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Copper(II)–Ammonia Complexation Equilibria in Aqueous Solutions at Temperatures from 30 to 250◦ C by Visible Spectroscopy Liliana N. Trevani, Jenene C. Roberts, and Peter R. Tremaine * Received February 21, 2001; revised April 30, 2001 The spectra of copper(II)–ammonia solutions in 2 mol-kg−1 NH4 NO3 (aq) were recorded as a function of pH with a new UV–visible flow cell, capable of operating at conditions up to 325◦ C and 300 bars. Equilibrium constants for the formation of copper(II)–ammonia ◦ complexes Cu(NH3 )2+ n , 1 ≤ n ≤ 4, from 30 to 150 C were determined by evolving factor analysis and nonlinear least-squares regression. Measurements at higher temperatures were limited by thermal decomposition of NH4 NO3 (aq). The formation constants of Cu(NH3 )2+ n decrease with temperature, consistent with extrapolations of literature data from measurements below 100◦ C. Measurements above 150◦ C were carried out in 0.5 mol-kg−1 CF3 SO3 H (aq), at the very high ammonia concentrations required to avoid the precipitation of CuO(s). The spectra are consistent with Cu(NH3 )2+ 4 as the predominant species, based on extrapolations of peak maxima and molar absorptivities from lower temperatures. Shifts in the spectra of Cu2+ and the Cu(NH3 )2+ n species to higher wavelength and increases in molar absorbance with increasing temperature are discussed in terms of the structure of the complexes. KEY WORDS: Stability constant; visible spectroscopy; high-temperature aqueous solution; copper ammonia complexes; factor analysis.

1. INTRODUCTION Modern drum boilers in high-performance thermal generating stations operate at temperatures up to 360◦ C under steam-saturation pressure. Although the bulk-water concentrations of impurities and chemical additives are controlled at part-per-billion levels, there is sufficient corrosion of copper alloys in the feedtrain to leach small, but significant, concentrations of dissolved copper into the feedwater.(1–3) Under boiler conditions, copper forms volatile complexes, which

Department of Chemistry, Memorial University of Newfoundland, St. John’s, NF, Canada, A1B 3X7. 585 C 2001 Plenum Publishing Corporation 0095-9782/01/0700-0585$19.50/0 °

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plate out on turbine blades as copper deposits. These cause major losses in turbine capability and efficiency. Ammonia is one of several ligands that may be responsible for copper corrosion in the feedtrain (25–150◦ C) and for enhanced solubilities in the boiler (250– 360◦ C). At room temperature, the hydrated copper (II) ion, Cu(H2 O)2+ 6 , is known to form distorted octahedral complexes with up to four molecules of ammonia, and a square pyramidal complex when a fifth molecule of ammonia is coordinated. Complexation takes place by successive displacement of water molecules according to the reaction:(4,5) [Cu(H2 O)6 ]2+ + nNH3 (aq) * ) [Cu(NH3 )n (H2 O)6−n ]2+ + nH2 O,

n = 1–5 (1) Despite the importance of the copper/ammonia system to industrial chemistry and coordination chemistry, only a few studies of the stability constants of the copper(II) complexes Cu(NH3 )2+ n have been carried out as a function of temperature, and all of these have been limited to temperatures below 98◦ C.(4,6–8) Little is known about the complexation behaviour of copper(I) with ammonia.(9) In this work, a new high-temperature, high-pressure spectroscopic flow cell was used to study the equilibria of copper(II)–ammonia complexes at temperatures to 250◦ C. These measurements are part of a broader study involving the development of a large thermochemical database for modeling copper transport in boiler systems,(10) and is intended to be the first in a series of complexation studies under hydrothermal conditions using UV-visible spectroscopy. NH4 NO3 was chosen as the supporting electrolyte to allow direct comparison with low-temperature studies by Bjerrum(4) and other researchers.(6–8) At temperatures higher than 150◦ C, NH4 NO3 was found to undergo thermal decomposition and nitrate was replaced by the non-complexing, thermally stable trifluoromethanesulfonate (triflate) anion, CF3 SO− 3. Factor analysis of the experimental absorbance data was used to determine the number of absorbing species, while two different approaches were used to determine the concentration profiles and stability constants for the complexes Cu(NH3 )2+ n (1 ≤ n ≤ 4) — evolving factor analysis (EFA) and nonlinear leastsquares regression (NLSR).(11–14) 2. EXPERIMENTAL 2.1. Materials Stock solutions were prepared from ACS reagent grade NH4 NO3 (Sigma Ultra), Cu(NO3 )2 · 2 1/2 H2 O (Fisher Scientific), and concentrated aqueous HNO3 (BDH) and NH3 solutions (BDH), with boiled, deionized Nanopure water (resistivity > 8 MÄ-cm). The NH3 solution was prepared immediately before use to avoid the presence of dissolved CO2 and standardized either by back-titration of

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an excess of standard HCl with NaOH using methyl orange as indicator(15) or by direct titration of a standard HCl solution, also using methyl orange as indicator.(16) Standard solutions of NaOH were prepared from a carbonate-free 50% solution (Fisher “Certified” ACS) and standardized by titration against potassium hydrogen phthalate using phenolphthalein as indicator.(16) Standard solutions of HCl were prepared from (BDH) ACS reagent-grade concentrated HCl and standardized by titration against freshly prepared and standardized NaOH, using phenolphthalein as indicator.(16) Stock solutions of NH4 NO3 were standardized by boiling with an excess of standard NaOH solution until no more NH3 was released with the steam. The excess NaOH was then determined by potentiometric titration with a standard HCl solution, using methyl red as indicator to confirm the potentiometric end point.(16) Standard solutions of Cu(NO3 )2 were prepared from the commercial product, then titrated with a standard solution of EDTA using Fast Sulphon Black F as indicator.(16) The HNO3 solution used to prepare the stock solution of copper was standardized by titration against a standard solution of NaOH using phenolphthalein as indicator.(16) The stock CF3 SO3 H solution was prepared from 99% trifluoromethanesulfonic acid (Alfa) and standardized by titration against tri(hydroxymethyl)aminomethane (Tris) using methyl red as indicator. 2.2. Instrumentation The high-temperature, high-pressure spectroscopic flow system constructed for this work is similar in concept to that developed by Chlistunoff et al.,(17) in which a high-pressure liquid chromatography (HPLC) injection system is used to pump solutions through a low-volume cell with sapphire windows, which is located in the sample compartment of a UV-visible spectrometer capable of fast acquisition of digitized spectral data. A schematic diagram of the high-pressure flow cell is shown in Fig. 1. Two cells, one constructed from 316 stainless steel (2.00-cm optical path length; 0.4-cm3 volume) and the other from titanium (1.72-cm optical path length; 0.34-cm3 volume), were used in the experiments. The optical path lengths were determined against a 1-cm commercial cuvette using a standard K2 Cr2 O7 solution or the standard copper solutions. The cell was mounted in a two-piece brass oven containing two wells in which Cromalux CIR-20203 120V 200W cartridge heaters were mounted. A coil of stainless steel or titanium HPLC tubing wound aroung a groove cut in the body of the oven served as a preheater. The temperature was controlled to ± 1◦ C using an Omega CN76000 temperature controller and measured by a Chromega-Alomega thermocouple located in the body of the cell. The oven was insulated using a ceramic machinable insulation (Rescor 310, Cotronics Ltd.). The entire insulated cell/oven system was mounted in a small box constructed of brass and aluminum and cooled by internal water

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Fig. 1. Schematic diagram of the high-temperature flow cell: (A) cell body; (B) sapphire window; (C) Teflon seals; (D) bolted end-cap; (E) inlet tube; (F) exit tube; (G) thermocouple; (H) cell compartment.

circulation to maintain the spectrophotometer compartment at room temperature. Independent thermocouples in the body of the cell and in the spectrometer compartment, connected to shut-off systems, provided over-temperature protection. A Varian Cary 50 spectrophotometer (190–1100 nm) interfaced to a 233 MHz Pentium II computer equipped with Cary Win UV Scan Application software was used to record the absorption spectra. The sample injection system, shown in Fig. 2, consisted of a Gilson 305 HPLC piston pump, equipped with a Gilson manometric module (Model 805), that was used to pump water through a six-port titanium valve fitted with a 18-cm3 sample injection loop, then on through a stainless steel or titanium preheater tube (30-cm length and 0.7-mm inner diameter) wrapped around the oven, and into the spectrometer cell. A second loop placed downstream of the cell allowed us to sample the solution after it had passed through the cell. Pressure was controlled by flowing the eluent solution into a pressure vessel equipped with a Tescom back-pressure regulator (Model 26-1700) and pressurized with nitrogen. 2.3. Operational Methods The ammonia concentration in the solutions was varied in a stepwise fashion by adding ammonia to solutions with variable concentrations of copper, but constant ionic strength (approximately 2 mol-kg−1 NH4 NO3 ). The solutions were stable for periods of several days with exception of those with pH values between

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Fig. 2. Schematic diagram of flow injection system: (1) deionized water reservoir; (2) Gilson 305 HPLC pump; (3) Gilson 805 manometric module; (4) six-port titanium valve and 18-cm3 sample injection loop; (5) preheater; (6) thermocouple; (7) aluminum and brass box with circulation of water; (8) ceramic insulation; (9) cartridge heaters; (10) cell sample chamber; (11) cell body; (12) end cap and retaining bolts; (13) six-port titanium valve and 10-cm3 sample loop; (14) N2 cylinder; (15) low-pressure waste container; (16) Tescom 26-1700 back-pressure regulator; (17) high-pressure waste vessel.

5 and 6, where a visible precipitate of Cu(OH)2 appeared after a few hours, consistent with predictions from our provisional database.(10) To avoid the precipitation of Cu(OH)2 , and to minimize the uptake of atmospheric CO2 , the solutions were prepared immediately before use. A summary of the solutions is given as supplementary information in the Appendix.

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Spectra were obtained at a constant pressure of 45 bar and a sample injection flow rate of 0.2 cm3 -min. At 25◦ C, the spectra showed no flow rate dependence, confirming that equilibrium had been reached. Higher flow rates provided a less favorable signal-to-noise ratio, while lower flow rates enhanced the thermal decomposition of the supporting electrolyte NH4 NO3 , which became severe at about 175◦ C. At temperatures higher than 175◦ C, the spectrum of the ammonium nitrate baseline solutions showed an enhancement in the absorbance at wavelengths lower than 600 nm when the flow rate was decreased, while etching of the sapphire windows caused a progressive and irreversible increase in the baseline at all flow rates. These effects were probably due to the formation of NO− 2 and other nitrogen oxide species from the thermal decomposition of nitrate, which has been reported to occur under hydrothermal conditions by Chlistunoff et al.(17) The formation of precipitate at high temperatures could be readily detected from baseline shifts in the spectrum of water, which were run before and after each injection of a copper solution. When precipitates did form, they were easily redissolved by injecting the baseline solution of supporting electrolyte — either NH4 NO3 or CF3 SO3 H. The thermal decomposition reactions restricted our measurements of the spectra of copper(II) as a function of NH3 in 2.0 mol-kg−1 NH4 NO3 to temperatures below 175◦ C. To extend this work to higher temperatures, we attempted to obtain spectra of the uncomplexed Cu2+ ion and the Cu(NH3 )2+ n complexes in 0.5 mol-kg−1 CF3 SO3 H solutions at temperatures up to 250◦ C. While spectra for aqueous Cu(CF3 SO3 )2 were readily measured, very high ammonia concentrations were required to avoid the precipitation of CuO from solutions of the ammonia complexes at these temperatures, so that it was not possible to obtain spectra of the lower complexes. To determine whether there was appreciable ion pairing with the nitrate ion in the range of temperatures studied, the spectrum of copper(II) ion in a solution of 1.7636 mol-kg−1 NaNO3 + 0.1697 mol-kg−1 HNO3 was recorded at 30, 100, 125, and 150◦ C. This mixture provided a nitrate concentration equivalent to that in the NH4 NO3 solutions while avoiding the high concentrations of acid that can be corrosive at elevated temperatures. The spectrum of the supporting electrolyte solution was used as the baseline correction, except for solutions with high ammonia concentrations for which water was used as a baseline. 2.4. Analysis of Spectra At room temperature, the visible spectra of copper(II) ammonia solutions display maxima in the range 950–550 nm, which correspond to “d–d ” transitions of

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(4,18) (18) the complexes Cu(NH3 )n (H2 O)2+ and Cu(NH3 )2+ The changes 6−n , n = 0–4, 5 . in band shape and molar absorptivity with systematic variations in the copper and ammonia concentrations can be used to derive the stability constants for complex formation by using factor analysis methods.(19) The experimental spectra at elevated temperatures contain a contribution from thermal expansion. According to Beer’s law for a system with several absorbing species k, the absorbance of a solution i at the wavelength j is proportional to the path length b (cm), the molar concentrations Ci,k (mol-dm−3 ), and the molar absorptivity εk,j (cm−1 -mol−1 -dm3 ):

Aij = 6bCik εkj

(2)

To convert the molar concentration scale of Beer’s law to the molal scale used as the standard thermodynamic convention for nonisothermal equilibrium constants, the measured absorbances Aij must be corrected for variations in solution density using the expression: Acorrected = Aij / f = 6bm ik εkj ij

(3)

For solutions prepared with an excess of supporting electrolyte, the correction factor f can be assumed to be independent of the other species in solution, so that: f = 1000ρsoln /(1000 + Mw m)

(4)

where Mw , m, and ρsoln are the molecular weight and molality of the supporting electrolyte, and the solution density, respectively. In this work, the density of aqueous NH4 NO3 and CF3 SO3 H was assumed equal to that of a NaCl solution with identical molality, as calculated from the equation of state by Archer,(20) while for solutions with high ammonia concentrations the density was assumed to be equal to that of the NH3 –H2 O mixture,(21) neglecting the contribution of the other species. A summary of the densities and the correction factors adopted to correct the experimental absorption curves is given in Tables I and II. Because the experiments were carried out at different total copper concentrations, in two different cells, and at different temperatures, it is more convenient to compare the results of individual experiments by expressing the absorption curves as extinction coefficients defined as: εij0 = Aij /{ f · bm(Cu)total }

(5)

where m(Cu)total represents the total copper molal concentration in solution i. The number of absorbing species in each solution was determined from the corrected absorbance spectra at each temperature by singular value decomposition

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Table I.

t(◦ C)

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Density of NaCl Solutions, Concentration Correction Factors, and Ionization Quotients of Ammonia Used in the Calculations as a Function of Temperature at 45 bar m(NaCl) (mol-kg−1 )

NaCl density (kg-dm−3 )

fcorrection factor (dm−3 )

log(Q ion )

0.02 mol-kg−1 Cu(NO3 )2 in 2.0 mol-kg−1 NH4 NO3 30 100 125 150

2.0 2.0 2.0 2.0

1.0719 1.0328 1.0148 0.9950

0.9240 0.8902 0.8748 0.8577

9.37 7.63 7.14 6.70

0.01 and 0.05 mol-kg−1 Cu2+ in 0.4826 mol-kg−1 CF3 SO3 as triflic acida 30 100 125 150 200 225 250

0.5 0.5 0.5 0.5 0.5 0.5 0.5

1.0174 0.9796 0.9609 0.9397 0.8896 0.8601 0.8268

0.9432 0.9081 0.8908 0.8712 0.8247 0.7974 0.7665

0.02 mol-kg−1 Cu(NO3 )2 in a solution 1.76 mol-kg−1 NaNO3 and 0.17 mol-kg−1 HNO3 30 100 125 150

1.9 1.9 1.9 1.9

1.0685 1.0294 1.0114 0.9915

0.9209 0.8872 0.8717 0.8545

a Prepared by dissolving 0.01 to 0.05 mol-kg−1

Cu(OH)2 in 0.4826 mol-kg−1 CF3 SO3 H(aq). The same correction factor was adopted for all solutions.

(SVD) of the data matrix,(22) using the commercial software SPECFIT (Spectrum Software Associates). At 30 and 150◦ C, where the highest numbers of spectra were obtained, (13,14) was used to estimate the species distribution as a function of the pH EFA Table II. Properties of Aqueous Ammonia Solutions at 45 bar a Ammonia molality t(◦ C)

3.7

mol-kg−1

7.7 mol-kg−1

14.5 mol-kg−1

Density/(kg-dm−3 ) 200 250

0.8307 Two-phase

0.8036 0.0227

0.7561 0.0222

fcorrection factor /dm−3 200 a From

0.7815 Ref. 21.

0.7104

0.6064

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without assuming a priori any chemistry model. The concentration profiles were constructed from Beer’s law and simple chemical rules, such as nonnegativity of concentrations. The stability constants were then calculated by assigning each concentration profile to a copper complex Cu(NH3 )2+ n consistent with the dependence of the concentration profiles on the pH. At 30◦ C, the concentration of free NH3 was calculated from the measured pH and the total molality of ammonia ◦ (NH3 + NH+ 4 + complexed ammonia). At 150 C, an iterative procedure was used, in which the initial pH estimate was based on chemical equilibrium calculations using the extrapolated stability constant data in Ref. 10. The stability constants at 30, 100, 125, and 150◦ C were also calculated by using the nonlinear least-squares regression routine (NLSR) included in SPECFIT software. The initial estimated stability constants were refined using the Marquardt algorithm to minimize the least-squares residuals between the experimental data and the model system.(11,12) Again, the experimental pH at 30◦ C and estimated pH from our extrapolated stability constants for the copper ammonia equilibria at high temperature(4,6,7) were used in the calculations. The ionization constant of aqueous ammonia was taken from Hitch and Mesmer.(23) 3. RESULTS −1 The spectra of uncomplexed copper(II) ion, Cu(H2 O)2+ 6 , in 0.5 mol-kg ◦ CF3 SO3 H at temperatures between 30 and 250 C are shown in Fig. 3. These spectra are characterized by a small enhancement and red shift in the maximum of absorption as the temperature increases. The spectra of copper(II) in CF3 SO3 H, NH4 NO3 , and the mixed solution of (NaNO3 + HNO3 ) at 30 and 150◦ C are compared in Figs. 4a and b. At 30◦ C, the similarity between the spectra in NH4 NO3 and NaNO3 is an indication that there is no significant complexation between copper(II) and ammonia under these conditions, although the differences between these spectra and the spectrum in CF3 SO3 H must be taken as an indication of complexation between copper(II) and the nitrate ion. At 150◦ C, appreciable differences between the spectra in all three media were observed, as shown in Fig. 4b. Figures 5a and b show the spectra of copper(II) in ammonia solutions at 30 and 150◦ C, respectively. Here, the principal feature is the shift toward lower wavelengths and higher intensities as the molality of free NH3 was increased. At room temperature, these systematic changes in the spectra are known to correspond to the octahedral hexaquocomplex, Cu(H2 O)2+ 6 , and the stepwise formation of the (18) At 150◦ C, the shapes of the spectra are similar, ammonia complexes Cu(NH3 )2+ n . but slightly red-shifted toward higher wavelengths. Although the absorbance of the ammonium nitrate solutions was very stable, the addition of increasing amounts of NH3 to the copper-containing solutions caused a small peak to emerge between 350 and 400 nm in some of the spectra taken

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Fig. 3. Absorption spectra of copper(II) in 0.4826 mol-kg−1 CF3 SO3 H from bottom to top: 30, 100, 125, 150, 225, and 250◦ C.

at 150◦ C, as shown in Fig. 5c. These spectra were discarded since the presence of this band may indicate an increase in the rate of NH4 NO3 decomposition, perhaps catalyzed by the presence of copper. The changes in the spectrum of copper(II) with increasing temperature are shown as a function of temperature in Fig. 6 for solutions with identical total copper concentrations. Figure 6a shows spectra for NH3 -rich solutions in which ◦ Cu(NH3 )2+ 4 is the principal complex at 30 C, while Fig. 6b shows spectra for 2+ solutions in which Cu and the lower complexes predominate. The similarities in the spectra at the highest and lowest temperatures, indicate that the principal 2+ in Fig. 6b, must also be present species at 30◦ C, Cu(NH3 )2+ 4 in Fig. 6a and Cu ◦ at 150 C. Figure 7 shows the spectrum of copper(II) in CF3 SO3 H at 200◦ C with NH3 molalities equal to 3.7, 7.7 and 14.5 mol-kg−1 . The higher absorbance and shift in the maximum to lower wavelengths relative to Cu2+ clearly indicate the presence of complexes. At lower concentrations of NH3 , the formation of CuO(s) could not be avoided, even at total copper molalities as low as 0.005 mol-kg−1 . The presence of CuO(s) was confirmed by powder X-ray diffraction of the solid deposited over the windows.

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Fig. 4. Absorption spectra of copper(II) in (1) 0.4826 mol-kg−1 CF3 SO3 H, (2) 1.7636 mol-kg−1 NaNO3 + 0.1697 mol-kg−1 HNO3 , and (3) 2 mol-kg−1 NH4 NO3 at 30 and 150◦ C.

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Fig. 5. Absorption spectra of Cu(NO3 )2 in 2 mol-kg−1 NH4 NO3 and variable concentrations of NH3 (listed in the Appendix) at a flow rate of 0.2 cm3 -min−1 and 45 bar at: (a) 30◦ C, (b) 150◦ C, and (c) low-wavelength region at 150◦ C with and without decomposition.

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Fig. 5. Continued.

At 250◦ C, the precipitation of CuO(s) also occurred at very high NH3 concentrations. A typical series of spectra is plotted in Fig. 8, showing the increases in absorbance due to light-scattering effects as a function of time when a solution of 0.01 mol-kg−1 Cu(CF3 SO3 )2 in 7.7 mol-kg−1 NH3 (aq) was pumped through the cell.

4. DISCUSSION 4.1. The Chemistry Model From the experimental results in Section 3, it is clear that a rigorous chemistry model must include at least the contributions of the copper(II)–ammonia com2−n plexes Cu(NH3 )2+ n and the copper(II)–nitrate complexes Cu(NO3 )n , according to Eqs. (6–9). 2+ * Cu(NH3 )2+ n (aq) + NH3 (aq) ) Cu(NH3 )n+1 (aq),

n = 0–4

£ ¤±© £ ¤ ª m Cu(NH3 )2+ Q ln = m Cu(NH3 )2+ n (aq) · m[NH3 (aq)] n+1 (aq)

(6) (7)

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Fig. 6. Absorption spectra of copper(II) as a function of temperature for solutions with approximately: (a) 0.02 mol-kg−1 Cu(NO3 )2 , 2.0 mol-kg−1 NH4 NO3 , and 0.5 mol-kg−1 NH3 and (b) 0.02 mol-kg−1 Cu(NO3 )2 , 2.0 mol-kg−1 NH4 NO3 , and 0.04 mol-kg−1 NH3 . Temperatures (◦ C) are: (1) 30, (2) 100, (3) 125, and (4) 150.

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Fig. 7. Absorption spectra of 0.01 m Cu(CF3 SO3 )2 in water and aqueous NH3 solutions at 200◦ C. Molarities of NH3 are: (a) 3.7 mol-kg−1 , (b) 7.7 mol-kg−1 , and (c) 14.5 mol-kg−1 .

2−n * Cu2+ (aq) + nNO− 3 (aq) ) Cu(NO3 )n (aq),

n = 0–2

£ ¤± − 2+ n βCu-NO3 ,n = m Cu(NO3 )2−n n (aq) {m[Cu (aq)] · m[NO3 (aq)] }

(8) (9)

To determine the overall stability constants for the Cu(NH3 )2+ n species, Eq. (7), the stability constants for the copper nitrate complexation reactions must be known. To date, only low-temperature data have been reported in the literature.(24,25) Smith and Martell(24) have compiled critically evaluated values for the first and second stability constants of reaction (8) at 25◦ C and ionic strength I = 1M, log(βCu-NO3 ,1 ) = −0.01 and log(βCu-NO3 ,2 ) = −0.6. The enthalpy and entropy −1 o and of the first step are also tabulated as 1r HCu -NO3 ,1 = −4.1kJ-mol −1 −1 o 1r SCu-NO3 ,1 = −14 J-K -mol . If these data are used to make a rough estimate of the formation constant of Cu(NO3 )+ at elevated temperatures, the percentage of

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Fig. 8. Spectra of copper(II) in 3.7 mol-kg−1 NH3 at 250◦ C showing the increase in absorbance associated with the precipitation of CuO(s) over time.

total copper that is complexed by nitrate is almost constant between 30 and 150◦ C, and approximately equal to 50%. The experimental spectra in Figs. 4a and b are consistent with this estimate, since the difference in the maximum absorptivity of copper(II) between media with and without nitrate is almost independent of temperature (1εmax = 2 cm−1 -mol−1 -dm3 at 30◦ C, and 1εmax = 5 cm−1 -mol−1 -dm3 at 150◦ C). In their potentiometric study, Isaev et al.(7) also reported that effect of nitrate on the stability constants for the formation of copper(II) ammonia complexes was independent of temperature from 10 to 98◦ C at NH4 NO3 concentrations up to 6 mol-dm−3 . Because reaction (6) involves NH3 (aq), the chemistry model must also include the ionization of ammonia, shown in Eq. (10). Equilibrium quotients for

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the ionization of ammonia taken from Hitch and Mesmer(23) were rewritten in the form of Eq. (11) using the dissociation quotient of water from Sweeton et al.(26) The values are summarized in Table I.

Q ion

+ NH3 (aq) + H+ (aq) * ) NH4 (aq) £ ¤± + = m NH+ 4 (aq) {m[NH3 (aq)] · m[H (aq)]}

(10) (11)

The proposed model relies on the assumption that contributions from other association equilibria can be ignored. Preliminary calculations based on our provisional thermodynamic database(10) showed that the hydrolysis of copper(II), Eq. (12), has a negligible effect on ammonia complexation at the NH4 NO3 molalities used in this work. + Cu2+ (aq) + NH3 (aq) + H2 O * ) Cu(OH)+ (aq) + NH4 (aq)

(12)

Likewise, calculations based on high-temperature ionization constants for nitric acid(27,28) showed that the contributions of undissociated HNO◦3 up to 150◦ C are insignificant, even in the 2 mol-kg−1 NH4 NO3 solutions at the lowest pH values. The contribution of nitrate ion-pairing equilibria to form the species NH4 NO◦3 could not be estimated, since there are no published data for these equilibria at high temperature. Therefore, as in previous work,(4–7) it was assumed to be small. The mass and charge balance equations on which the model is based are summarized in Eqs. (13–16). m[Cu2+ (aq)] +

4 2 X £ ¤ X £ ¤ m Cu(NH3 )2+ m Cu(NO3 )2−n n (aq) + n (aq) n=1

n=1

= m(Cu)total

(13)

m[NH+ 4 (aq)] + m[NH3 (aq)] +

4 X

£ ¤ n · m Cu(NH3 )2+ n (aq)

n=1

=

m[NH+ 4 (aq)]initial

m[NO− 3 (aq)] +

2 X

+ m[NH3 (aq)]initial = m(ligand)total

(14)

£ ¤ − n · m Cu(NO3 )2−n n (aq) = m(NO3 )total

(15)

n=1

m[H+ (aq)] + 2

4 X £ ¤ + + m Cu(NH3 )2+ n (aq) + m[Cu(NO3 ) (aq)] + m[NH4 (aq)] n=0

=

m[NO− 3 (aq)]

+ m[OH− (aq)]

(16)

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4.2. Concentration Profiles and Stability Constants from Evolving Factor Analysis (EFA) In the course of this work, spectra were obtained from over 250 solutions, of which 116 were selected for the final analysis. The highest numbers of spectra were obtained at 30◦ C (24 spectra) and 150◦ C (54 spectra). Because the results at 30◦ C included experimental equilibrium pH measurements, they could be analyzed in detail and compared with studies by other workers to test our methodology. To avoid biasing the fits to our high-temperature data by assuming a specific speciation model, EFA was used to estimate the molar absorptivities and the concentration profiles of the statistically significant copper(II) species. Conditions favoring the formation of the species Cu(NH3 )2+ 5 at room temperature were deliberately excluded from our analysis by limiting the pH range, in an attempt to reduce the number of species present in the solutions. At 30◦ C, EFA was able to identify either four or five significant factors, depending on the range of wavelengths and the number of spectra considered in the analysis. The five-factor model was in good agreement with the species dis2+ tribution given by other authors for Cu2+ , Cu(NH3 )2+ , Cu(NH3 )2+ 2 , Cu(NH3 )3 , 2+ and Cu(NH3 )4 . When working with a constant nitrate concentration as backspecies could not be discriminated. ground electrolyte, the Cu2+ and Cu(NO3 )2−n n species by introAn attempt to differentiate between the Cu2+ and Cu(NO3 )2−n n ducing the spectrum of Cu(CF3 SO3 )2 into the data file only resulted in minor changes in the molar absorptivities and the concentration profiles of the individual species, but the number of colored species identified by EFA did not change. Consequently, the stability constants were estimated by adopting the spectrum of copper(II) in 2 mol-kg−1 NH4 NO3 as the spectrum of free Cu2+ , with the reare included with activity coefficient sult that ion pairs of the form Cu(NO3 )2−n n effects. EFA was able to identify only four statistically significant factors from the spectra at 150◦ C, despite their similarity to the spectra at 30◦ C (Figs. 5a and b). Additional calculations showed that when a fifth factor was included in the model, a new species appeared in the pH region corresponding to Cu(NH3 )2+ 2 , although its contribution was low and its spectrum noisy. Since there is no reason to postulate the absence of Cu(NH3 )2+ 2 , it is likely that its spectrum could be represented as a linear combination of the others within the experimental uncertainties in the data and, therefore, was not detected by EFA as a statistically significant species. This problem was also evident when analyzing the experimental data obtained at 30◦ C, regardless of whether four or five factors were used in the EFA treatment. At high temperature, the situation is worse because of the increased experimental noise in the spectra and the lack of experimental pH measurements.

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In an attempt to find conditions where the contribution of Cu(NH3 )2+ 2 could be resolved, the experimental spectra obtained at 150◦ C were divided into two groups based on the four-factor EFA results and the assumptions that (1) only the contributions of Cu2+ , Cu(NH3 )2+ , and Cu(NH3 )2+ 2 were statistically significant in the 2+ 2+ , Cu(NH most acidic solutions, and (2) Cu(NH3 )2+ 3 )3 and Cu(NH3 )4 are the pre2 dominant species at highest pH. Although the number of spectra included in each data set was not enough to reach well-defined, noise-free concentration profiles, the agreement between the spectra of Cu(NH3 )2+ 2 , obtained by fitting the data in each region, was excellent and the species distributions were consistent with each 2+ other. In addition, the spectra of Cu2+ , Cu(NH3 )2+ , Cu(NH3 )2+ 3 , and Cu(NH3 )4 are almost identical to those obtained by applying the four-factor model to the entire set of spectra. The independent four-factor EFA treatments of the acidic and basic solutions yielded well-defined, statistically significant concentration profiles 2+ for the species Cu2+ and Cu(NH3 )2+ , in acid, and Cu(NH3 )2+ 3 and Cu(NH3 )4 , in base. These were used to estimate values of Q11 and Q14 . The results are tabulated in Table III, along with the estimated equilibrium pH, on which the EFA analysis was based,(10) and that calculated from the final fit. As can be seen in Table III, the difference between the estimated pH and that from the fitted model was less than 0.1 pH units for solutions with pH > 4 at 150◦ C. Here, pH is expressed as −log[m(H+ )]. In contrast, differences as high as +1 pH unit were obtained for some of the most acidic solutions. This behavior is due to the low concentrations of free ammonia in the acidic region, which make it necessary to determine the pH by an independent method in order to calculate accurate equilibrium molalities of NH◦3 . Similar differences were also obtained at 30◦ C, when values from the fitted model were compared with estimated pH values, while fits based on the experimental pH yielded much better agreement. The contribution of copper–nitrate ion pairs may also contribute to the uncertainies at low pH. The stepwise stability constants at 30 and 150◦ C were calculated from the concentration profiles given by EFA for the four-factor model, assuming the species 2+ Cu2+ , Cu(NH3 )2+ , Cu(NH3 )2+ 3 , and Cu(NH3 )4 ; and for the five-factor model, 2+ 2+ 2+ 2+ assuming the species Cu , Cu(NH3 ) , Cu(NH3 )2+ 2 , Cu(NH3 )3 , and Cu(NH3 )4 . The concentration of free ammonia was determined from the experimental pH at 30◦ C and from extrapolated pH values at high temperature.(10) The stepwise constants obtained for both temperatures are summarized in Table IV. As expected, at 30◦ C the four- and five-factor models show a reasonable agreement with each other and with previously reported stability constants using NH4 NO3 as background electrolyte.(10) The EFA values for the stepwise stability constants at 150◦ C in Table IV, log(Q 11 ) = 3.28 ± 0.07 and log(Q 14 ) = 1.11 ± 0.16, are higher than the extrapolated values at infinite dilution from Ref. 10, log(Q 11 ) = 3.64 and log(Q 14 ) = 0.71, although the results lie within the expected error limits assocated with the extrapolations.

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Table III.

* Estimated pH and Stability Constants for the Reaction: NH3 (aq) + Cu(NH3 )2+ n (aq) ) −1 NH NO from EFA at 150◦ Ca Cu(NH3 )2+ 4 3 n+1 (aq) in 2 mol-kg

Calculated pHd

Extrapolated pHd

1pH

5.97 5.90 5.75 5.46 5.42 5.16 5.09 4.99 4.94 4.79 4.72 4.54 4.61 4.47 4.51 4.29 3.73 4.36 3.94 3.77 3.97 3.82 3.39 3.39

5.99 5.91 5.76 5.49 5.46 5.21 5.12 5.02 5.01 4.80 4.75 4.62 4.59 4.55 4.52 4.22 3.74 3.51 3.51 3.19 3.16 2.80 2.64 2.44

−0.02 −0.01 −0.01 −0.03 −0.04 −0.05 −0.03 −0.03 −0.07 −0.01 −0.03 −0.08 0.02 −0.08 −0.01 0.07 −0.01 0.85 0.43 0.58 0.81 1.02 0.75 0.95

Q 11

Q 14 Only Cu(NH3 )2+ 4 1.51 (1.51) 1.31 (1.30)c 1.18(1.14)b,c 1.12 (1.09)b,c 0.97 (0.92)c 0.88 (0.86) 1.03 (1.00) 0.89 (0.82) 0.44 (0.43) 0.43 (0.41)

High Cu(NH3 )2+ 2 High Cu(NH3 )2+ 2 High Cu(NH3 )2+ 2 High Cu(NH3 )2+ 2 High Cu(NH3 )2+ 2 3.38 (3.33) 2.54 (3.38) 2.84 (3.26)c 2.81 (3.35)b,c 2.51 (3.30)b,c 2.19 (3.19)c 2.70 (3.21) Only Cu2+

a Values

in parentheses were obtained by using extrapolated pH to calculate the free ammonia concentration. b Solutions with compositions close to the crossing points in the speciation diagram. c Solutions used to estimate the formation constants reported in Table IV. d Expressed as pH = −log [m(H+ )].

Table IV. Estimated Stepwise Stability Constants for the Reaction: NH3 (aq) + 2+ −1 NH NO from EFA * Cu(NH3 )2+ 4 3 n (aq) ) Cu(NH3 )n+1 (aq) in 2 mol-kg t(◦ C)

log(Q 11 )

log(Q 12 )

log(Q 13 )

log(Q 14 )

30 30 150

3.94 ± 0.03a 4.06 ± 0.11b 3.28 ± 0.07a

— 3.37 ± 0.07b —

— 2.52 ± 0.10b —

1.95 ± 0.06a 1.48 ± 0.14b 1.11 ± 0.16a

a Four-factor b Five-factor

model. model.

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4.3. Concentration Profiles and Stability Constants from Nonlinear Least-Squares Regression (NLSR) The EFA analysis presented above yielded stepwise formation constants of ◦ ◦ Cu(NH3 )2+ n for all the species at 30 C, and for n = 1 and n = 4 at 150 C (Table IV). A more robust methodology was needed to obtain accurate values at other temperatures, where the data sets are smaller, and to improve the approximate values for the intermediate species at 150◦ C. Since the species are well defined, NLSR was chosen as an appropriate method to resolve the remaining stability constants and the corresponding heats of reaction. Because a speciation model is assumed, NLSR methods are less susceptible to the greater experimental noise that is inherent in high-temperature measurements; it is also expected to give more satisfactory results when working with the smaller data sets obtained at 100 and 125◦ C. By treating nitrate ion-pair formation as an ionic strength effect, the only unknown formation constants, and, consequently, the only fitting parameters to be optimized by the NLSR procedure, correspond to the stepwise constants Qln in reaction (6). The NLSR algorithm in SPECFIT requires the equilibrium pH of each solution as input. The experimental pH at 30◦ C and extrapolated hightemperature values from our provisional database(10) were used for this purpose in our calculations. The results are listed in Table V. The stability constants determined by NLSR from the 30◦ C data agreed well with the values obtained from EFA using the five-factor model. However, at 150◦ C, a model that included only the 2+ four species Cu2+ , Cu(NH3 )2+ 3 , and Cu(NH3 )4 resulted in stability constants with lower standard deviations and a better correlation matrix than the five-species fit. To obtain meaningful formation constants for Cu(NH3 )2+ 2 , it was necessary to use the spectrum for Cu(NH3 )2+ obtained with EFA by fitting data in the lower pH 2 region (Table III) as a known spectrum in the NLSR fit, before proceeding to fit the five-species model to the experimental data. The optimized cumulative stability * Table V. Estimated Stepwise Stability Constants for the Reaction: NH3 (aq) + Cu(NH3 )2+ n (aq) ) −1 NH NO from NLSR Cu(NH3 )2+ 4 3 n+1 (aq) in 2 mol-kg t(◦ C) 30 30 100 125 125 150 a Four-factor b Five-factor

model. model.

log(Q 11 )

log(Q 12 )

log(Q 13 )

log(Q 14 )

3.96 ± 0.05 4.25 ± 0.15 3.79 ± 0.28 3.12 ± 0.34 3.81 ± 0.08 3.20 ± 0.04

— 3.36 ± 0.40 2.91 ± 0.72 — 2.34 ± 0.22 2.20 ± 0.08

— 2.99 ± 0.54 1.91 ± 0.91 — 1.60 ± 0.33 1.40 ± 0.09

2.07 ± 0.18a 1.80 ± 0.60b 1.67 ± 0.94b 1.30 ± 0.08a 1.04 ± 0.46b 1.22 ± 0.09b

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o for the Table VI. Cumulative Stability Constants, log(βl,n ) and Enthalpies of Reaction, 1r Hl,n Complexation of Cu2+ (aq) by Ammonia in 2 mol-kg−1 NH4 NO3 : Cu2+ (aq) + n NH3 (aq) * ) Cu(NH3 )2+ n (aq)

t(◦ C)

log(β11 )

log(β12 )

log(β13 )

log(β14 )

“Best” experimental stability constants from NLSR 30 100 125 150

4.25 ± 0.15 3.79 ± 0.28 3.81 ± 0.08 3.20 ± 0.04

7.61 ± 0.25 6.70 ± 0.44 6.15 ± 0.14 5.40 ± 0.04

10.60 ± 0.29 8.61 ± 0.47 7.75 ± 0.19 6.80 ± 0.05

12.40 ± 0.31 10.28 ± 0.47 8.79 ± 0.27 8.02 ± 0.04

log(β1,1,298 )

log(β1,2,298 )

log(β1,3,298 )

log(β1,4,298 )

Stability constants, logβ1,n,298 , at 25◦ C This work, Eq. (18) Isaev et al.a

4.35 ± 0.23 4.22 ± 0.01

7.85 ± 0.34 7.97 ± 0.02

10.94 ± 0.33 10.93 ± 0.03

12.82 ± 0.48 13.13 ± 0.04

Species

o 1r H1,1

o 1r H1,2

o 1r H1,3

o 1r H1,4

o /(kJ-mol−1 ) at 25◦ C Cumulative enthalpies of reaction, 1r H1,0

This work, Eq. (8)b Vasil’ev et al.c Isaev et al.d

−17.2 ± 5.9 −22.18 −45 ± 8

−41.59 ± 8.9 −45.2 2(−45 ± 8)

−74.7 ± 8.5 −67.9 3(−45 ± 8)

−88.4 ± 12.5 −95.2 4(−45 ± 8)

= 2 mol-dm, Ref. 7. value over the range 30–150◦ C; and 25–98◦ C, respectively. c No uncertainty estimates cited. From Ref. 6. d Mean value over the range 25 to 98◦ C, respectively; I = 2 mol-dm−3 . From Ref. 7.

aI

b Mean

constants from this five-species treatment, £ ¤ 2+ n βln = m Cu(NH3 )2+ n (aq) /{m[Cu (aq)] · m[NH3 (aq)] }

(17)

and their standard errors are listed in Table VI at 30, 100, 125, and 150◦ C. These values were considered to be our “best” estimates of βln from the experimental spectral data. The corresponding concentration profiles and the molar absorptivities of the individual species from the NLSR fit are plotted in Figs. 9 and 10, respectively. Although differences in the molar absorptivities of the individual species were observed when using EFA or NLSR, the calculated stability constants achieved from each method are in acceptable agreement, as can be seen in Tables IV and V, where the overall stability constants are compared. Those cases where a four-factor model showed lower standard deviations and a better correlation matrix were also included in the Tables. Figure 11 is a plot of the formation constants log(βln ) as a function of reciprocal temperature with error bars corresponding to the standard deviations listed

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Fig. 9. Concentration profiles obtained by NLSR of experimental visible spectra at (◦ C): (a) 30, (b) 125, and (c) 150.

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Fig. 9. Continued.

in Table V. A weighted least-squares fit of the expression: ¡ ¢ o /R (1/298.15 − 1/T ) log(βln,T ) = log(βln,298 ) + [1/ln(10)] 1H298

(18)

yielded estimates of the cumulative formation constants at 25◦ C, log(βln,298 ), and the mean enthalpy change of the cumulative reactions 1r Ho1,n , that can be used to describe the temperature dependence of log(βln,T ). Values for log(βln,298 ) and 1r Ho1,n are listed in Table VI. Since the complexation reaction, Eq. (6), is isocoulombic, Eq. (18) can be expected to yield reasonably accurate extrapolations to temperatures above the range of our measurements. These fitted values, log(β1,n,298 ) = (4.35 ± 0.23), (7.85 ± 0.34), (10.94 ± 0.33), and (12.82 ± 0.48), are in good agreement with the experimental values of Isaev et al.(7) at I = 2 mol-dm−3 , log(β1,n,298 ) = (4.22 ± 0.01), (7.97 ± 0.02), (10.93 ± 0.03), and (13.97 ± 0.04) for n = 1–4, respectively. Our enthalpy values, 1r Ho298,n = (−17.2 ± 5.9), (−41.59 ± 8.9), (−74.7 ± 8.5), and (−88.4 ± 12.5) kJ-mol−1 , are in excellent agreement with calorimetric results at I = 2 mol-dm−3 o recently reported by Vasil’ev and Borodin(6) 1H298,n = −22.18, −45.2, −67.9, −1 and −95.2 kJ-mol for n = 1–4, respectively. Both sets of enthalpy data differ from the mean values obtained by Isaev et al.,(7) from fitting Eq. (18) to

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Fig. 10. Molar absorptivities in agreement with the species distribution shown in Fig. 9 obtained by NLSR of experimental visible spectra at (◦ C): (a) 30, (b) 125, and (c) 150.

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Fig. 10. Continued. o temperature-dependent potentiometric data, 1r H298,n ≈ n(−45 ± 8) kJ-mol−1 . o These more negative values of 1r H298,n arise because these authors reported a more pronounced decrease in the stability constants with increasing temperature than was observed in our work.

4.4. Temperature Dependence of the Spectra The wavelengths of maximum absorption (λmax ) and maximum molar absorptivities (εmax ) of the spectra of copper(II) in triflic acid from Fig. 3 are tabulated in Table VII and plotted in Fig. 12 as a function of temperature. The band shape and the behavior of λmax and εmax are similar to those observed for aqueous Cu(ClO4 )2 by Scholz et al.(29) in a study that extended up to 400◦ C and 2000 bars. The common feature of both studies is the red shift in the values of λmax and the increase in intensity with increasing temperature, which correspond to changes in the 3d–3d electronic transitions in the uncomplexed Cu2+ aqua ion. Subtraction of the spectrum at 30◦ C from the other spectra for Cu(CF3 SO3 )2 in Fig. 3, which are already corrected for the effects of thermal expansion, yields the difference spectra shown in Fig. 13. Peak maxima are tabulated in Table VII. The striking consistency of the wavelengths (918 ± 10 nm) suggests that the increase in intensity and red shift of the spectrum of aqueous Cu2+ at elevated temperatures may arise from the

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Fig. 11. Logarithm of the overall formation constants β1,n obtained with NLSR as a function of the reciprocal temperature.

presence of a new species. A similar analysis of the difference spectrum of aqueous cobalt by Swaddle and Fabes(30) showed the presence of tetrahedral Co(H2 O)2+ 4 which forms from octahedral Co(H2 O)2+ 6 by an endothermic equilibrium reaction at elevated temperatures. Although the interpretation of the copper(II) difference spectrum is less straightforward, our treatment is similar. The visible spectrum of copper(II) at 25◦ C is understood to arise from the hexaaquocomplex, Cu(H2 O)2+ 6 , which is distorted from octahedral symmetry by strong Jahn–Teller effects to yield a tetragonal structure in which two of the CuOH2 bonds are much weaker than the other four. The tetragonal distortion removes the degeneracies in the octahedral t62g e3g electronic configuration, so that the resulting broad band contains contributions in the visible spectrum from the [z2 → (x2 − y2 )], [(xz, yz) → (x2 − y2 )] and [xy → (x2 − y2 )] transitions, with a wide distribution due to secondary hydration effects, a distribution of distorted

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Table VII.

Experimental Parameters for the Absorption Band of Cu2+ (aq) in 0.4826 mol-kg−1 CF3 SO3 H as a Function of Temperature 30◦ C

100◦ C

125◦ C

150◦ C

200◦ C

250◦ C

859 18.87

Full spectraa λmax (nm) εmax (cm−1 -dm3 -mol−1)

814 11.49

835 13.96

843 14.82

846 15.72

866 18.24

100◦ C

125◦ C

150◦ C

200◦ C

250◦ C

Difference spectra, [ε(t) − ε(t = 30◦ C)]b λmax (nm) εmax (cm−1 -dm3 -mol−1 ) a Fig. b Fig.

909 3.05

908 4.11

928 5.16

923 8.16

913 8.90

3. 13.

stereochemistries, and thermal motion.(31) In single crystals of (NH4 )4 [Cu(H2 O)6 ] (SO4 )2 these transitions occur at 1560 nm (6400 cm−1 ), ∼840 nm (11,540 cm−1 ; 12,350 cm−1 ), and 938 nm (10,650 cm−1 ), respectively.(32) Recent measurements by electrospray mass spectrometry and subsequent calculations by static density functional theory and ab initio molecular dynamics simulations,(33) have examined the hydration of Cu2+ in low-pressure water vapor. The calculations show the existence of a stable, square-planar structure for Cu(H2 O)2+ 4 . Furthermore, as the number of water molecules increases past four, the additional ligands are hydrogen-bonded to the planar primary hydration shell rather than filling the vacant axial position. We speculate that the emergence of a well-defined band in the difference spectrum at elevated temperatures corresponds either to an equilibrium between the tetragonal hexa-aqua copper(II) and the square-planar tetra-aqua complex, similar to that observed for cobalt 2+ Cu(H2 O)2+ 6 = Cu(H2 O)4 + 2H2 O

(19)

or to the progressive distortion of the tetragonal complex toward the square-planar structure by increases in the mean length of the axial Cu-OH2 bonds. Values of λmax and εmax for the ammonia complexes, corresponding to the deconvoluted spectra from the EFA and NLSQ analyses, are tabulated in Tables VIII and IX, and plotted in Fig. 14. At 30◦ C, the positions of the maxima of absorption compare quite well with Bjerrum’s experimental and predicted room temperature values,(18) which are also included in Table VIII. Simple ligand field calculations by 2+ Bjerrum et al.(18) suggest that the cis-Cu(NH3 )2+ 2 and trans-Cu(NH3 )2 complexes will display bands with absorption maxima at 620 and 670 nm, respectively, while Cu(NH3 )2+ 3 displays a maximum at 645 nm. The spectra of the cis and trans isomers could be not resolved.

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Fig. 12. (a) λmax of the “d–d” band and (b) εmax of copper(II) in 0.4826 mol-kg−1 CF3 SO3 H as function of temperature.

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Fig. 13. Difference spectra of aqueous copper (II), [ε(t) − ε(t = 30◦ C)].

As can be seen from the plots in Fig. 14, the spectra of the Cu(NH3 )n (H2 O)2+ 6−n complexes in 2 mol-kg−1 NH4 NO3 all undergo a slight red shift and significant enhancement in the maximum of absorbance at elevated temperatures. Difference spectra, calculated by subtracting the spectra at 30◦ C from the other spectra in Fig. 10, showed the appearance of a new band at higher wavelength, similar to that observed for Cu2+ (aq), but with much more uncertainty. More accurate experimental data would be required to interpret the changes in λmax and εmax in terms of the structure of the complexes. Although stability constants could not be obtained at 200 and 250◦ C, the positions of the maxima of absorption and the molar absorptivities at 200◦ C can be compared with extrapolations of the values for λmax and εmax in Tables VIII and IX as a means of identifying the predominant species at these higher temperatures. Extrapolations to 200◦ C by assuming a linear temperaturedependence yielded estimated maxima of absorption and molar absorptivities for

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Band Position of [Cu(NH3 )n ]2+ (aq) as a Function of Temperature Given by EFA and NLSR

Table VIII.

λmax (nm) 30◦ C Species

EFA

100◦ C

NLSR

EFA

NLSR

125◦ C

150◦ C

EFA

NLSR

EFA

NLSR

836 771 671 622

844 752 694 615

Four-factor modela Cu2+ (aq) Cu(NH3 )2+ (aq) Cu(NH3 )2+ 3 (aq) Cu(NH3 )2+ 4 (aq)

809 733 655 595

814 722 665 596

— — — —

— — — —

— — — —

851 771 709 609

EFA

NLSR

EFA

NLSR

EFA

NLSR

EFA–NLSR

— — — — —

846 773 701 637 610

836 762 701 658 623

Five-factor modela Cu2+

(aq) Cu(NH3 )2+ Cu(NH3 )2+ 2 Cu(NH3 )2+ 3 Cu(NH3 )2+ 4

(aq) (aq) (aq) (aq)

814 743 675 621 598

808 743 706 640 591

— — — — —

828 766 706 676 608

From Bjerrum (Ref. 4) and Bjerrum et al. (Ref. 18) at room temperatureb Cu2+ (aq) Cu(NH3 )2+ Cu(NH3 )2+ 2 Cu(NH3 )2+ 3 Cu(NH3 )2+ 4 a Estimated

(aq) (aq) (aq) (aq)

790 745 (710) 680 (670) (cis)-620 (620) (trans) 645 (660) 590 (590)

values, ±10 nm. values between parenthesis.

b Experimental

2+ −1 −1 3 Cu(NH3 )2+ 3 : λmax ≈ 666 nm and εmax ≈ 51 cm -mol -dm and for Cu(NH3 )4 , −1 −1 3 λmax ≈ 633 nm and εmax ≈ 60 cm mol -dm . At 200◦ C, the spectrum of 0.01 mol-kg−1 copper(II) in the 3.7 mol-kg−1 solution of aqueous ammonia displayed a maximum at λmax ≈ 635 nm with a molar absorptivity of εmax ≈ 46 cm−1 -mol−1 -dm3 (Fig. 7). Although the position of the peak is in very good agreement with the predicted value for Cu(NH3 )2+ 4 , the discrepancy in molar absorptivity is higher than expected, based on the results obtained at lower temperatures. Because of concerns that the absorbance could have been affected by the precipitation of CuO(s), a new run was carried out with a more dilute solution, 0.005 mol-kg−1 Cu2+ in 3.53 mol-kg−1 ammonia. In this case, the results λmax = 633 nm and εmax = 56 cm−1 mol−1 dm3 , were very close to those extrapo(33) show that, like Cu(H2 O)2+ lated for Cu(NH3 )2+ 4 . Calculations by Berces et al. 4 , 2+ the four-coordinate complex Cu(NH3 )4 exists as a stable, square-planar structure in the gas phase. As the number of water molecules increases past four in

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Table IX.

Molar Absorptivity of [Cu(NH3 )n ]2+ (aq) as a Function of Temperature Given by EFA and NLSR εmax (cm−1 -dm3 -mol−1 ) 30◦ C

Species

100◦ C

EFA

NLSR

EFA

12.9 23.1 39.1 50.8

12.8 25.6 34.2 54.4

— — — —

EFA

NLSR

EFA

12.8 22.5 31.4 43.0 49.8

12.5 19.7 29.3 40.8 54.6

NLSR

125◦ C

150◦ C

EFA

NLSR

EFA

NLSR

— — — —

— — — —

16.4 25.2 37.8 58.2

18.9 28.6 48.0 57.1

18.3 30.6 42.1 62.4

NLSR

EFA

NLSR

EFA–NLSR

— — — — —

16.6 25.5 40.8 52.2 59.1

19.4 28.2 37.5 47.0 57.2

Four-factor model Cu2+ (aq) Cu(NH3 )2+ (aq) Cu(NH3 )2+ 3 (aq) Cu(NH3 )2+ 4 (aq)

Five-factor model Cu2+ (aq) Cu(NH3 )2+ Cu(NH3 )2+ 2 Cu(NH3 )2+ 3 Cu(NH3 )2+ 4

(aq) (aq) (aq) (aq)

— — — — —

16.0 24.2 32.7 43.8 57.6

From Bjerrum (Ref. 4) and Bjerrum et al. (Ref. 18) at room temperature Cu2+ (aq) Cu(NH3 )2+ Cu(NH3 )2+ 2 Cu(NH3 )2+ 3 Cu(NH3 )2+ 4

(aq) (aq) (aq) (aq)

∼15 ∼25 ∼30 ∼42 ∼55

Cu(H2 O)2+ 4 , the additional ligands are hydrogen bonded to the planar primary hydration shell rather than filling the vacant axial position. The energetic preference for a square planar structure over tetrahedral coordination in Cu(NH3 )2+ 4 is much less than that for water, and, since the calculation was not done for mixed water– ammonia complexes, it is possible that Cu(NH3 )2+ 4 is tetrahedral. Although the is known to exist at room temperature,(4,5) square pyramidal complex Cu(NH3 )2+ 5 it seems likely that the complex with four ammonia ligands, Cu(NH3 )2+ 4 , is the predominant species in concentrated solutions at elevated temperatures. 5. CONCLUSIONS This work constitutes the first reported study of the visible spectra and stability constants for the aqueous copper(II)–ammonia system at temperatures above 100◦ C. The species distribution obtained by nonlinear least-squares regression of the experimental data reveals the existence of four copper–ammonia complexes ◦ Cu(NH3 )2+ n at temperatures as high as 150 C.

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Fig. 14. (a)λmax of the “d-d” band and (b) molar absorptivities εmax of copper-ammonia complexes in 2 mol-kg−1 NH4 NO3 as a 2+ function of the temperature: (●) Cu(NH3 )2+ 4 , (▼) Cu(NH3 )3 , (■) 2+ , and (▲) Cu2+ . Filled symbols, EFA; , ( ◆ ) Cu(NH ) Cu(NH3 )2+ 3 2 unfilled symbols, NLSR.

617

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The stability constant values measured at 150◦ C were significantly higher than those predicted by Isaev et al.(7) Although the stability constants decrease with temperature, complexation with ammonia could be observed at temperatures up to 250◦ C, at which point the precipitation of CuO(s) could not be avoided. The stability constants from this work provide a means of analyzing the role of copper(II)–ammonia complexes in the dissolution, precipitation, and volatility of copper and copper oxides in the steam generators of electric power plants. ACKNOWLEDGMENTS We are grateful to Mr. Jan Stodola of Ontario Power Generation for stimulating discussions that led to our undertaking this project, to Mr. Chris Collins for carrying out many of the chemical equilibrium calculations, and to Mr. Randy Thorne of the Memorial University Machine Shop for construction of the UVvisible flow cell and much input into its design. Dr. M. Brooker provided helpful guidance on least-squares and factor analysis methods; Dr. Cory Pye provided several key literature references on the electronic structure of copper complexes; and Dr. Rodney Clarke prepared Figs. 1 and 2. The project was supported by an Industrially Oriented Research Grant from Ontario Power Generation Ltd. and the Natural Science and Engineering Research Council of Canada (NSERC). Additional financial support from an NSERC Summer Research Scholarship (to J.R.), an NSERC Operating Grant (to P.T.), and Memorial University of Newfoundland is gratefully acknowledged.

APPENDIX Tables A1, A2, and A3 list the solution compositions used in this work, expressed as total copper (II), ligand, and nitrate molalities. Table A1.

Summary of Solution Compositions at 30◦ C Expressed as Total Copper (II), Ligand, and Nitrate Concentrations

pH (experimental values)

Cu(II) (mol-kg−1 )

Ligand (mol-kg−1 )

Nitrate (mol-kg−1 )

2.1810 2.1052 2.0741 2.0646 2.0643 2.0610

2.0374 2.0233 2.0227 2.0390 2.0294 2.0414

(t = 30◦ C) 8.11 7.78 7.48 7.12 7.09 6.95

0.0201 0.0205 0.0199 0.0200 0.0200 0.0200

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Table A1. Continued pH (experimental values)

Cu(II) (mol-kg−1 )

6.57 6.56 6.42 6.31 5.87 5.81 5.74 5.62 5.41 5.38 5.15 5.00 4.71 5.52 3.69 3.50

0.0201 0.0208 0.0204 0.0201 0.0200 0.0205 0.0205 0.0200 0.0200 0.0205 0.0201 0.0205 0.0200 0.0201 0.0201 0.0201 0.0498 0.0228

Ligand (mol-kg−1 )

Nitrate (mol-kg−1 )

2.0588 2.0339 2.0454 2.0266 2.0624 2.0489 2.0474 2.0386 2.0475 2.0475 2.0372 2.0429 2.0324 2.0409 2.0308 2.0447 2.0242 2.0342 2.0212 2.0407 2.0156 2.0389 2.0176 2.0436 2.0033 2.0353 1.9987 2.0339 1.9983 2.0385 1.9898 2.0293 0.0499 m CF3 SO3 H 1.7636 m NaNO3 and 0.1697 m HNO3

Table A2. Summary of Solution Compositions at 100, 125, and 150◦ C Expressed as Total Copper(II), Ligand, and Nitrate Concentrations pH (extrapolated values)

Cu(II) (mol-kg−1 )

Ligand (mol-kg−1 )

Nitrate (mol-kg−1 )

t = 100◦ C 6.88 6.33 6.32 5.82 5.64 5.51 5.50 5.48 4.88 4.74 4.33 3.84 3.11 2.55

0.0204 0.0181 0.0206 0.0205 0.0193 0.0172 0.0204 0.0205 0.0194 0.0207 0.0205 0.0206 0.0200 0.0205 0.0498 0.0228

2.5418 2.1117 2.1005 1.9730 2.1778 2.0395 2.0956 2.0389 2.1212 2.0838 2.1154 2.0876 2.0751 2.0563 2.0711 2.0412 2.0164 2.0152 1.9350 1.9367 2.0241 2.0387 2.0142 2.0389 1.9666 2.0021 1.9994 2.0417 0.0499 mol-kg−1 CF3 SO3 H 1.7636 mol-kg−1 NaNO3 + 0.1697 mol-kg−1 HNO3

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pH (extrapolated values)

Cu(II) (mol-kg−1 )

Ligand (mol-kg−1 )

Nitrate (mol-kg−1 )

t = 125◦ C 5.89 5.43 5.40 5.17 5.12 4.94 4.61 4.32 4.13 3.87 3.54 2.48 2.43

0.0205 0.0102 0.0205 0.0103 0.0205 0.0205 0.0154 0.0209 0.0209 0.0205 0.0205 0.0206 0.0297 0.0498 0.0228

2.1858 2.0352 2.0616 2.0559 2.0984 2.0219 2.0442 2.0434 2.0717 2.0391 2.0605 2.0319 2.0328 2.0283 2.0250 2.0199 2.0098 2.0403 2.0215 2.0104 2.0197 2.0394 1.9940 2.0408 1.9970 2.0373 0.0499 mol-kg−1 CF3 SO3 H 1.7636 mol-kg−1 NaNO3 + 0.1697 mol-kg−1 HNO3 t = 150◦ C

6.45 6.21 6.03 6.02 5.99 5.91 5.76 5.76 5.64 5.49 5.46 5.44 5.30 5.21 5.12 5.11 5.05 5.02 5.01 4.93 4.81 4.80 4.77 4.75 4.62 4.59 4.55 4.52

0.0087 0.0083 0.0078 0.0205 0.0204 0.0201 0.0200 0.0103 0.0104 0.0205 0.0206 0.00987 0.0103 0.0205 0.0104 0.0104 0.0196 0.0205 0.0199 0.0110 0.0103 0.0103 0.0185 0.0206 0.0200 0.0204 0.0200 0.0101

2.8304 2.6320 2.4447 2.4906 2.5419 2.3935 2.2975 2.3522 2.3132 2.1853 2.1778 2.2705 2.2035 2.1052 2.0706 2.1995 2.0902 2.0956 2.0758 2.3311 2.1496 2.0442 2.1418 2.0711 2.0610 2.0751 2.0534 2.1536

1.7812 1.9777 2.0013 2.0401 2.1117 2.0354 2.0377 2.1132 2.1190 2.0378 2.0395 2.1394 2.1162 2.0233 2.0093 2.1384 2.0311 2.0389 2.0229 2.2871 2.1172 2.0149 2.1103 2.0412 2.0414 2.0563 2.0384 2.1389

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Table A2. Continued pH (extrapolated values)

Cu(II) (mol-kg−1 )

4.52 4.37 4.35 4.22 4.21 4.09 4.05 3.99 3.98 3.91 3.74 3.71 3.51 3.51 3.19 3.16 3.02 2.91 2.80 2.64 2.44 2.33 2.27 0.87

0.0204 0.0199 0.0103 0.0200 0.0207 0.0196 0.0206 0.0100 0.0205 0.0103 0.0205 0.00928 0.0200 0.0205 0.0206 0.0205 0.0196 0.0200 0.0200 0.0201 0.0201 0.0206 0.0297 0.0211 0.0498 0.0228

Ligand (mol-kg−1 )

Nitrate (mol-kg−1 )

2.0624 2.0489 2.0784 2.0718 2.1302 2.1229 2.0475 2.0475 1.9350 1.9764 2.0214 2.0261 2.0310 2.0721 2.0348 2.0367 2.0324 2.0409 2.1097 2.1132 2.0241 2.0387 2.1341 2.1399 2.0242 2.0342 2.0212 2.0407 2.0142 2.0389 2.0176 2.0436 2.0109 2.0374 2.0014 2.0314 2.0033 2.0353 1.9988 2.0339 1.9898 2.0293 1.9994 2.0417 1.9976 2.0575 1.9521 2.2019 0.0499 mol-kg−1 CF3 SO3 H 1.7636 mol-kg−1 NaNO3 + 0.1697 mol-kg−1 HNO3

Summary of Solution Compositions above 200◦ C Expressed as Total Copper(II), Ligand, and Nitrate Concentrationsa

Table A3.

pH

Cu(II) (mol-kg−1 )

na na na na

0.0107 0.0108 0.0105 0.0098

NH3 (mol-kg−1 )

CF3 SO3 H (mol-kg−1 )

t = 200 and 250◦ C 3.7 7.7 14.5

0.4963b 0.1046 0.1018 0.0953

t = 200 and 250◦ C na a Solutions

0.0108

0.5086

where the formation of precipitate could be readily detected from baseline shifts in the spectrum of water were excluded. b Only at 200◦ C.

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