J. Chem. Eng. Data 1996, 41, 1505-1513
1505
Dissociation Constant of N-Methyldiethanolamine in Aqueous Solution at Temperatures from 278 K to 368 K A Ä lvaro Pe´ rez-Salado Kamps and Gerd Maurer* Lehrstuhl fu¨r Technische Thermodynamik, Universita¨t Kaiserslautern, D-67653 Kaiserslautern, Germany
The chemical equilibrium constant for the dissociation of protonated N-methyldiethanolamine (MDEA, CH3N(C2H5OH)2) in aqueous solutions is determined from electromotive force measurements at temperatures from 278 K to 368 K. Experimental results are reported and compared to literature values. Experimental results (on molality scale) are correlated by ln K ) [-819.7/(T/K)] - 79.474 + 10.9756 ln(T/K).
Introduction Aqueous alkanolamine solutions are widely used for the absorption of sour gases like carbon dioxide or hydrogen sulfide from gaseous effluents, e.g. natural gases, refinery gases, and synthesis gases. Especially N-methyl-2,2′iminodiethanol, commercially often called N-methyldiethanolamine (MDEA), is used for the selective removal of hydrogen sulfide from gases containing carbon dioxide. Due to the slower reaction of MDEA with carbon dioxide compared to hydrogen sulfide, in a properly designed absorption column a carbon dioxide rich gas is driven off on the top whereas a hydrogen sulfide rich solution is obtained on the bottom. As the reaction between hydrogen sulfide and MDEA is reversible, the solution rich in hydrogen sulfide is regenerated in a subsequent step, thereby producing hydrogen sulfide as a top product. Continuing earlier work on the simultaneous solubility of carbon dioxide and hydrogen sulfide in aqueous MDEA solutions (Kuranov et al., 1996), and in order to improve the modeling of vapor-liquid equilibrium of these systems, the chemical equilibrium constant for the dissociation of MDEAH+ (i.e. protonated MDEA) was measured in the temperature range from 278 K to 368 K. Experimental results are reported and compared to literature values. Procedure The equilibrium constant for the dissociation of MDEAH+ in aqueous solution:
MDEAH+(aq) h MDEA(aq) + H+(aq) was determined from electromotive force (EMF) measurements. EMF measurements were performed in an electrochemical cell consisting of a separate glass pH electrode and a (Ag, AgCl) electrode in a chloride-containing aqueous electrolyte solution:
glass pH electrode|aqueous electrolyte solution (cont. Cl- ions)|AgCl(s), Ag(s) The solution must contain chloride, since it is a reaction partner in the half-reaction at the (Ag, AgCl) electrode. Glass pH electrodes have two well-known unpleasant properties (see for example Eisenman (1967) or Pitzer (1991)): (1) Failure to obey the Nernst equation perfectly. This error arises from the fact that the asymmetry poten* Author to whom correspondence should be addressed. Fax: +49-6312053835. E-mail:
[email protected].
S0021-9568(96)00141-0 CCC: $12.00
Figure 1. Scheme of the experimental arrangement: (A) glass pH electrode, (B) (Ag, AgCl) electrode, (C) platinum electrode, (D) electrometer, (E) thermostat, (F) measurement of temperature by platinum resistance thermometer.
tial of a glass pH electrode can vary with the pH of the solution under investigation. Nevertheless, the assumption is normally made that in passing from a standardizing solution to a test solution, the asymmetry potential remains constant. This is probably true in intermediate pH ranges but not for transitions between low- and high-pH solutions. The order of magnitude of this error is about 1 mV. (2) A tendency to drift in potential by millivolts over periods of minutes to days, depending on the electrode and electrolyte solution. Thus, the standard potential of a glass pH electrode might depend on time. This error arises from the fact that the asymmetry potential of a glass pH electrode can vary with time. However, a glass electrode cell can be used to measure the change in activity between two solutions of different composition. Therefore, a twocell system was used (cf. Figure 1). In such a system, two solutions are being compared. The same electrodes are used in both cells (Serjeant and Warner, 1978). They are transferred back and forth between the two cells while the equilibrium potential is recorded continuously. The time period between two measurements should be as short as possible. With a proper electrometer, adequate shielding and temperature matching of cells, accurate measurements can be achieved. The glass electrode method is experimentally simpler than the hydrogen electrode method, because elaborate precautions for eliminating oxygen are not necessary. It can provide accurate chemical reaction constants and activity coefficient data more rapidly and can also be used under conditions (e.g. in reductive solutions) where the hydrogen electrode fails. The glass electrode method has been applied in the present work for determining the equilibrium constant for the dissociation of MDEAH+. In cell I aqueous hydrogen chloride is used as the electrolyte solution: © 1996 American Chemical Society
1506 Journal of Chemical and Engineering Data, Vol. 41, No. 6, 1996 Table 1. Experimental Equilibrium Data cell I
cell II
t/°C
m ˜ HCl,I/(mol/kg)
EI/mV
m ˜ HCl,II/(mol/kg)
m ˜ MDEA/(mol/kg)
EII/mV
EII - EI/mV
109Kexp
5.15 5.15 5.1 5.25 5.3 5.25 5.2 5.15 5.15 5.3 5.15 5.3 5.2 5.0 5.15 5.0 5.1 5.15 5.15 5.1 5.1 15.1 15.15 15.1 15.2 15.2 15.25 15.15 15.05 15.1 15.25 15.05 15.25 15.1 14.95 15.15 15.1 15.1 15.15 15.1 15.05 15.1 25.05 25.15 25.1 26.15 25.2 26.15 25.05 25.1 25.05 26.25 25.05 26.2 25.15 25.05 25.1 25.1 25.1 25.05 25.05 25.05 35.0 35.05 35.0 36.15 35.15 35.15 35.0 35.0 35.05 35.15 34.95 35.2 35.0 35.0
0.010 149 0.010 150 0.010 173 0.010 156 0.009 851 0.009 870 0.010 163 0.010 157 0.010 151 0.010 155 0.010 165 0.010 156 0.010 181 0.009 869 0.010 157 0.010 158 0.010 158 0.010 164 0.010 151 0.010 150 0.010 170 0.010 149 0.010 150 0.010 173 0.010 156 0.009 851 0.009 870 0.010 163 0.010 157 0.010 151 0.010 155 0.010 165 0.010 156 0.010 181 0.009 869 0.010 157 0.010 158 0.010 158 0.010 164 0.010 151 0.010 150 0.010 170 0.010 149 0.010 150 0.010 173 0.010 156 0.009 851 0.009 870 0.010 163 0.010 157 0.010 151 0.010 155 0.010 165 0.010 156 0.010 181 0.010 157 0.010 158 0.010 158 0.010 164 0.010 151 0.010 150 0.010 170 0.010 149 0.010 150 0.010 173 0.010 156 0.009 851 0.009 870 0.010 163 0.010 157 0.010 151 0.010 155 0.010 165 0.010 156 0.010 181 0.009 869
-148.4 -148.9 -148.4 -148.9 -145.7 -146.5 -147.5 -147.7 -146.9 -144.4 -148.2 -146.6 -148.0 -145.5 -148.4 -147.5 -148.4 -146.5 -147.5 -146.8 -147.4 -152.4 -152.8 -152.4 -152.6 -147.5 -151.3 -151.5 -152.1 -151.0 -148.9 -152.1 -150.8 -152.1 -149.3 -152.0 -150.8 -152.7 -150.1 -151.1 -150.6 -150.9 -156.8 -157.4 -157.3 -157.4 -152.9 -155.1 -156.5 -156.3 -156.3 -154.1 -157.2 -155.7 -157.3 -157.3 -156.8 -157.0 -155.4 -156.5 -155.6 -155.6 -161.2 -162.0 -161.6 -161.3 -156.3 -160.4 -161.0 -161.6 -160.9 -158.6 -161.6 -160.2 -162.1 -158.7
0.010 155 0.010 162 0.010 188 0.010 074 0.009 819 0.009 874 0.010 241 0.010 154 0.010 151 0.010 157 0.010 159 0.010 152 0.010 153 0.009 877 0.010 162 0.010 155 0.010 166 0.010 152 0.010 156 0.010 156 0.010 072 0.010 155 0.010 162 0.010 188 0.010 074 0.009 819 0.009 874 0.010 241 0.010 154 0.010 151 0.010 157 0.010 159 0.010 152 0.010 153 0.009 877 0.010 162 0.010 155 0.010 166 0.010 152 0.010 156 0.010 156 0.010 072 0.010 155 0.010 162 0.010 188 0.010 074 0.009 819 0.009 874 0.010 241 0.010 154 0.010 151 0.010 157 0.010 159 0.010 152 0.010 153 0.010 162 0.010 155 0.010 166 0.010 152 0.010 156 0.010 156 0.010 072 0.010 155 0.010 162 0.010 188 0.010 074 0.009 819 0.009 874 0.010 241 0.010 154 0.010 151 0.010 157 0.010 159 0.010 152 0.010 153 0.009 877
0.025 25 0.050 12 0.074 96 0.099 48 0.099 82 0.100 64 0.125 79 0.150 38 0.175 05 0.200 16 0.250 31 0.300 20 0.350 32 0.400 33 0.450 07 0.500 29 0.600 00 0.699 99 0.800 07 0.900 26 0.991 64 0.025 25 0.050 12 0.074 96 0.099 48 0.099 82 0.100 64 0.125 79 0.150 38 0.175 05 0.200 16 0.250 31 0.300 20 0.350 32 0.400 33 0.450 07 0.500 29 0.600 00 0.699 99 0.800 07 0.900 26 0.991 64 0.025 25 0.050 12 0.074 96 0.099 48 0.099 82 0.100 64 0.125 79 0.150 38 0.175 05 0.200 16 0.250 31 0.300 20 0.350 32 0.450 07 0.500 29 0.600 00 0.699 99 0.800 07 0.900 26 0.991 64 0.025 25 0.050 12 0.074 96 0.099 48 0.099 82 0.100 64 0.125 79 0.150 38 0.175 05 0.200 16 0.250 31 0.300 20 0.350 32 0.400 33
246.8 269.6 281.3 287.0 289.0 289.4 296.1 300.1 304.2 307.5 311.7 316.4 319.8 325.2 325.6 327.5 331.8 336.4 339.0 342.3 344.2 244.4 267.9 280.4 286.6 291.0 289.0 295.1 298.9 303.6 307.1 311.7 316.4 319.9 325.0 325.4 327.4 332.4 336.4 339.4 342.2 344.6 241.6 266.0 278.6 285.7 289.1 288.4 293.7 298.9 302.6 306.9 311.1 316.4 319.1 325.1 327.5 332.1 336.2 338.7 341.9 344.0 238.3 263.1 276.4 284.5 288.5 285.6 291.9 296.3 300.9 305.2 309.6 314.9 317.8 323.2
395.2 418.5 429.7 435.9 434.7 435.9 443.6 447.8 451.1 451.9 459.9 463.0 467.8 470.7 474.0 475.0 480.2 482.9 486.5 489.1 491.6 396.8 420.7 432.8 439.2 438.5 440.3 446.6 451.0 454.6 456.0 463.8 467.2 472.0 474.3 477.4 478.2 485.1 486.5 490.5 492.8 495.5 398.4 423.4 435.9 443.1 442.0 443.5 450.2 455.2 458.9 461.0 468.3 472.1 476.4 482.4 484.4 489.1 491.6 495.2 497.5 499.6 399.5 425.1 438.0 445.8 444.8 446.0 452.9 457.9 461.8 463.8 471.2 475.1 479.9 481.9
1.069 1.070 1.083 1.185* 1.248* 1.185* 1.074 1.106 1.132 1.278* 1.142 1.224* 1.171 1.165 1.156 1.227 1.193 1.251 1.226 1.232 1.250 1.770 1.793 1.779 1.942* 1.990* 1.858* 1.798 1.848 1.884 2.067* 1.884 2.007* 1.926 1.984 1.994 2.147 1.949 2.165 2.093 2.138 2.158 2.840 2.834 2.819 3.189* 3.136* 3.134* 2.838 2.887 2.933 3.334* 2.959 3.305* 3.066 3.100 3.221 3.193 3.402 3.342 3.437 3.559 4.487 4.521 4.496 5.005* 4.908* 4.697* 4.505 4.598 4.670 5.018* 4.741 5.004* 4.853 5.122
Journal of Chemical and Engineering Data, Vol. 41, No. 6, 1996 1507 Table 1 (continued) cell I
cell II
t/°C
m ˜ HCl,I/(mol/kg)
EI/mV
m ˜ HCl,II/(mol/kg)
m ˜ MDEA/(mol/kg)
EII/mV
EII - EI/mV
109Kexp
35.0 35.0 34.95 35.0 34.95 35.0 34.95 44.9 44.9 44.95 45.25 45.15 46.2 44.95 44.95 44.95 46.2 44.95 46.2 44.95 44.95 45.0 44.9 44.9 44.9 44.85 45.0 54.95 55.05 54.95 56.15 55.15 55.1 54.9 55.0 55.0 54.95 55.15 54.9 55.0 54.95 55.0 54.95 55.05 55.0 54.9 64.9 64.95 64.95 65.15 66.2 64.9 64.95 64.95 66.25 65.0 66.3 64.95 64.95 64.85 65.0 64.95 65.0 75.05 75.1 74.95 76.25 75.2 75.0 74.95 74.95 75.1 75.0 75.2 75.0 75.0
0.010 157 0.010 158 0.010 158 0.010 164 0.010 151 0.010 150 0.010 170 0.010 149 0.010 150 0.010 173 0.010 156 0.009 851 0.009 870 0.010 163 0.010 157 0.010 151 0.010 155 0.010 165 0.010 156 0.010 181 0.010 157 0.010 158 0.010 158 0.010 164 0.010 151 0.010 150 0.010 170 0.010 149 0.010 150 0.010 173 0.010 156 0.009 851 0.009 870 0.010 163 0.010 157 0.010 151 0.010 165 0.010 156 0.010 181 0.010 157 0.010 158 0.010 158 0.010 164 0.010 151 0.010 150 0.010 170 0.010 149 0.010 150 0.010 173 0.010 156 0.009 870 0.010 163 0.010 157 0.010 151 0.010 155 0.010 165 0.010 156 0.010 181 0.010 157 0.010 158 0.010 164 0.010 151 0.010 150 0.010 149 0.010 150 0.010 173 0.010 156 0.009 851 0.010 163 0.010 157 0.010 151 0.010 155 0.010 165 0.010 156 0.010 181 0.009 869
-162.4 -161.3 -161.5 -160.9 -160.6 -160.4 -161.0 -166.8 -167.6 -167.2 -167.4 -162.6 -166.0 -166.8 -167.4 -166.8 -164.8 -167.4 -166.1 -167.5 -167.4 -167.3 -167.4 -166.5 -166.4 -166.0 -165.1 -171.7 -172.3 -172.2 -174.3 -168.0 -173.0 -171.6 -172.2 -171.8 -172.3 -171.9 -172.4 -172.5 -172.1 -171.8 -171.4 -171.0 -171.0 -171.2 -178.0 -176.9 -178.6 -177.8 -179.6 -178.1 -178.2 -178.1 -175.7 -179.2 -177.0 -178.6 -178.7 -179.1 -178.0 -177.5 -177.1 -181.7 -183.1 -183.9 -184.6 -177.6 -183.3 -183.9 -183.5 -183.3 -184.2 -185.3 -183.8 -182.6
0.010 162 0.010 155 0.010 166 0.010 152 0.010 156 0.010 156 0.010 072 0.010 155 0.010 162 0.010 188 0.010 074 0.009 819 0.009 874 0.010 241 0.010 154 0.010 151 0.010 157 0.010 159 0.010 152 0.010 153 0.010 162 0.010 155 0.010 166 0.010 152 0.010 156 0.010 156 0.010 072 0.010 155 0.010 162 0.010 188 0.010 074 0.009 819 0.009 874 0.010 241 0.010 154 0.010 151 0.010 159 0.010 152 0.010 153 0.010 162 0.010 155 0.010 166 0.010 152 0.010 156 0.010 156 0.010 072 0.010 155 0.010 162 0.010 188 0.010 074 0.009 874 0.010 241 0.010 154 0.010 151 0.010 157 0.010 159 0.010 152 0.010 153 0.010 162 0.010 155 0.010 152 0.010 156 0.010 156 0.010 155 0.010 162 0.010 188 0.010 074 0.009 819 0.010 241 0.010 154 0.010 151 0.010 157 0.010 159 0.010 152 0.010 153 0.009 877
0.450 07 0.500 29 0.600 00 0.699 99 0.800 07 0.900 26 0.991 64 0.025 25 0.050 12 0.074 96 0.099 48 0.099 82 0.100 64 0.125 79 0.150 38 0.175 05 0.200 16 0.250 31 0.300 20 0.350 32 0.450 07 0.500 29 0.600 00 0.699 99 0.800 07 0.900 26 0.991 64 0.025 25 0.050 12 0.074 96 0.099 48 0.099 82 0.100 64 0.125 79 0.150 38 0.175 05 0.250 31 0.300 20 0.350 32 0.450 07 0.500 29 0.600 00 0.699 99 0.800 07 0.900 26 0.991 64 0.025 25 0.050 12 0.074 96 0.099 48 0.100 64 0.125 79 0.150 38 0.175 05 0.200 16 0.250 31 0.300 20 0.350 32 0.450 07 0.500 29 0.699 99 0.800 07 0.900 26 0.025 25 0.050 12 0.074 96 0.099 48 0.099 82 0.125 79 0.150 38 0.175 05 0.200 16 0.250 31 0.300 20 0.350 32 0.400 33
324.1 326.1 330.7 335.4 338.0 340.6 342.9 233.8 259.7 273.2 280.8 285.3 282.2 289.0 293.8 298.2 302.7 307.1 312.3 316.1 322.2 324.2 328.9 333.0 336.1 338.6 341.5 229.1 256.7 269.8 275.7 282.5 278.3 286.1 291.2 295.7 305.0 308.4 313.9 319.9 322.0 326.7 331.2 334.1 336.8 339.1 223.9 252.3 265.3 273.4 272.7 281.8 286.9 291.7 294.8 301.2 303.3 310.1 316.6 318.6 328.0 330.8 333.4 219.1 248.9 261.4 268.8 276.2 278.1 283.8 288.1 292.0 297.8 303.0 307.3 310.3
486.5 487.4 492.2 496.3 498.6 501.0 503.9 400.6 427.3 440.4 448.2 447.9 448.2 455.8 461.2 465.0 467.5 474.5 478.4 483.6 489.6 491.5 496.3 499.5 502.5 504.6 506.6 400.8 429.0 442.0 450.0 450.5 451.3 457.7 463.4 467.5 477.3 480.3 486.3 492.4 494.1 498.5 502.6 505.1 507.8 510.3 401.9 429.2 443.9 451.2 452.3 459.9 465.1 469.8 470.5 480.4 480.3 488.7 495.3 497.7 506.0 508.3 510.5 400.8 432.0 445.3 453.4 453.8 461.4 467.7 471.6 475.3 482.0 488.3 491.1 492.9
4.840 5.224 5.202 5.230 5.438 5.595 5.604 6.884 6.849 6.898 7.384* 7.418* 7.743* 6.911 6.977 7.134 8.005* 7.318 8.202* 7.433 7.641 7.951 7.942 8.267 8.421 8.752 9.207 10.691 10.439 10.630 11.906* 11.096* 10.773 10.692 10.798 10.957 11.211 12.274* 11.489 11.916 12.467 12.780 12.882 13.496 13.716 13.984 15.614 16.162 15.776 17.382* 17.524* 15.977 16.478 16.428 19.637* 16.589 21.414* 17.611 17.930 18.293 19.351 20.259 21.138 24.183 22.586 23.335 26.415* 24.838* 24.019 23.861 24.560 25.125 25.230 24.798* 26.338 28.131
1508 Journal of Chemical and Engineering Data, Vol. 41, No. 6, 1996 Table 1 (continued) cell I
cell II
t/°C
m ˜ HCl,I/(mol/kg)
EI/mV
m ˜ HCl,II/(mol/kg)
m ˜ MDEA/(mol/kg)
EII/mV
EII - EI/mV
109Kexp
75.0 74.95 75.05 74.95 74.95 75.05 75.0 85.0 85.0 85.1 85.1 85.05 86.2 85.15 85.05 85.2 86.25 85.05 86.35 85.25 85.15 85.0 85.0 85.1 85.15 85.2 85.1 95.0 95.0 94.6 94.9 94.9 94.95 95.1 94.95 94.5 94.85 94.8 94.95 94.95 94.95 95.0 94.9 95.0
0.010 157 0.010 158 0.010 158 0.010 164 0.010 151 0.010 150 0.010 170 0.010 149 0.010 150 0.010 173 0.010 156 0.009 851 0.009 870 0.010 163 0.010 157 0.010 151 0.010 155 0.010 165 0.010 156 0.010 181 0.010 157 0.010 158 0.010 158 0.010 164 0.010 151 0.010 150 0.010 170 0.010 149 0.010 173 0.009 870 0.010 163 0.010 157 0.010 151 0.010 155 0.010 165 0.010 156 0.010 181 0.009 869 0.010 157 0.010 158 0.010 164 0.010 151 0.010 150 0.010 170
-181.8 -182.3 -182.6 -183.4 -183.4 -182.4 -183.0 -189.9 -188.9 -190.2 -192.8 -187.9 -192.0 -190.0 -188.3 -190.5 -190.4 -191.4 -190.8 -191.2 -189.7 -190.4 -188.8 -188.6 -187.8 -188.2 -188.7 -194.4 -196.8 -197.2 -196.5 -192.8 -196.6 -196.3 -196.8 -196.1 -196.6 -195.5 -194.7 -196.0 -196.7 -196.4 -196.2 -196.3
0.010 162 0.010 155 0.010 166 0.010 152 0.010 156 0.010 156 0.010 072 0.010 155 0.010 162 0.010 188 0.010 074 0.009 819 0.009 874 0.010 241 0.010 154 0.010 151 0.010 157 0.010 159 0.010 152 0.010 153 0.010 162 0.010 155 0.010 166 0.010 152 0.010 156 0.010 156 0.010 072 0.010 155 0.010 188 0.009 874 0.010 241 0.010 154 0.010 151 0.010 157 0.010 159 0.010 152 0.010 153 0.009 877 0.010 162 0.010 155 0.010 152 0.010 156 0.010 156 0.010 072
0.450 07 0.500 29 0.600 00 0.699 99 0.800 07 0.900 26 0.991 64 0.025 25 0.050 12 0.074 96 0.099 48 0.099 82 0.100 64 0.125 79 0.150 38 0.175 05 0.200 16 0.250 31 0.300 20 0.350 32 0.450 07 0.500 29 0.600 00 0.699 99 0.800 07 0.900 26 0.991 64 0.025 25 0.074 96 0.100 64 0.125 79 0.150 38 0.175 05 0.200 16 0.250 31 0.300 20 0.350 32 0.400 33 0.450 07 0.500 29 0.699 99 0.800 07 0.900 26 0.991 64
313.2 316.1 321.0 324.7 327.2 330.3 332.1 213.4 242.5 257.2 263.6 267.7 265.3 272.4 279.7 282.7 286.3 292.6 297.3 301.2 309.3 311.1 316.7 319.9 321.2 323.5 325.8 207.3 250.7 259.8 267.3 276.4 277.9 281.3 288.1 292.4 296.4 300.8 302.4 305.5 313.0 314.7 318.7 319.1
495.0 498.4 503.6 508.1 510.6 512.7 515.1 403.3 431.4 447.4 456.4 455.6 457.3 462.4 468.0 473.2 476.7 484.0 488.1 492.4 499.0 501.5 505.5 508.5 509.0 511.7 514.5 401.7 447.5 457.0 463.8 469.2 474.5 477.6 484.9 488.5 493.0 496.3 497.1 501.5 509.7 511.1 514.9 515.4
29.587 29.287 29.589 29.541 30.868 32.491 33.517 32.319 34.302 33.130 34.751 35.461 35.229* 35.916 36.659 36.540 39.277* 37.076 41.421* 40.308* 41.394 42.110 44.207 47.161 53.058 54.668 55.672 48.545 48.851 49.886* 51.065 52.931 52.671 55.172 54.959 57.951* 59.922 61.081 67.767 65.448 70.659 77.093 76.301 84.671
HCl give
glass pH electrode|HCl (aq, m ˜ HCl,I)|AgCl(s), Ag(s) cell I As the activity of a pure solid is set to unity, for cell I the Nernst equation results in
RT ln(aH+aCl-)I EI ) E°(T) F
RT ln(aH+aCl-)II F
n˜ MDEA ) nMDEA + nMDEAH+
(4)
n˜ HCl ) nCl-
(5)
The condition of electroneutrality results in
0 ) nH+ - nOH- + nMDEAH+ - nCl-
(6)
In cell II the dissociation of water is taken into account:
H2O h H+(aq) + OH-(aq)
cell II
The conditions for chemical equilibrium for both reactions present are
The Nernst equation results in
EII ) E°(T) -
(3)
(1)
EI is the electromotive force of cell I, and E° is its standard potential. Since HCl is completely dissociated in diluted aqueous solution, the dissociation of water can be neglected. For a given temperature and overall molality of HCl (m ˜ HCl,I) activities (aH+)I and (aCl-)I were calculated using the excess Gibbs energy model of Pitzer (cf. appendices 1 and 2). Cell II is filled with an aqueous solution of MDEA and HCl:
glass pH electrode|MDEA(aq, m ˜ MDEA), HCl(aq, m ˜ HCl,II)|AgCl(s), Ag(s)
n˜ W ) nW + nOH-
(2)
The mass balance equations for water, MDEA, and
{
KW(T) ) exp -
}
∞ ∞ pure µH aH+aOH+,m + µOH-,m - µW,liq ) RT aW
(7)
{
K(T) ) exp -
}
Journal of Chemical and Engineering Data, Vol. 41, No. 6, 1996 1509
∞ ∞ ∞ µMDEA,m + µH +,m - µMDEAH+,m ) RT aMDEAaH+ (8) aMDEAH+
The influence of pressure on the chemical reactions is neglected. The chemical equilibrium constant KW for the dissociation of water was taken from the literature (Fisher et al., 1972). Activities were approximated using only the modified Debye-Hu¨ckel term in Pitzer’s equation, i.e. neglecting binary and ternary parameters. As both cells are at the same temperature, they have the same standard potential E°. Thus, subtracting eq 1 from eq 2 results in
ln(aH+aCl-)II )
F (E - EII) + ln(aH+aCl-)I RT I
(9)
For given temperatures and compositions in both cells (cell ˜ MDEA, m ˜ HCl,II), the electromotive forces EI I, m ˜ HCl,I; cell II, m ()EI(T,m ˜ HCl,I)) and EII ()EII(T,m ˜ MDEA,m ˜ HCl,II) were measured. With this information, the set of equations (eqs 3-9) can be solved in an iterative procedure to yield the “true” number of moles of each species present in cell II, as well as a preliminary number for the dissociation ˜ MDEA,m ˜ HCl,II). This dissociaconstant of MDEAH+: Kexp(T,m tion constant is called preliminary because it is calculated out of a set of equations in which for cell II activities are not exactly known but only approximated using the modified Debye-Hu¨ckel term in Pitzer’s equation. For constant temperature T and constant overall molality of HCl (m ˜ HCl,II) measurements were performed at different overall molalities of MDEA (m ˜ MDEA). The true equilibrium constant for the dissociation of MDEAH+ is determined in a two-step extrapolation procedure:
lim ˜ MDEA,m ˜ HCl,II)} ) Kexp(T,m ˜ HCl,II) {Kexp(T,m m ˜ HCl,II)const m ˜ MDEAf0 (10) lim Kexp(T,m ˜ HCl,II) ) K(T) m ˜ HCl,IIf0
Figure 2. Influence of the overall molality of MDEA on the experimental results for ln Kexp. Table 2. Extrapolated Experimental Results for the Dissociation Constant of MDEAH+ ht/°C
109K
(∆ h K/%
5.12 15.09 25.08 35.00 44.94 54.98 64.94 75.00 85.09 94.95
1.080 1.787 2.798 4.454 6.740 10.40 15.52 23.13 32.82 48.41
1.65 2.03 1.03 1.18 0.89 0.97 0.88 2.39 2.13 2.13
(11)
˜ HCl,II j 0.01 mol/ However, if m ˜ HCl,II is small enough (e.g. m kg), the second extrapolation is not necessary. Experimental Section For the EMF measurements a high-resolution electrometer (Metrohm, pH Voltmeter, type 713, resolution 0.1 mV) with a very large input resistance (>1013 Ω) was used. A glass pH electrode (Metrohm, separate pH glass electrode with inner (Ag, AgCl) reference electrode, type 6.0133.100) was combined with a (Ag, AgCl) electrode of the thermal type (Sensortechnik Meinsberg, type SG, specially manufactured). The electrolyte solutions were saturated with AgCl to avoid the dissolution of AgCl from the (Ag, AgCl) electrode. A platinum electrode (Sensortechnik Meinsberg, hydrogen electrode, type MC30), which was also immersed in the electrolyte solution, was used for electrostatic and electromagnetic shielding of the cell. When not in use, the electrodes were stored in distilled water, which was also saturated with AgCl. Electrodes have to be washed before they are transferred from one cell to the other. Washing was accomplished by carefully rinsing an electrode first with distilled water and then transferring it through five glass bottles, each containing the same solution as the cell into which the electrode was supposed to be immersed for the EMF measurement. The cells were completely filled
with the electrolyte solution, hermetically sealed, and mounted in a thermostatically controlled bath. The temperature was measured by resistance thermometry (estimated uncertainty: (0.05 K). A constant electrometer reading was attained about 15-30 min after the electrodes had been transferred into a cell. Substances. MDEA (Merck Schuchardt, N-methyl-2,2′iminodiethanol for synthesis, purity 98.4 mass % according to analyze certification (GC), water content less than 0.2 mass %, other impurities unknown) and HCl (Merck, HCl Ultrapur) were used without further purification. Water was deionized and further purified by vacuum distillation. HCl stock solutions were gravimetrically analyzed with a relative uncertainty of (0.05%. Results Measurements were performed from 278 K to 368 K at 10 K intervals. The overall molality of HCl in both cells ˜ HCl,II ≈ 0.01 was held constant in all solutions (m ˜ HCl,I ≈ m mol/kg). The overall molality of MDEA was between 0.025 mol/kg and 1 mol/kg. The experimental results for the ˜ HCl,I) and EII(T,m ˜ MDEA,m ˜ HCl,II) EMF-measurements EI(T,m are given in Table 1 together with the preliminary (i.e. not extrapolated) numbers for the dissociation constant of MDEAH+ (Kexp). In Figure 2, ln Kexp is plotted against the overall molality of MDEA. Extrapolations were done by linear regression. In Table 1 superscript * denotes results
1510 Journal of Chemical and Engineering Data, Vol. 41, No. 6, 1996 Table 3. Comparison of Correlated Values with Literature Data 109K
a
T/K
this work
293.0 298.15 298.2 299.9 303.0 308.15 311.0 318.0 318.15 333.0 333.15 333.2 361.0 388.0 422.1
2.21 ( 0.03 2.81 ( 0.03 2.82 ( 0.03 3.05 ( 0.03 3.51 ( 0.04 4.42 ( 0.05 5.01 ( 0.06 6.78 ( 0.06 6.82 ( 0.06 12.62 ( 0.12 12.70 ( 0.12 12.73 ( 0.12 37.06 ( 0.79 95.8a 286.4a
Schwabe et al. (1959)
Kim et al. (1987)
3.07
3.02 ( 0.24
Oscarson et al. (1989)
Littel et al. (1990) 1.74 ( 0.08
2.76 ( 0.20 2.99 ( 0.21 3.25 ( 0.15 4.89 5.00 ( 0.36 5.30 ( 0.25 7.57 10.4 ( 0.5 13.8 12.9 ( 0.9 38.0 ( 2.7 97.9 ( 7.0 287.5 ( 20.6
Extrapolated values.
Table 4. Comparison of Reaction Standard State Properties with Literature Data this work ∆rG°m/(kJ/mol) ∆rH°m/(kJ/mol) ∆rS°m/(J/(mol‚K)) ∆rC°P,m/(J/(mol‚K))
48.81 ( 0.03 34.0 -49.6 91.3
Schwabe et al. (1959)
Kim et al. (1987)
Oscarson et al. (1989)
48.59 ( 0.17 35.7 -43.2
48.63 ( 0.17 35.2 ( 0.3 -45.1 ( 1.6
48.86 ( 0.18 35.2 ( 1.0 -45.8 ( 4.0 73.3
of experiments where temperature deviated by more than (0.15 K from the corresponding isotherm. Those results were not considered in the extrapolation and are not shown in Figure 2. Average temperatures (th) and chemical equilibrium constants as resulting from the linear extrapolation (K) are given in Table 2. Additionally, the relative deviation ((∆ h K) is given in Table 2. It represents the average deviation between the direct experimental data and the linear fit and thus provides insight into the quality of the extrapolation. ∆ h K is predominantly below 2% and at maximum smaller than 2.4%. The final results for the chemical equilibrium constant (on molality scale) are correlated by
ln K )
-819.7 - 79.474 + 10.9756 ln(T/K) (T/K)
(12)
with an average deviation of 0.9% (0.004) and a maximum deviation of 2% (0.009) in K (pK). Those deviations have to be compared with the experimental uncertainty. The scattering of the results for Kexp is due to uncertainties in EI - EII of about (0.5 mV. A systematic error can result from impurities in MDEA. In the evaluation of the extrapolated data no impurities were taken into account. However, when MDEA samples are treated as a mixture of 98.4 mass % of MDEA and 1.6 mass % of water, the numerical values for K are reduced by about 2%. Comparison with Literature Data Experimental results for the chemical equilibrium constant for the dissociation of MDEAH+ have been reported by Schwabe et al. (1959) at temperatures between 298.15 K and 333.15 K, Kim et al. (1987) at 298.15 K, Oscarson et al. (1989) at temperatures between 298.2 K and 422.1 K, and Littel et al. (1990) at temperatures between 293 K and 333 K. The results of Schwabe et al., Oscarson et al., and Littel et al. are based on a different reference state (using molarity scale). They were converted to the reference state used in the present work by
K)
1 c° K FW m° c
( )
(13)
where FW is the mass density of pure water which was taken from Saul and Wagner (1987). In Table 3 correlated values from the present work, including experimental uncertainties, are compared with literature data. For the results by Schwabe et al. experimental uncertainties were estimated to ∆pK ≈ (0.03. Kim et al. give ∆pK ) (0.03. Oscarson et al. give ∆pK ) (0.03 at 298.2 K. Littel et al. give ∆pK ) (0.02. Figure 3 shows chemical equilibrium constants from the present work in comparison with literature data. Values from the present work agree with the results of Schwabe et al. within about 10%; however, there is a systematic deviation as the results by Schwabe et al. are always larger than those from the present work. The value reported by Kim et al. agrees very well with the value of Schwabe et al. The data reported by Littel et al. are always smaller than those from the present work. The differences scatter from about 7% up to 22%. The results of the present work are in excellent agreement with the results by Oscarson et al. Differences are within the experimental uncertainties given by Oscarson et al., also at temperatures above 368 K, where the results of the present work are extrapolated. Applying the well-known thermodynamic relations:
∆rGm ) -RT ln K
(14)
d ln K d(1/T)
(15)
∆rHm ) -R
∆rSm ) (∆rHm - ∆rGm)/T ∆rCP,m )
d∆rHm dT
(16) (17)
the change of standard state properties (T ) T° ) 298.15 K) for the dissociation of MDEAH+ in water were calculated from eq 12 resulting in ∆rG°m ) 48.81 kJ/mol, ∆rH°m ) 34.0 kJ/mol, ∆rS°m ) -49.6 J/(mol‚K), ∆rCP,m ) const. ) 91.3
Journal of Chemical and Engineering Data, Vol. 41, No. 6, 1996 1511
Figure 3. Dissociation constant of MDEAH+.
J/(mol‚K). These standard state properties are compared to literature data in Table 4. For that comparison the experimental results for the equilibrium constant of Schwabe et al. and of Oscarson et al. were approximated by
Schwabe et al. ln K )
-4794.1 + 6.018 - 1.6744 ln(T/K) (18) (T/K)
Oscarson et al. -1609.2 ln K ) - 64.506 + 8.8096 ln(T/K) (19) (T/K) As can be seen from Table 4 numbers for ∆rG°m and ∆rH°m from all sources nearly agree within the sum of experimental uncertainties with the results of the present work. The number for ∆rS°m from the present work favorably agrees with the result from Oscarson et al., while, as was to be expected, the largest deviation is observed for ∆rCP,m. However, considering the experimental uncertainies the agreement with the ∆rCP,m results from the work of Oscarson et al. still seems to be reasonable.
k ) Boltzmann constant K ) equilibrium constant for the dissociation reaction of MDEAH+ KW ) equilibrium constant for the dissociation reaction of water mi ) true molality of component i m ˜ i ) overall molality of component i m° ) reference molality (m° ) 1 mol/kg) MW ) molar mass of water in g/mol M* W ) see eq 21 ni ) true number of moles of component i n˜ i ) overall number of moles of component i NA ) Avogadro constant pK ) -log10 K Q1, ..., Q5 ) coefficients for the temperature dependence of the H+/Cl- interaction parameters R ) universal gas constant S ) entropy t ) Celsius temperature T ) absolute temperature zi ) number of charges of component i Greek Letters R ) constant in Bij expression βij(0), βij(1) ) binary interaction parameters in Pitzer’s equation ∆ ) difference ∆r ) molar reaction change 0 ) vacuum permittivity W ) relative dielectric constant of water γ* i,m ) activity coefficient of component i normalized to infinite dilution (on molality scale) µi ) chemical potential of component i ν+, ν- ) number of cations and anions in electrolyte MX FW ) saturated liquid mass density of pure water Subscripts
Conclusions The chemical equilibrium constant for the dissociation of MDEAH+ in aqueous solution was determined from EMF measurements at temperatures from 278 K to 368 K. The results extend the temperature region of literature data which ranges from about 293 K to 422 K. New data agree best with the results reported by Oscarson et al. (1989). Differences between both sources are within the experimental uncertainties reported by those authors. Nomenclature
ai ) activity of component i Aφ ) Debye-Hu¨ckel parameter b ) constant in modified Debye-Hu¨ckel expression Bij ) second virial coefficient in Pitzer’s equation (for interactions between species i and j) c° ) reference molarity (c° ) 1 mol/L) Cijk ) third virial coefficient in Pitzer’s equation (for interactions between species i, j, and k) CΦ ) see eq 32 CP ) heat capacity e ) charge of proton E ) electromotive force E° ) standard potential f ) modified Debye-Hu¨ckel term F ) Faraday constant G ) Gibbs energy H ) enthalpy Im ) ionic strength (on molality scale)
c ) on molarity scale exp ) experimental i, j, k ) component i, j, k m ) on molality scale r ) reaction I, II ) cell I, cell II Superscripts E ) excess * ) normalized to infinite dilution ∞ ) infinite dilution in pure water ° ) reference state, standard state Abbreviations aq ) in aqueous solution EMF ) electromotive force liq ) liquid MDEA ) n-methyldiethanolamine MX ) general electrolyte M ) cation M X ) anion X s ) solid W ) water Appendix 1. Brief Outline of Pitzer’s Model Pitzer’s equation (1973) for the excess Gibbs energy of an aqueous, salt-containing system is
1512 Journal of Chemical and Engineering Data, Vol. 41, No. 6, 1996
GE nWRTM* W
) f(Im) +
mi mj
∑∑
i*Wj*Wm°
m°
The activity of water follows from the Gibbs-Duhem equation:
Bij(Im) + mi mj mk
∑ ∑ ∑ m° m° m°
Cijk (20)
i*Wj*Wk*W
where M* W is defined as
M* W )
MWm° g 1000 kg
(21)
where Im is the ionic strength:
Im )
1
∑z 2 i
(22)
( )
2
i
mi
(23)
m°
and b ) 1.2. Aφ is the Debye-Hu¨ckel parameter for the osmotic coefficient:
(
2
1 e 2πNAFWm° 3x 4π0WkT
Aφ )
)
(24)
2 (1) βij [1 - (1 + RxIm) exp(-RxIm)] R2Im (25)
where βij(0) and βij(1) are binary interaction parameters. For the case considered here, R ) 2.0. Cijk are ternary interaction parameters. The chemical potential of each dissolved species is normalized to infinite dilution in pure water on the molality scale:
µi )
∞ µi,m (T,p)
+ RT ln ai
mi mj mk
ijk
i*Wj*Wk*W
mi
-
∑ m°
i*W
}
(30)
The following section reports relations for the temperature dependence of ion interaction parameters H+/Cl(Pitzer, 1987). T is the temperature in Kelvin and TR ) 298.15 K. p is the pressure in bars and is set to 1. F is the mass density of pure water at the particular p and T (in kg/m3). In the present work, F was set equal to the saturated liquid density of pure water (FW).
f(T) ) Q1 + Q2 ln(F/997) + Q3(F - 997) + Q4(T - TR) + Q5(p - 1) (31)
Q1 Q2 Q3 Q4 Q5
(0) βH +,Cl-
(1) βH +,Cl-
CΦ
0.176 90 -9.140 × 10-2 0 -4.034 × 10-4 6.20 × 10-6
0.2973 16.147 -1.7631 × 10-2 0 7.20 × 10-5
0.724 × 10-3 0 0 -6.072 × 10-5 0
For systems containing a single general electrolyte Mν+Xν-, the binary and ternary parameters involving two or more species of the same sign of charge are usually neglected. The ternary parameters CM,X,X and CM,M,X are usually reported as third virial coefficients CΦ for the osmotic coefficient. Instead of rewriting eqs 29 and 30 in terms of CΦ, we preferred to set CM,X,X to zero and calculated the ternary parameters CM,M,X from numbers reported for CΦ:
1 CH+,H+,Cl- ) CΦ 3
(32)
Literature Cited
ai )
mi γ* m° i,m
(27)
The chemical potential of water is normalized to the pure liquid substance:
µW ) µpure W (T,p)liq + RT ln aW
(28)
The activity coefficient of a dissolved species i is:
[
2 ln γ* i,m ) -Aφzi
∑
∑∑
∑ ∑ ∑ m° m° m°C
(26)
where
2
exp(-RxIm)] - 2
1.5
W is the relative dielectric constant of water and was taken from Bradley and Pitzer (1979). Bij(Im) is the ionic strength dependent second virial coefficient:
Bij(Im) ) βij(0) +
mi mj [βij(0) + βij(1) × ln aW ) M* W 2Aφ i*Wj*Wm° m° 1 + bxIm
Appendix 2. Interaction Parameters for Pitzer's Equation
The function f(Im) is a modified Debye-Hu¨ckel term:
4Im ln(1 + bxIm) f(Im) ) -Aφ b
{
Im1.5
mj
xIm
1 + bxIm
Bij(Im) -
j*Wm°
exp(-RxIm)
]
2 +
zi2 R2Im2
b
[(
1 - 1 + RxIm +
mj mk
∑ ∑ m° m°β
j*Wk*W
]
ln(1 + bxIm) +
(1) jk
+3
mj mk
∑ ∑ m° m°C
j*Wk*W
)
R2 Im × 2
ijk
(29)
Bradley, D. J.; Pitzer, K. S. Thermodynamics of electrolytes. 12. Dielectric properties of water and Debye-Hu¨ckel parameters to 350 °C and 1 kbar. J. Phys. Chem. 1979, 83, 1599-1603. Eisenman, G. Interpretation of pH and Cation Measurement. In Glass Electrodes for Hydrogen and Other Cations, Principles and Practice; Mattlock, G., Band, D. M., Eds.; Marcel Dekker, Inc.: New York, 1967; Chapter 2. Fisher, J. R.; Barnes, H. L. The Ion-Product Constant of Water to 350°. J. Phys. Chem. 1972, 76, 90-99. Kim, J.-H.; Dobrogowska, C.; Hepler, L. G. Thermodynamics of ionization of aqueous alkanolamines. Can. J. Chem. 1987, 65, 17261728. Kuranov, J.; Rumpf, B.; Smirnova, N. A.; Maurer, G. Solubility of Single Gases Carbon Dioxide and Hydrogen Sulfide in Aqueous Solutions of N-Methyldiethanolamine in the Temperature Range 313-413 K at Pressures up to 5 MPa. Ind. Eng. Chem. Res. 1996, 35, 1959-1966. Littel, R. J.; Bos, M.; Knoop, G. J. Dissociation Constants of Some Alkanolamines at 293, 303, 318, and 333 K. J. Chem. Eng. Data 1990, 35, 276-277. Oscarson, J. L.; Wu, G.; Faux, P. W.; Izatt, R. M.; Christensen, J. J. Thermodynamics of protonation of alkanolamines in aqueous solution to 325 °C. Thermochim. Acta 1989, 154, 119-127. Pitzer, K. S. Thermodynamics of electrolytes. 1. Theoretical basis and general equations. J. Phys. Chem. 1973, 77, 268-277. Pitzer, K. S. A thermodynamic model for aqueous solutions of liquidlike density. Rev. Mineral. 1987, 17, 97-142.
Journal of Chemical and Engineering Data, Vol. 41, No. 6, 1996 1513 Pitzer, K. S. Experimental Methods: Potentiometric. In Activity Coefficients in Electrolyte Solutions, 2nd ed.; Butler, J. N., Roy, R. N., Eds.; CRC Press: Boca Raton, Ann Arbor, Boston, London, 1991; Chapter 4 (ISBN 0-8493-5415-3). Saul, A.; Wagner, W. International equations for the saturation properties of ordinary water substance. J. Phys. Chem. Ref. Data 1987, 16, 893-901. Schwabe, K.; Graichen, W.; Spiethoff, D. Physicochemical investigations on alkanolamines. Z. Phys. Chem. (Munich) 1959, 20, 68-82 (in German).
Serjeant, E. P.; Warner, A. G. Accuracy of the Hydrogen Ion Selective Glass Electrode. Anal. Chem. 1978, 50, 1724-1727.
Received for review April 18, 1996. Accepted August 22, 1996.X
JE960141+ X
Abstract published in Advance ACS Abstracts, October 1, 1996.
