COMSOL 6.4 - Acid-Base Equilibria and Copper Speciation in Ammonia Solution

Acid-Base Equilibria and Copper Speciation in Ammonia Solution

Cupric ions show a strong affinity to ammonia in aqueous solutions, forming strongly colored deep blue complexes. The relative amounts of the different ammine ligand complexes, with varying coordination numbers, are governed by the stability constants of the equilibria forming the coordination compounds. By entering a series of equilibrium reactions, and an external source of ammonia, the Time Dependent study can be used to produce a speciation diagram, which shows how the concentration of the different complexes vary with the total concentration of added ammonia.

Model Definition

A 0D component employing the interface is used to describe the system. The equilibria for a simplified model is entered as features in the interface. The equilibria used in this model are presented in Table 1, together with approximate equilibrium constants at room temperature, partially derived from Ref. 1.

Table 1: Equilibria Governing the speciation in the model.
Reactants	Products	Equilibrium constant¹
H2O	H+ + OH-	1.8e-16[M]
NH4+	H+ + NH3	5.5e-10[M]
CuNH3++	NH3 + Cu++	5.0e-05[M]
Cu(NH3)2++	NH3 + CuNH3++	5.0e-05[M]
Cu(NH3)3++	NH3 + Cu(NH3)2++	1.3e-03[M]
Cu(NH3)4++	NH3 + Cu(NH3)3++	6.3e-03[M]
Cu(NH3)5++	NH3 + Cu(NH3)4++	4.0[M]
2 Cu++ + OH- + H2O	Cu2(OH)2++ + H+	45[M^-2]

The autoprotolysis constant of water uses an explicit concentration of water rather than the common assumption of setting its activity to one.

No solid phases are accounted for, nor any ionic strength effects. Instead, focus is on initialization and mass conservation. By adding an feature, a parameter sweep is modeled by setting a constant rate of addition for one or more components, and use the time-dependent solver to adaptively step through the specified range of values. For initial values, a total concentration of copper is given as the initial value of free cupric ions, the bulk density of water gives its concentration, and a small value is assigned to the swept species which represents the initial value of the sweep. Under the section of the feature, the functionality is enabled. This tells the solver to first solve the equilibria, while ignoring any kinetic reactions, in a mass-consistent manner prior to the time-stepping phase, which in turn allows for specifying initial values far from equilibrium. Note that mass-preserving initialization requires all components to be present (that is, larger than zero) for the set of initial values. This is due the initializer working with a log-transformed version of the problem, in which a concentration of zero cannot be represented by a finite number. For this model, this requirement is already fulfilled, but for other models a reasonable amount might be some fraction of what is expected to be produced during the first time step.

Results and Discussion

The evolution of concentrations, as total concentration of ammonia is increased, is presented in Figure 1. As might be expected, ammonia is primarily present as ammonium at low total concentrations of ammonia, and primarily as the free base at high total concentration. In the transition region, when the total concentration of ammonia is similar to the total concentration of copper(II) ions in the system, the picture is more complicated, and ammine complexes of different coordination numbers form.

Figure 1: Concentration of species versus time. The constant source of ammonia gives a linear relationship between total concentration ammonia and time.

Since mass-preserving initialization was enabled, it may be interesting to study how the mass conservation is upheld throughout the time stepping. The results for conservation of protons, hydroxide ions, ammonia moieties, and copper are presented in Figure 2.

Figure 2: Mass conservation of the constituents in the model. Note that the number of invariants here equal the difference between number of species and equilibria.

An instructive plot can be made over the predominance of the different groups of complexes. By looking at the weighted sum with respect to copper content we can see in Figure 3 how the addition of ammonia alters the speciation of the cupric ion.

Figure 3: Relative speciation of copper (II) ions into different classes of complexes, and their variation versus total concentration of ammonia.

The early onset of change is due to the basicity ammonia, where the uptake of protons yields a net increase of available hydroxide ion, which forms a binuclear complex of cupric ions with bridging hydroxide. Eventually, as the total availability of ammonia increases, ammine complexes outcompete the hydroxide, yielding a mixture of mononuclear ammines of increasing coordination index as the concentration of ammonia increases.

Reference

1. P. Djurdjevic and others, “Metal Ammine Formation in Solution. XXIV. The Copper (II) — and Some Other Metal (II) — Mono-and Diethanolamine Systems,” Acta. Chem. Scand., vol. 37, pp. 881–890, 1983.

Chemical_Reaction_Engineering_Module/Tutorials/ion_speciation

Modeling Instructions

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New

In the window, click

Model Wizard

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In the tree, select > .

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Click

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Click

Reaction Engineering (re)

Reaction 1

In the toolbar, click

In the window for , locate the section.

In the text field, type H2O=H++OH-.

Locate the section. In the Keq0j text field, type 1.80505415e-16[M].

Reaction 2

In the toolbar, click

In the window for , locate the section.

In the text field, type NH4+=H++NH3.

Locate the section. In the Keq0j text field, type 5.49540874e-10[M].

Reaction 3

In the toolbar, click

In the window for , locate the section.

In the text field, type CuNH3++=NH3+Cu++.

Locate the section. In the Keq0j text field, type 5.01187234e-05[M].

Reaction 4

In the toolbar, click

In the window for , locate the section.

In the text field, type Cu(NH3)2++=NH3+CuNH3++.

Locate the section. In the Keq0j text field, type 5.01187234e-05[M].

Reaction 5

In the toolbar, click

In the window for , locate the section.

In the text field, type Cu(NH3)3++=NH3+Cu(NH3)2++.

Locate the section. In the Keq0j text field, type 0.00125893[M].

Reaction 6

In the toolbar, click

In the window for , locate the section.

In the text field, type Cu(NH3)4++=NH3+Cu(NH3)3++.

Locate the section. In the Keq0j text field, type 0.00630957[M].

Reaction 7

In the toolbar, click

In the window for , locate the section.

In the text field, type Cu(NH3)5++=NH3+Cu(NH3)4++.

Locate the section. In the Keq0j text field, type 3.98107171[M].

Reaction 8

In the toolbar, click

In the window for , locate the section.

In the text field, type 2Cu++ + OH- + H2O = Cu2(OH)2++ + H+.

Locate the section. In the Keq0j text field, type 45.34091032[M^-2].

Definitions

Variables 1

In the window, under right-click and choose .

Global Definitions

Parameters 1

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
init_conc_H2O	55.4[M]	55400 mol/m³	From density and molar mass
init_conc_Cu	0.01[M]	10 mol/m³	Initial concentration copper
init_conc_NH3	1e-12[M]	1E-9 mol/m³	Initial concentration ammonia
src_rate_NH3	1e-3[M/s]	1 mol/(m³·s)	Rate of [NH3] addition
t0	init_conc_NH3/src_rate_NH3	1E-9 s	First output time
final_conc_NH3	1[M]	1000 mol/m³	Final total concentration ammonia
tend	final_conc_NH3/src_rate_NH3	1000 s	Final output time

Definitions

Variables 1

In the window, under > click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Unit	Description
c_sum_ammines	re.c_CuNH32_2p+re.c_CuNH33_2p+re.c_CuNH34_2p+re.c_CuNH35_2p+re.c_CuNH3_2p	mol/m³	Ammine complexes
c_sum_hydroxides	2*re.c_Cu2OH2_2p	mol/m³	Hydroxy complexes
c_sum_Cu_tot	re.c_Cu_2p + c_sum_hydroxides + c_sum_ammines	mol/m³	Total conc. copper
c_sum_NH3_tot	re.c_NH4_1p+re.c_NH3+re.c_CuNH3_2p+2re.c_CuNH32_2p+3re.c_CuNH33_2p+4re.c_CuNH34_2p+5re.c_CuNH35_2p	mol/m³	Total conc. ammonia
c_ref_NH3_tot	init_conc_NH3 + (t-t0)*src_rate_NH3	mol/m³	Total conc. ammonia (ref)
c_sum_H1p_tot	re.c_H_1p+re.c_NH4_1p+re.c_H2O	mol/m³	Total conc. protons
c_sum_OH1m_tot	re.c_OH_1m+re.c_H2O+2*re.c_Cu2OH2_2p	mol/m³	Total conc. hydroxide

Reaction Engineering (re)

Initial Values 1

In the window, under > click .

In the window for , locate the section.

In the table, enter the following settings:


Species	Concentration (mol/m^3)
Cu++	init_conc_Cu
H2O	init_conc_H2O
NH3	init_conc_NH3

Locate the section. Select the checkbox.

Additional Source 1

In the toolbar, click

In the window for , locate the section.

In the table, enter the following settings:


Species	Additional rate expression (mol/(m^3*s))
NH3	src_rate_NH3

Study 1

Step 1: Time Dependent

In the window, under click .

In the window for , locate the section.

In the text field, type 10^range(log10(t0/1[s]),0.5,log10(tend/1[s])).

From the list, choose .

In the text field, type 1e-6.

Solution 1 (sol1)

In the toolbar, click

In the window, expand the node, then click .

In the window for , click to expand the section.

Select the checkbox. In the associated text field, type 0.1*t0.

Find the subsection. From the list, choose .

Thanks to mass-preserving initialization we already have a consistent starting point.

In the toolbar, click

Results

Concentration (re)

In the window for , click to expand the section.

From the list, choose .

Locate the section.

Select the checkbox. In the associated text field, type Concentration (mol / m<sup>3</sup>).

Locate the section. Select the checkbox.

In the text field, type 1e-3.

In the text field, type 1e3.

In the text field, type 1e-9.

In the text field, type 1e5.

Select the checkbox.

Locate the section. From the list, choose .

Species concentrations

In the window, expand the node, then click .

In the window for , type Species concentrations in the text field.

Click to expand the section. From the list, choose .

In the table, enter the following settings:


Legends
H<sup>+</sup>
OH<sup>-</sup>
NH<sub>3</sub>
Cu(NH<sub>3</sub>)<sub>2</sub> <sup>2+</sup>
Cu(NH<sub>3</sub>)<sub>3</sub> <sup>2+</sup>
CuNH<sub>3</sub> <sup>2+</sup>
Cu(NH<sub>3</sub>)<sub>4</sub> <sup>2+</sup>
Cu(NH<sub>3</sub>)<sub>5</sub> <sup>2+</sup>
Cu<sup>2+</sup>
H<sub>2</sub>O
NH<sub>4</sub> <sup>+</sup>
Cu<sub>2</sub>(OH)<sub>2</sub> <sup>2+</sup>

Click to expand the section. Find the subsection. From the list, choose .

From the list, choose .

Concentration (re)

Right-click > > and choose .

Total conc. ammonia

In the window for , type Total conc. ammonia in the text field.

Locate the section. Click

In the table, enter the following settings:


Expression	Unit	Description
c_sum_NH3_tot	mol/m^3	Total conc. ammonia

Locate the section. From the list, choose .

From the list, choose .

Drag and drop above .

Locate the section. Find the subsection. Select the checkbox.

Clear the checkbox.

This is Figure 1.

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Evaluation Group 1

In the toolbar, click

Relative Conservation Errors

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In the window for , type Relative Conservation Errors in the text field.

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In the table, enter the following settings:


Expression	Unit	Description
c_sum_H1p_tot/init_conc_H2O-1	1	H+
c_sum_OH1m_tot/init_conc_H2O-1	1	OH-
c_sum_NH3_tot/c_ref_NH3_tot-1	1	NH3
c_sum_Cu_tot/init_conc_Cu-1	1	Cu

In the toolbar, click

Evaluation Group 1

Go to the window.

Click the button in the window toolbar.

Results

In the window, click .

In the toolbar, click

In the window for , click the button in the window toolbar.

Mass Conservation

In the window, under click .

In the window for , type Mass Conservation in the text field.

Locate the section. From the list, choose .

Locate the section.

Select the checkbox. In the associated text field, type Relative error.

Table Graph 1

In the window, click .

In the window for , locate the section.

Find the subsection. From the list, choose .

From the list, choose .

Click to expand the section. Select the checkbox.

This is Figure 2.

Complex predominance

In the toolbar, click

and choose .

In the window for , type Complex predominance in the text field.

Click to expand the section. From the list, choose .

Locate the section. Select the checkbox.

Select the checkbox. In the associated text field, type Fraction of all copper.

Locate the section. Select the checkbox.

Select the checkbox.

In the text field, type 1e-3.

In the text field, type 1e2.

In the text field, type 0.

In the text field, type 1e-3.

In the text field, type 1e2.

Locate the section. From the list, choose .

Total conc. ammonia

Right-click and choose .

In the window for , type Total conc. ammonia in the text field.

Locate the section. Click

In the table, enter the following settings:


Expression	Unit	Description
c_sum_NH3_tot	mol/m^3	Total conc. ammonia

Locate the section. Select the checkbox.

Locate the section. From the list, choose .

From the list, choose .

Locate the section. Find the subsection. Select the checkbox.

Clear the checkbox.

Complex predominance

Right-click and choose .

Complex classes

In the window for , type Complex classes in the text field.

Locate the section. Click

In the table, enter the following settings:


Expression	Unit	Description
c_sum_ammines/c_sum_Cu_tot	1	Ammine complexes
c_sum_hydroxides/c_sum_Cu_tot	1	Hydroxy complexes
re.c_Cu_2p/c_sum_Cu_tot	1	Free cupric

Locate the section. Find the subsection. From the list, choose .

From the list, choose .

Locate the section. Find the subsection. Select the checkbox.

Clear the checkbox.

This is Figure 3.

In the toolbar, click