Addition/Correction pubs.acs.org/jced
Correction to “Density, Viscosity, Speed of Sound, Bulk Modulus, Surface Tension, and Flash Point of Binary Mixtures of Butylcyclohexane + Toluene or + n‑Hexadecane” Dianne J. Luning Prak Chemistry Department, United States Naval Academy 572M Holloway Road Annapolis, Maryland 21402, United States
J. Chem. Eng. Data 2016, 61, 3595−3606. DOI:10.1021/acs.jced.6b00516 components, and ηmixture is the dynamic viscosity of the mixture. The viscosity deviations for the binary mixtures of butylcyclohexane in n-hexadecane shown in the corrected Figure 5 are negative at 293.15 K, and for the other temperatures are smaller than the combined expanded uncertainties of the values. Liu and Zhu1 showed that the viscosity deviations for butylcyclohexane in n-heptane, n-octane, n-nonane, and n-decane were negative, while the deviations for butylcyclohexane in n-dodecane and n-tetradecane were positive values that were close to zero.1 For comparison, binary mixtures were prepared at a mole fraction of 0.5000 of butylcyclohexane in decane (Aldrich, 99.4% mole fraction purity by GC analysis), dodecane (Aldrich, 99.5% mole fraction purity by GC analysis), and tetradecane (Aldrich, 99.7% mole fraction purity by GC analysis) and measured at 293.15 K. At this mole fraction of 0.5, the viscosity deviations were −0.04 ± 0.03, 0.00 ± 0.03, −0.01 ± 0.03, and −0.08(6) ± 0.03 mPa·s for the decane, dodecane, tetradecane, and hexadecane mixtures, respectively. These viscosity deviations agree within the error of measurement with the values reported by
I
n the original paper, the density values for the mixtures of n-butylcyclohexane and n-hexadecane were shifted one row in Table 3. The corrected Table 3 is given below. All the calculations in the original paper were based on the correct values. Only the tabular data were offset by a row. In the original paper, the excess molar volumes for the binary mixtures studied were given in Table 4 in the right-hand column. The mole fraction for n-hexadecane and butylcyclohexane system was incorrectly typed as 0.5293 and should have been 0.5182. Table 4 shows this correction. This correction does not change the analysis presented in the original paper. The viscosity deviations shown in Figure 5 for butylcyclohexane/n-hexadecane mixtures were incorrectly reported in the original manuscript. The correct viscosity deviations were calculated using the following equation, which was eq 7 in the original manuscript: Δη = ηmixture − (x1η1 + x 2η2)
(1)
where η1 and η2 are the dynamic viscosities of the pure components, and x1 and x2 are the mole fractions of the pure
Table 3. Experimental Values of Density ρ, in kg·m−3, at Temperature T, Mass Fraction w, and Mole Fraction x, for the System n-Butylcyclohexane (1) + Toluene (2) or + n-Hexadecane (2) at Pressure p = 0.1 MPaa density/kg·m−3 at T/K = w1
x1
293.15
303.15
313.15
323.15
333.15
343.15
353.15
745.71 748.02 750.22 752.47 754.73 757.04 759.39 761.76 764.16 766.60
738.81 741.10 743.20 745.35 747.50 749.80 752.10 754.35 756.6 ± 0.7 759.00
731.9 734.1 736.1 738.3 740.3 742.5 744.7 746.9 749.1 ± 0.6 751.4
n-Butylcyclohexane (1) + Toluene (2) correctly reported 0.0000 0.1002 0.2000 0.3001 0.3998 0.4998 0.6001 0.7000 0.7999 0.8998
0.0000 0.1524 0.2876 0.4091 0.5182 0.6173 0.7078 0.7902 0.8658 0.9355
773.41 775.85 778.23 780.67 783.16 785.72 788.34 791.01 793.72 796.48
n-Butylcyclohexane (1) + n-Hexadecane (2) 766.47 759.55 752.63 768.90 761.94 754.99 771.24 764.25 757.24 773.65 766.60 759.55 776.08 768.99 761.87 778.59 771.43 764.25 781.15 773.92 766.67 783.74 776.44 769.12 786.38 779.00 771.60 789.06 781.60 774.12
a
ρ is the density, T is the temperature, w1 is the mass fraction of n-butylcyclohexane in mixtures with toluene or n-hexadecane and x1 is the mole fraction of n-butylcyclohexane in mixtures with other compounds. Standard uncertainties u are u(T) = 0.01 K, expanded uncertainties Uc are Uc (ρ) = 0.07 kg·m−3 for T < 343.15 K and Uc (ρ) = 0.2 kg·m−3 for T ≥ 343.15 K (level of confidence = 0.95, k = 2) unless otherwise indicated by “ ± ” and combined expanded uncertainty is Uc (x1) = 0.0001 and Uc (w1) = 0.0001, except for x1 = 0.1542 (butylcyclohexane and n-hexadecane mixture) where Uc (x1) = 0.0002. The differences in uncertainty for different temperatures arise from differences in the level of precision for the two instruments. The DSA 5000 is more precise. The average pressure for these measurements was 0.102 MPa with an expanded uncertainty Uc(P) = 0.002 MPa (level of confidence = 0.95, k = 2). Published: July 20, 2017 © 2017 American Chemical Society
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DOI: 10.1021/acs.jced.7b00516 J. Chem. Eng. Data 2017, 62, 2473−2474
Journal of Chemical & Engineering Data
Addition/Correction
Table 4. Correlation of Density ρ to Mole Fraction of Butylcyclohexane, x1, in Binary Mixtures with n-Hexadecane or Toluene and the Excess Molar Volume VmE at a Specified Mole Fraction x1 and Temperature T, and 0.1 MPaa T/K
A4
A3
A2 Toluene: ρ/kg·m
A1 −3
= A4x1 + 4
Ao
A3x13
+
A2x12
R2
x1 and VEm/cm3·mol−1
σ
+ A1x1 + A0
x1 = 0.4964
correctly reported 9.7 ± 0.2 9.3 ± 0.2 8.9 ± 0.1 8.5 ± 0.1 8.1 ± 0.1 7.9 ± 0.3 7.6 ± 0.2
293.15 303.15 313.15 323.15 333.15 343.15 353.15
n-Hexadecane: ρ/ kg·m−3= A3x13 + A1x1 + Ao 16.3 ± 0.2 773.36 ± 0.06 16.1 ± 0.2 766.43 ± 0.06 15.9 ± 0.2 759.51 ± 0.05 15.6 ± 0.1 752.60 ± 0.05 15.3 ± 0.1 745.68 ± 0.05 14.7 ± 0.3 738.8 ± 0.1 14.3 ± 0.2 731.9 ± 0.1
x1 = 0.5182 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999
0.03 0.03 0.03 0.03 0.03 0.06 0.04
0.12 0.10 0.08 0.06 0.05 NRb NRb
a ρ is the density, T is temperature, VEm is the excess molar volume, and x1 is the mole fraction of n-butylcyclohexane in mixtures with other compounds. The “ ±” for the coefficients Ao, A1, A2, A3, and A4 represent the 95% confidence interval. The σ is the standard error of the fit as given by eq 2. bNot reported. The error in these values are greater than the values themselves.
The adjustable parameters Aj were determined by minimizing the sum of the square of the difference between the calculated excess molar volume of the binary mixture and the value calculated by the model in eq 2. A one-term fit was not used because the viscosity deviations were not symmetrical about x1 = x2 = 0.5. A two-parameter fit was selected because adding more terms did not significantly improve the fit as indicated by the standard error. For the butylcylohexane mixtures at 293.15 K Δη = x1x 2[−0.351 − 0.025(x1 − x 2)]
(3)
with a standard error of 0.002 mPa·s. The fits for toluene are given in the Supporting Information (Table S7) in the original paper. The model fits the data well as shown in Figure 5. The funding grant numbers in the original paper are incorrect and have been corrected.
Figure 5. Viscosity deviations Δη as a function the mole fraction of n-butylcyclohexane x1 in toluene mixtures at ■, 293.15 K; ▲, 313.15 K; and ⧫, 333.15 K, and in n-hexadecane mixtures at □, 293.15 K. Error bars for the data shown here are the combined expanded uncertainties with 0.95 level of confidence (k = 2). The line shown for the butylcyclohexane is eq 3, and lines shown for the toluene mixtures are described in the original paper.
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AUTHOR INFORMATION
Notes Funding
This work was funded by the Office of Naval Research, grant #N0001416WX01648 and #N0001417WX00892.
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Liu and Zhu of −0.029 ± 0.007, 0.016 ± 0.007, and 0.020 ± 0.007 mPa·s for decane, dodecane, and tetradecane, respectively. The viscosity deviations for all these binary mixtures with butylcyclohexane are small and in some cases do not differ from zero within the error of the measurement. The slightly negative value of n-hexadecane suggests that the presence of the butylcyclohexane may interrupt the short-range orientation of the hexadecane molecules and allow them move more easily past each other in the mixture than would be expected by an ideal mixture, which is represented by the linear combination of the two components weighed by the mole fraction. This disruption in orientation was also indicated by the positive excess molar volume found for the hexadecane mixtures as discussed in the original paper. In all binary mixtures, the deviations from ideal become smaller as temperature increases. The viscosity deviations were fit with Redlich−Kister type expression: 1
REFERENCES
(1) Liu, H.; Zhu, L. Excess molar volumes and viscosities of binary systems of butylcyclohexane and n-alkanes (C7 to C14) at T = 293.15 to 313.15 K. J. Chem. Eng. Data 2014, 59, 369−375.
n
Δη = x1x 2 ∑ Aj (x1 − x 2) j = x1x 2[A 0 + A1(x1 − x 2)] j=0
(2)
where Aj are adjustable parameters, j is the order of the polynomial, and x1 is the mole fraction of butylcyclohexane and x2 is the mole fraction of either toluene or n-hexadecane. 2474
DOI: 10.1021/acs.jced.7b00516 J. Chem. Eng. Data 2017, 62, 2473−2474
