The densities and viscosities of 2bromopropanemethanol binary mixtures had been determined using an digital vibrating Utube densimeter and Ubbelohde capillary viscometer respectively from (298.15 to 318.15) K. The dependence of densities and viscosities on temperature and concentration had been correlated. The excess molar volume and the excess viscosity of the binary system were calculated from the experimental density and viscosity data. The excess molar volumes were related to compositions by polynomial regression and regression parameters and total RMSD deviations were obtained; the excess viscosities was related to compositions by RedlichKister equation and regression coefficients and total RMSD deviation of the excess viscosity for 2bromopropane and methanol binary system were obtained. The results showed that the model agreed very well with the experimental data.
INTRODUCTION
Isopropyl mercaptan is an important pharmaceutical intermediate and chemical material with wide use and optimum application prospect. Li
et al
.
1
have developed a new technique for the synthesis of isopropyl mercaptan using NaHS and 2bromopropane as the raw material and methanol as the solvents.
1
,
2
This new technique is characterized by mild reaction conditions, high product purity and reduced waste. In the synthesis and purification process of isopropyl mercaptan, it is useful to know the basic data of densities and viscosities and so on of 2bromopropane in methanol. The densities and viscosities are basic data used in chemical engineering designs, process optimization, and molecular thermodynamics study of solution. Therefore, in this study, densities and viscosities of 2bromopropane in methanol had been measured at temperature from (298.15 to 318.15) K. From measurements of densities and viscosities, the excess molar volumes and the excess viscosities of 2bromopropane in methanol were calculated. Results were fit to obtain the adjustable parameters and the deviations between the measured and fitted values. These quantities could be used to study the molecular interactions among the components of the mixture.
EXPERIMENTAL SECTION
 Materials
2bromopropane and methanol were of AR grade and they were obtained from Shanghai Chemical Reagent Co. and had mass fraction purities of 0.995. The water used in the experiments was deionized. The conductivity was less than 1 × 10
^{4}
S·m
^{1}
.
 Measurements of Densities
The densities of the mixtures and the corresponding pure substances were measured with an Anton Paar Model DMA 5000 digital vibrating Utube densimeter, provided with automatic viscosity correction, having a stated accuracy of ± 5 × 10
^{6}
g·cm
^{3}
. The temperature in the cell was regulated to ± 0.001 K with a builtin solidstate thermostat. The temperature in the cell was measured by means of two integrated Pt 100 platinum thermometers, and the stability was better then ± 0.002 K. The reliability of the apparatus was verified daily with dry air and distilled freshly degassed water. To minimize the errors in composition, all mixtures were prepared by mass using the cell and the procedure described previously
3
and a Mettler AG 204 balance with a precision of 1 × 10
^{4}
g. 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 uncertainty in density was about ± 1 × 10
^{5}
g·cm
^{3}
.
 Measurements of Viscosities
Viscosity was measured using a commercial Ubbelohde capillary viscometer (type 1836A, Shanghai Glass Instruments Factory, China) of 0.55 mm diameter, calibrated with doubledistilled water at (298.15 and 313.15) K. A thoroughly cleaned and perfectly dried viscometer, filled with experimental solutions, was placed exactly vertical in an insulated jacket, wherein constant temperature (± 0.02 K) was maintained by circulating water from a thermoelectric controller (type 501, Shanghai Laboratory Instrument Works Co., Ltd.) at the required temperature. After thermal stability was attained, the flow times of the solutions were recorded with an electronic digital stopwatch correct to ± 0.01 s. At least five repetitions of each datum point obtained were reproducible to ± 0.06 s, and the results were averaged. Because all flow times were greater than 200 s and the capillary diameter (0.55 mm) was far less than its length (100 mm), the kinetic energy and end corrections, respectively, were found to be negligible. The viscosity was then calculated from the relationship
4
where η,
ρ
,
t
and η
_{w}
,
ρ
_{w}
,
t
_{w}
are the viscosity, density, and flow time of the mixture and water respectively come from the literature.
5
The uncertainty in the viscosity measurement is estimated to be ± 0.6%.
 Experiment Reliability Proof
The measure densities and viscosities of 2bromopropane and methanol at 313.15 K had been compared with literature values. The results were listed in
1
. It could be seen that our experimental values of densities and viscosities were in good agreement with those reported in the literature.
6
Densities and Viscosities of 2bromopropane and Methanol at 313.15 K
Densities and Viscosities of 2bromopropane and Methanol at 313.15 K
RESULTS AND DISCUSSION
The experimental densities at various temperatures as a function of mole fraction for 2bromopropane in methanol were presented in
2
,
. 1
and
. 2
. It could be seen from
2
and
. 1
that densities decreased with increasing temperature at a definite concentration of 2bromopropane in methanol and increased with increasing concentration of 2bromopropane in methanol at constant temperature. From
. 2
, it could be found that densities and temperature gave the straight linear relationship.
Experimental Densities ρ/g․cm3of 2bromopropane in Methanol as a Function of Mole Fraction from T = (298.15 to 313.15 K)
Experimental Densities ρ/g․cm^{3} of 2bromopropane in Methanol as a Function of Mole Fraction from T = (298.15 to 313.15 K)
Density of 2bromopropane in methanol at various temperatures. ■, 298.15 K; ●, 303.15 K; ▲, 308.15 K; ▼, 313.15 K; ◆, 318.15 K; —, calculated.
Relative changes in density of 2bromopropane in methanol on temperature at different mole fraction. ■, 0.0; □, 0.1; ●, 0.2; ○, 0.3; ▲, 0.4; △, 0.5; ▼, 0.6; ▽, 0.7; ◆, 0.8; ◇, 0.9; ★, 1.0.
Viscosity of 2bromopropane in methanol at various temperatures. ■, 298.15 K; ●, 303.15 K; ▲, 308.15 K; ▼, 313.15 K; ◆, 318.15 K; —, calculated.
Relative changes in viscosity of 2bromopropane in methanol on temperature at different mole fraction. ■, 0.0; □, 0.1; ●, 0.2; ○, 0.3; ▲, 0.4; △, 0.5; ▼, 0.6; ▽, 0.7; ◆, 0.8; ◇, 0.9; ★, 1.0.
The experimental viscosities at various temperatures as a function of mole fraction for 2bromopropane in methanol were presented in
3
and
. 3
and
. 4
. It could be found from
3
and
. 3
that viscosities decreased with increasing temperature at a definite concentration of 2bromopropane in methanol, and decreased with increasing concentration of 2bromopropane in methanol at constant temperature, reached a minimum value at about x = ~ 0.6 and then increased. The temperature influenced strongly the viscosity but the compositions for the minimum in viscosity were found to be almost constant and independent of temperature. From
. 4
it could be found that viscosities and temperature gave the straight linear relationship.
Experimental Viscosities η/mPa․s of 2Bromopropane in Methanol as a Function of Mole Fraction from T = (298.15 to 313.15 K)
Experimental Viscosities η/mPa․s of 2Bromopropane in Methanol as a Function of Mole Fraction from T = (298.15 to 313.15 K)
 Correlation of Density
The dependence of density on temperature and concentration were calculated from the equation 2.
7
where,
x
represents mole fraction of 2bromopropane,
ρ
is the density of the mixtures,
T
is the absolute temperature; and
a
_{0}

a
_{5}
are regression coefficients. The calculated values and deviations were listed in
4
. Densities were calculated according to eq 2 using values for parameters
a
_{0}

a
_{5}
that were listed in
5
. Some calculated results could be seen in
. 1
.
The rootmeansquare deviation is defined by.
8
Where
N
is the number of experimental points,
ρ
_{ci}
represents the densities calculated from equations, and
ρ
_{i}
represents the experimental density values.
The relative average deviations (RAD) is defined as,
8
From comparison of the calculated and experimental values, the total RMSD and average relative deviations (RAD) of 55 data points were less than 2% and 0.1%, respectively. It was clear that eq 2 could be successfully used to correlate densities of methanol2bromopropane binary mixtures.
Regression coefficient and deviation of densities and viscosities for the methanol2bromopropane binary system
Regression coefficient and deviation of densities and viscosities for the methanol2bromopropane binary system
Regression coefficients of densities and viscosities for the methanol2bromopropane binary system
Regression coefficients of densities and viscosities for the methanol2bromopropane binary system
 Excess Molar Volumes and Excess Viscosities
The excess molar volumes V
^{E}
and the excess viscosities were calculated from the equation 6, 7, respectively.
7
where,
x
_{1}
and
x
_{2}
represent mole fraction of 2bromopropane and methanol, respectively, and M
_{1}
and M
_{2}
represent molar masses of 2bromopropane and methanol, respectively,
ρ
_{12}
,
ρ
_{1}
and
ρ
_{2}
are the densities of the mixtures, or 2bromopropane and methanol, respectively.
where, η
_{12}
is the viscosity of the mixture; η
_{1}
and η
_{2}
is the viscosity of 2bromopropane and methanol, respectively.
The excess molar volume (
V
^{E}
) calculated from the density data was listed in
6
. The excess molar volume over the entire range of mole fraction x and temperature range between (298.15 and 318.15) K were plotted in
. 5
. It could be seen that the values of the excess molar volume (
V
^{E}
) were found to be positive and a great temperature effect for the whole concentration was found. The excess molar volume maximum was found to be almost temperature independent at x = ~ 0.4. The excess molar volume represented the difference in molar specific value for 2bromopropane and methanol, if the value was large, it indicated that there was a volume contraction in the system and also indicated that 2bromopropane and methanol were completely miscible system.
Excess Molar Volumes of 2Bromopropanemethanol
Excess Molar Volumes of 2Bromopropanemethanol
Excess molar volume for 2bromopropane and methanol for whole range of mole fractions at different temperatures. ■, 298.15 K; ●, 303.15 K; ▲, 308.15 K; ▼, 313.15 K; ◆, 318.15 K; —, calculated.
The excess viscosities calculated from the viscosity data was listed in
7
. The excess viscosities over the entire range of mole fraction x and temperature range between (298.15 and 318.15) K were plotted in
. 6
. It could be seen that the values of the excess viscosities were found to be negative, and the excess viscosities decreased with increasing concentration, reached a minimum value at about x = ~ 0.5 and then increased. Increasing temperature decreased the value of the excess viscosities at a definite concentration 2bromopropane in methanol of for 2bromopropane and methanol binary system, but the composition for the minimum value was almost constant.
The excess molar volume (
V
^{E}
) was correlated by the equation 8,
7
where,
A
^{'}
_{0}
,
A
^{'}
_{1}
,
A
^{'}
_{2}
and
A
^{'}
_{3}
are equation parameters;
x
is mole fraction of 2bromopropane.
Excess viscosity for 2bromopropane and methanol for whole range of mole fractions at different temperatures. ■, 298.15 K; ●, 303.15 K; ▲, 308.15 K; ▼, 313.15 K; ◆, 318.15 K; —, calculated.
Excess Viscosities of 2Bromopropane  methanol
Excess Viscosities of 2Bromopropane  methanol
Regression coefficients and deviation of the excess volume for 2bromopropane and methanol binary system
Regression coefficients and deviation of the excess volume for 2bromopropane and methanol binary system
Regression coefficients and deviation of the excess viscosity for 2bromopropane and methanol binary system
Regression coefficients and deviation of the excess viscosity for 2bromopropane and methanol binary system
The excess properties indicate the departure from the ideal condition and can be correlated by the RedlichKister equation,
7
where,
x
_{1}
and
x
_{2}
is mole fraction of 2bromopropane and solvent.
B
^{'}
_{i}
is the optimum values for the RedlichKister coefficients.
The optimum values for polynomial regression coefficients (
A
^{'}
_{i}
) and the RedlichKister coefficients (
B
^{'}
_{i}
) were obtained respectively by fitting experimental data at various temperature and concentration, the regression coefficients of the excess volume and the excess viscosity along with their deviation were listed in
8
and
9
, respectively. Some results could be seen in
. 5
and
. 6
. From comparison of the calculated and experimental values of the excess volume and the excess viscosity, the total RMSD of 55 data points were less than 9% and 0.1%, respectively, and average relative deviations (RAD) were less than 2.88% and 2.39%, respectively. On the basis of the obtained RAD and RMSD values, we concluded that eq 8 and eq 9 could be successfully used for the correlation of the excess volume and the excess viscosity.
CONCLUSION
Densities and viscosities of 2bromopropane and methanol were measured for the entire range of molar fractions and for the temperature range between (298.15 and 318.15) K. and the Densities and viscosities on temperature and concentration were calculated by the regression. Regression coefficients and deviation were obtained.
The excess molar volume and the excess viscosity were determined from the experimental density and viscosity data. The excess molar volumes were related to compositions by polynomial regression and regression parameters and total RMSD deviations were obtained; the excess viscosities was related to compositions by RedlichKister equation and regression coefficients and total RMSD deviation of the excess viscosity for 2bromopropane and methanol binary system were obtained. The total RMSD deviations of two equations were less than 8.6% and 0.1%, respectively. The results showed that the model agreed very well with the experimental data.
Li H.
,
Zhang Z.
,
Zhao L.
,
Guo F.
2008
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Liu Y. P
,
Sun B. G.
,
Xie J. C.
,
Zheng F. P.
,
Xiao Y.
2004
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Tasic A. Ž.
,
Grozdanic D. K.
,
Djordjevic B. D.
,
Šerbanovic S. P.
,
Radojkovic N.
1995
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DOI : 10.1021/je00019a009
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