J. Chem. Eng. Data 1989, 3 4 , 339-346
339
Temperature and Concentration Dependence of Viscosity of Aqueous Electrolytes from 20 to 50 OC. Chlorides of Na', K+, Mg2+, Ca2+, Ba2+, Sr2+, Co2+, Ni2+9 Cu2+, and Cr3+ M. Afzal," M. Saleem, and M. Tarlq Mahmood Department of Chemistry, Quaid-I-Azam University, Islamabad, Pakistan
Viscosities of aqueous solutions of the chlorldes of potassium, sodium, calcium, magnesium, strontium, barium, cobalt, nickel, chromium, and copper were determined by using a thermostated Ubbelohde flow viscometer In the wide range of concentrations and temperatures at 5 O C Intervals from 20 to 50 O C . From the experimental results, the Ion-solvent Interaction terms ( B coefflclents) were evaluated In the concentration range of 0.1-5.0 M; the data were also represented by a newly suggested empirical equation of the form Q = a. exp(boM coM2). The viscosity coefflclents estimated from the parameters of this empirical equation were found to be comparable with literature values, but some discrepancies may be due to low-purity chemicals. It was also concluded that the viscosities of these Ions in aqueous solutions could be understood In terms of hydration number, charge on the Ions, and their Ionic radii.
+
I ntroductlon Considerable interest has been shown in the study of the viscometric behavior of electrolytes in water. The aim of these studies was to determine the 6 coefficient of the Jones and Dole equation ( 7 ) and from it to be able to define the properties of the electrolyte in solution. The relative viscosity of dilute electrolytes has proved to be an effective method for studying ion-solvent interactions, through use of the Jones-Dole equation q/qo - l = AC"2 BC, where v/qo is the viscosity of the salt solution relative to that of the solvent, water, and C is the molar concentration. The quantities A and B are interaction coefficients whose values depend upon the particular electrolyte, temperature, and solvent under consideration. This empirical equation is valid only at lower concentration. Several other empirical as well as theoretical equations are available in the literature (2-4), but unfortunately, they fail to be applicable at high concentrations, except for the Vand equation (5) and other related equations (6, 7). Although the Vand equation empirically describes the experimental data at higher concentrations, the theoretical concept on which the Vand equation was developed cannot be valid at these high concentrations. Recently some authors (8) have attempted to describe the concentration dependence of viscosity in terms of a new empirical equation shown to be obtainable from the Vogel-Tammann-Fulcher (VTF) equation (9).A least-squares fitting of the viscosity data to this isothermal equation has been made, and a surprisingly good fit has been obtained for all the systems under investigation. A straight line obtained from the plot of In q versus (boM4C o M 2 )of eq 1 (below) verifies the suitability of this equation in describing the concentration dependence to high concentrations at 20-50 O C and also shows that how well the equation represents our data.
+
*
Author to whom all CorresDondence should be addressed. 0021-9568/89/ 1734-0339$01.50/0
Table I. Viscosities (cP) for Aqueous Sodium Chloride concn, M 20 "C 25 "C 30 "C 35 "C 40 "C 45 " C 50 "C 0.1 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
1.001 0.890 1.036 0.921 1.081 0.963 1.133 1.013 1.199 1.072 1.269 1.133 1.352 1.204 1.447 1.292 1.555 1.387
0.801 0.829 0.869 0.915 0.969 1.025 1.090 1.163 1.249
0.724 0.656 0.751 0.682 0.788 0.717 0.830 0.755 0.879 0.800 0.930 0.846 0.991 0.899 1.058 0.960 1.132 1.027
0.597 0.623 0.655 0.689 0.730 0.773 0.822 0.875 0.935
0.546 0.569 0.601 0.633 0.671 0.709 0.753 0.802 0.856
Table 11. Viscosities (cP) for Aqueous Potassium Chloride concn. M 20 " C 25 "C 30 " C 35 " C 40 " C 45 " C 50 " C 0.1 0.25 0.5 0.75 1.00 1.25 1.5 2.0 2.5 3.0
0.994 0.991 0.987 0.983 0.983 0.981 0.982 0.985 0.995 1.005
0.882 0.882 0.881 0.880 0.881 0.881 0.884 0.890 0.902 0.914
0.795 0.795 0.794 0.791 0.802 0.802 0.806 0.815 0.827 0.841
0.719 0.720 0.722 0.725 0.729 0.733 0.737 0.748 0.763 0.774
0.652 0.655 0.657 0.661 0.665 0.671 0.676 0.686 0.699 0.715
0.594 0.596 0.600 0.605 0.610 0.615 0.622 0.632 0.645 0.661
0.544 0.547 0.551 0.556 0.561 0.566 0.572 0.585 0.598 0.615
Table 111. Viscosities (cP) for Aqueous Barium Chloride concn, M 20 "C 25 "C 30 "C 35 "C 40 "C 45 "C 50 " C 0.1 0.25 0.5 0.75 1.0 1.25 1.5
1.018 1.053 1.113 1.179 1.255 1.340 1.443
0.907 0.938 0.995 1.058 1.127 1.207 1.298
0.815 0.846 0.900 0.958 1.023 1.096 1.181
0.737 0.766 0.816 0.870 0.932 1.001 1.077
0.669 0.696 0.743 0.794 0.850 0.923 0.984
0.609 0.635 0.679 0.726 0.780 0.837 0.901
0.558 0.581 0.624 0.668 0.716 0.771 0.830
Table IV. Viscosities (cP) for Aaueous Strontium Chloride concn, M 20 " C 25 " C 30 " C 35 " C 40 " C 45 " C 50 "C 0.1 0.5 1.0 1.5 2.0 2.5 3.0
1.023 1.134 1.301 1.518 1.814 2.212 2.792
0.911 1.012 1.165 1.363 1.626 1.979 2.487
0.816 0.920 1.058 1.237 1.472 1.790 2.246
0.742 0.671 0.830 0.757 0.960 0.874 1.127 1.028 1.340 1.218 1.628 1.483 2.034 1.851
0.611 0.688 0.797 0.937 1.115 1.350 1.677
0.559 0.629 0.734 0.862 1.027 1.246 1.535
Table V. Viscosities (cP) for Aqueous Magnesium Chloride concn, M 20 " C 25 " C 30 " C 35 "C 40 " C 45 " C 50 " C 0.1 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 5.0
1.040 0.933 1.209 1.069 1.461 1.295 1.791 1.587 2.221 1.900 2.804 2.462 3.607 3.156 4.700 4.082 6.242 5.439 12.94 10.91
0.832 1.960 1.162 1.419 1.761 2.193 2.794 3.597 4.703 9.374
0 1989 American Chemical Society
0.753 0.682 0.618 0.868 0.789 0.715 1.049 0.949 0.861 1.277 1.153 1.043 1.573 1.416 1.279 1.964 1.759 1.585 2.491 2.219 1.994 3.189 2.832 2.543 4.158 3.671 3.262 8.131 7.089 6.218
0.567 0.654 0.786 0.952 1.163 1.432 1.802 2.281 2.899 5.507
340 Journal of Chemical and Engineering Data, Vol. 34, No. 3, 7989
Table VI. Viscosities (cP) for Aqueous Calcium Chloride concn, M 20 "C 25 "C 30 "C 35 "C 40 "C 45 "C 50 "C 0.1 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 5.0
1.026 1.142 1.318 1.538 1.820 2.185 2.698 3.415 4.492 8.507
0.912 1.019 1.176 1.375 1.627 1.955 2.331 3.034 3.970 7.373
0.818 0.918 1.061 1.244 1.473 1.767 2.175 2.733 3.558 6.487
0.740 0.829 0.966 1.128 1.337 1.604 1.967 2.468 3.195 5.733
0.672 0.754 0.875 1.028 1.217 1.461 1.786 2.235 2.872 5.078
0.612 0.688 0.799 0.937 1.111 1.331 1.626 2.031 2.603 4.508
0.561 0.628 0.734 0.858 1.021 1.219 1.487 1.851 2.362 4.053
Table VII. Viscosities (cP) for Aqueous Cobalt Chloride concn, M 20°C 25 "C 30°C 35 "C 40 "C 45 "C 50 "C 0.1 0.5 1.0 1.5 2.0 2.5 3.0
1.040 1.207 1.445 1.762 2.159 2.689 3.399
0.923 1.068 1.284 1.561 1.910 2.363 2.983
0.832 0.960 1.154 1.413 1.707 2.111 2.647
0.749 0.867 1.043 1.270 1.536 1.904 2.362
0.655 0.784 0.944 1.144 1.383 1.695 2.105
0.619 0.713 0.855 1.051 1.249 1.526 1.889
0.567 0.650 0.781 0.946 1.138 1.384 1.708
Table VIII. Viscosities (cP) for Aqueous Copper Chloride concn, M 20 "C 25 "C 30°C 35 "C 40 "C 45 "C 50 "C 0.1 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
1.034 1.190 1.405 1.655 1.952 2.299 2.721 3.270 3.924
0.919 0.826 0.746 1.057 0.949 0.857 1.244 1.117 1.008 1.461 1.309 1.176 1.712 1.524 1.355 2.023 1.791 1.592 2.370 2.093 1.855 2.826 2.476 2.185 3.369 2.929 2.566
0.676 0.776 0.908 1.057 1.223 1.419 1.648 1.930 2.253
0.616 0.706 0.823 0.956 1.094 1.273 1.471 1.715 1.994
0.563 0.645 0.751 0.867 0.985 1.150 1.323 1.543 1.777
Table IX. Viscosities (cP) for Aqueous Chromium Chloride concn, M 20 "C 25 "C 30 "C 35 "C 40 "C 45 "C 50 "C 0.1 0.25 0.5 0.75 1.0 1.25 1.5 1.75 2.0
1.059 1.184 1.382 1.621 1.937 2.296 2.836 3.423 4.639
0.942 1.043 1.223 1.431 1.703 2.014 2.485 2.985 4.035
0.847 0.938 1.096 1.284 1.523 1.798 2.203 2.642 3.548
0.766 0.845 0.989 1.154 1.366 1.611 1.966 2.346 3.138
0.695 0.763 0.893 1.044 1.227 1.446 1.754 2.089 2.771
0.635 0.697 0.8111 0.945 1.112 1.314 1.574 1.868 2.470
0.581 0.637 0.739 0.862 1.010 1.888 1.425 1.683 2.207
Table X. Viscosities (cP) for Aaueous Nickel Chloride concn, M 20 "C 25 "C 30 "C 35 "C 40 "C 45 "C 50 "C 0.1 0.5 1.5 2.0 2.5 3.0 3.5 4.0
1.037 1.204 1.776 2.189 2.732 3.491 4.502 6.022
0.919 1.071 1.579 1.928 2.406 3.037 3.909 5.195
0.825 0.962 1.416 1.729 2.145 2.700 3.450 4.527
0.745 0.867 1.274 1.556 1.921 2.398 3.055 3.983
0.677 0.786 1.149 1.398 1.721 2.142 2.707 3.526
0.614 0.717 1.043 1.266 1.555 1.927 2.417 3.130
0.563 0.654 0.947 1.148 1.405 1.734 2.170 2.789
Table XI. Interaction Coefficients for Aqueous Sodium Chloride in the Concentration Range 0.1-4.0 M temp, "C 20 25 30 35 40 45 50
CP 1.001-1.555 0.890-1.388 0.801-1.249 0.725-1.132 0.656-1.027 0.597-0.935 0.546-0.856 7 range,
a,
0.994 0.883 0.799 0.718 0.651 0.593 0.541
bo 0.075 0.078 0.084 0.087 0.091 0.094 0.098
co
0.009 0.008 0.007 0.006 0.006 0.005 0.004
stand. devn, In 17 0.153 0.154 0.154 0.155 0.155 0.154 0.155
Table XII. Interaction Coefficient for Aqueous Potassium Chloride in the Concentration Range 0.1-3.0 M temp, "C 20 25 30 35 40 45 50
1range,
CP
0.994-1.006 0.882-0.915 0.795-0.841 0.719-0.774 0.652-0.715 0.594-0.661 0.544-0.615
a.
0.996 0.883 0.794 0.718 0.651 0.592 0.542
bo -0.002 -0.011 0.0 0.009 0.017 0.026 0.029
stand. devn, In 17 0.0077 0.0129 0.0192 0.0253 0.0303 0.0353 0.0403
co
0.008 0.007 0.006 0.005 0.004 0.003 0.004
Table XIII. Interaction Coefficients for Aqueous Barium Chloride in the Concentration Range 0.1-1.5 M temp, "C 20 25 30 35 40 45 50
7 range,
CP
1.018-1.444 0.907-1.298 0.815-1.181 0.737-1.077 0.669-0.984 0.609-0.901 0.558-0.830
a0
1.000 0.888 0.797 0.720 0.653 0.594 0.543
bo 0.196 0.213 0.229 0.239 0.251 0.260 0.268
stand. devn, in 7 0.128 0.132 0.136 0.139 0.143 0.144 0.146
CO
0.032 0.025 0.021 0.019 0.016 0.015 0.009
Table XIV. Interaction Coefficients for Aqueous Strontium Chloride in the Concentration Range 0.1-3.0 M temo. "C
n ranee, CP
an
bo
cn
20 25 30 35 40 45 50
1.0237-2.7918 0.9111-2.4868 0.8169-2.2464 0.7423-2.0341 0.6715-1.8506 0.6114-1.6770 0.5599-1.5347
1.0064 0.8944 0.8042 0.7277 0.6594 0.5985 0.5467
0.2101 0.2218 0.2342 0.2399 0.2462 0.2548 0.2647
0.0428 0.0392 0.0354 0.0337 0.0320 0.0290 0.0262
stand. devn. In R 0.3636 0.3639 0.3643 0.3648 0.3657 0.3650 0.3660
Table XV. Interaction Coefficients for Aqueous Calcium Chloride in the Concentration Range 0.1-5.0 M temp, "C 20 25 30 35 40 45 50 ~~
range, CP a. 1.0267-8.5074 1.0294 0.9118-7.3731 0.9162 0.8189-6.4877 0.8176 0.7401-5.7331 0.7376 0.6722-5.0781 ~.~- . . .~0.6677 . .. 0.6123-4.5081 0.6072 0.5612-4.0537 0.5551 7
stand. bo co devn, In 17 0.1846 0.0468 0.6670 0.1882 0.0451 0.6589 0.2071 0.0408 0.6538 0.2158 0.0383 0.6471 0.2239 .~ ~0.0358 .~ . . . 0.6677 ~ ~.. 0.2305 0.0336 0.6332 0.2359 0.0319 0.6277 ~
Table XVI. Interaction Coefficients for Aqueous Magnesium Chloride in the Concentration Ranee 0.1-5.0 M 1
t e m n "C n ranee. CP 20 1.0403-12.944 25 0.9327-10.908 30 0.8319-9.3745 35 0.7532-8.1315 40 0.6817-7.0890 45 0.6184-6.2185 50 0.5670-5.508 I~
I
0
1
a,
1.0319 0.9194 0.8213 0.7430 0.6744 0.6109 0.5606
b, 0.2881 0.2941 0.2999 0.3059 0.3168 0.3222 0.3319
cn
0.0413 0.0406 0.0349 0.0349 0.0338 0.0320 0.0312
stand. devn. In n 0.7944 0.7796 0.7643 0.7515 0.7385 0.7284 0.7165 I
.
Table XVII. Interaction Coefficients for Aqueous Chromium Chloride in the Concentration Range 0.1-2.0 M temp, "C 20 25 30 35 40 45
