity of mixtures. Among these the group contribution methods seem to be particularly promising. The development of group contribution method requires that an adequate data base should be made available. The data base must consist of a sufficient number of systems containing all the chemical functional groups taken into account in the operating domain of the method.

In continuation of the our investigative work on the viscosity of binary and ternary mixtures (García and Postigo 1997, Dominguez et al. 1998, Mariano et al. 1999) and as a contribution to the development of the above mentioned data base, this paper reports experimental viscosity data at atmospheric pressure and 283.15, 298.15 and 313.15 K for the binary mixtures: tetrahydrofuran + 1-butanol, tetrahydrofuran + 2-butanol and tetrahydrofuran + 1-chlorobutane. To our knowledge, there is no viscosity data reported in the literature for these mixtures.

**EXPERIMENTAL**

The chemicals used in the present study were tetrahydrofuran (better than 99,5 mol%), 1-butanol (better than 99,8 mol%), 2-butanol (better than 99,5 mol%) obtained from Merk, and 1-chlorobutane (better than 99,5 mol%) provided by Fluka. All liquids were used without further purification. However, they were stored over molecular sieves (Union Carbide 0.4 nm, Fluka) for several days and degassed just before use.

The methods used in our laboratory have been described previously [Lafuente et al*.* 1996, Camacho y Postigo 1998]. Densities were determined with a vibrating tube densimeter Mettler, model DA 310 A, with temperature automatically controlled at 0.01^{ }K. Calibration was done with air and doubly distilled water with a precision of 10^{-2 }kg m^{-3}. Viscosities of the pure liquids and of the mixtures were determined with a viscosimeter Schott-Gerate, model AVS 440, using Ubbelhode viscosimeters thermostated at 0.01^{ }K. The estimated error was less than 0.005 mPa s.

Mixtures were prepared by mixing weighed amounts of the pure liquids using a Sartorius balance. Caution was taken to prevent evaporation.

**RESULTS AND DISCUSSION**

The experimental results for the pure liquids are reported in Table I together with literature values for comparison.

From the viscosity and density measurements the excess viscosities, h^{E}, and the excess energy of activation for viscous flow, DG^{*E}, were calculated using the expressions (Matos et al., 1996, Delmas et al., 1975):

(1) |

where h_{1} and h_{2} are the viscosities of the components, x_{1 }and x_{2} are the mole fraction and h the viscosity of the mixture, and

(2) |

where R is the universal constant for gases, T the absolute temperature and V, V_{1} and V_{2} represent the molar volumes of the solutions and of the pure components respectively.

The experimental results obtained for the three binary systems at the three temperatures are listed in Table II.

Each set of the results, h^{E} and DG^{*E}, was fitted with the polynomial of the type:

(3) |

where X^{E} represents h^{E} or DG^{*E}, x_{i} and x_{j} are the mole fractions of components i, j, a_{k} are the adjustable parameters and n is the number of parameters.

The method of least squares was used to determine the values of the coefficients a_{k}. In each case, the optimum number of coefficients was ascertained from an examination of the standard deviation, *s*, of the estimate with n:

(4) |

were X^{E}_{Exp.} and X^{E}_{Calc.} represents h^{E} or DG^{*E} experimental and calculated with Eq. 3 respectively, n_{Exp.} is the number of experimental data and n is the number of parameters. The values of the parameters, a_{k, }along with the standard deviation, *s*, are given in Table III for three mixtures studied here.

Figures 1, 3 and 5 show the variation with the composition of excess viscosity for the mixtures tetrahydrofuran + 1-butanol, tetrahydrofuran + 2-butanol and tetrahydrofuran + 1-chlorobutane, respectively at the temperature of 283.15 K, 298.15 K and 313.15 K.

Excess viscosities are negative over the entire composition range at the three temperature for the systems tetrahydrofuran + 1-butanol and tetrahydrofuran + 2-butanol, the absolute minimum excess viscosities values at the three temperatures follow the sequence 1-butanol < 2-butanol. Minimun excess viscosities values are shifted towards lower concentrations of tetrahydrofuran. When temperature increase the excess viscosities decrease in absolute value in such a way that mixtures with 1-butanol show the lowest decrease. The viscosity behavior of these mixtures is mainly due to changes in the liquid associated structures of butanols.

The tetrahydrofuran + 1-chlorobutane shows very small positive values of excess viscosity, indicating that the interactions are very small in this mixtures, nearly to an ideal system.

Figures 2, 4 and 6 show the excess energy of activation for viscous flow versus the composition of the first component at the temperature of 283.15 K, 298.15 K and 313.15 K for the mixtures tetrahydrofuran + 1-butanol, tetrahydrofuran + 2-butanol and tetrahydrofuran + 1-chlorobutane, respectively. The excess energy of activation for viscous flow are negative over the entire composition range at the three temperature for the systems, tetrahydrofuran + 1-butanol and tetrahydrofuran + 2-butanol. The tetrahydrofuran + 1-chlorobutane shows small positive values at all temperatures.

From the different expressions existing in the literature, the following equations relating viscosities of binary mixtures as a function of those of the pure components were selected:

McAllister (1960) (for three body interactions):

(5) |

where: |

In the above equations M_{i} and n_{i} are the molecular mass and the kinematic viscosity of the ith component, respectively. n_{12} and n_{21} are adjustable parameters. M is the mean molecular mass of the mixture computed as M = x_{1} M_{1} + x_{2} M_{2}.

Katti and Chaudri (1964):

(6) |

where W_{vis} is the interaction parameter.

Grumberg and Nissam (1949):

(7) |

where d is an interaction parameter that is a function of the nature of the components and temperature. This parameter has been regarded as a measure of the strength of the interaction between the components.

The values of the adjustable parameters, from Eqs. 5 to 7, were obtained by fit to the viscosity data and are given in Table IV along with average deviation between experimental and calculates viscosities.

**CONCLUSIONS**

We report experimental viscosity data at atmospheric pressure and 283.15, 298.15 and 313.15 K for the binary mixtures: tetrahydrofuran + 1-butanol, tetrahydrofuran + 2-butanol and tetrahydrofuran + 1-chlorobutane. The mixtures tetrahydrofuran with butanols show significant negative excess viscosity, probably, due to changes in the liquid associated structures of alkanols. The tetrahydrofuran + 1-chlorobutane shows small positive values of excess viscosity at the three temperatures indicating a nearly ideal behaviour. From the different equations applied to correlate viscosity – composition data, the McAllister (1960) model is the best for the all mixtures studied in this work.

**ACKNOWLEDGMENT**

The authors are grateful for financial assistance from Universidad de Zaragoza and Universidad Nacional del Comahue.

**List of Symbols**

a_{k} | adjustable parameter, Eq. 3. |

d | interaction parameter, Eq. 7. |

G^{*E} | excess activation energy of viscous flow, J mol^{-1}. |

M | mean molecular mass of the mixture. |

M_{i} | molecular mass of the ith component. |

R | gas constant, 8.314 J mol^{-1} K^{-1}. |

s | standard deviation, defined by Eq. 4. |

T | absolute temperature, K. |

V | molar volumes of the solutions, m^{3} mol^{-1}. |

V_{i} | molar volumes of the pure components i, m^{3} mol^{-1}. |

W_{vis} | interaction parameter, Eq. 6. |

x_{i} | mole fraction of component i in the liquid. |

X^{E} | represents h^{E} or DG^{*E}. |

**Greek letters**

h | viscosity of the mixture, mPa s. |

h^{E} | excess viscosity, mPa s. |

h_{i} | dynamic viscosity of the component i, mPa s. |

n_{i} | kinematic viscosity of the component i, m^{2} s^{-1}. |

n_{12 }and n_{21 } | interaction parameter, Eq. 5. |

**Subscripts**

Calc. | Calculated value. |

Exp. | Experimental value. |

i, j | Component i, j in a mixture. |

**Superscripts**

E | Excess. |

**REFERENCES**

Camacho, A. and Postigo, M., Molar, partial molar excess volumes of benzene with methyl esters at 25ºC, J. Solution Chem. 27(8), 719 (1998). [ Links ]

Delmas, G., Purves, P. and de Saint-Romain, P., Viscosities of mixturesof branched and normal alkanes with tetrabutyltin. Effect of the orientational order of long-chain alkanes on the entropy of mixing. J. Phys. Chem. 79, 1970-1974 (1975). [ Links ]

Domínguez, M., Santafé, J., López, M. C., Royo, F. M. and Urieta, J. S., Viscosities of the ternary mixture (1-butanol + n-hexane + 1-chlorobutane) at 298.15 K and 313.15 K, Fluid Phase Equilibria152, 133-148 (1998). [ Links ]

García, D. A. and Postigo, M. A., Excess molar volumes of tetrhydrofuran + 1,4 dioxane and tetrhydrofuran + tetrachloroethene systems between 293.15 K and 313.15 K, Latin American Applied Research 22, 207-213 (1992). [ Links ]

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Grumberg, L. and Nissan, A. H., Mixture law for viscosity. Nature 164, 799-800 (1949). [ Links ]

Katti, P. K. and Chaudri M. M., Viscosities of binary mixtures of benzyl acetate with dioxane, aniline, and m-cresol. J Chem Eng Data 9(3), 442-443 (1964). [ Links ]

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*To whom correspondence should be addressed