PHREEQC from Scratch #7: Solubility Diagrams (Gibbsite)

Learn how to calculate and visualize the amphoteric solubility of Gibbsite (Al(OH)₃) across pH 3 to 14. We introduce the Fix_H+ technique to artificially lock pH using the PHASES block.
Geochemistry
PHREEQC
Tutorial
English
Author

DeepFlow

Published

May 3, 2026

Introduction: Why Solubility Diagrams Matter

Aluminum is one of the most abundant metallic elements in the Earth’s crust, yet its geochemical behavior changes drastically depending on pH. It exhibits high solubility in strongly acidic and strongly alkaline environments, but precipitates almost entirely as Gibbsite (\(\mathrm{Al(OH)_3}\)) near neutral pH (pH 6–8).

Quantitatively understanding this “amphoteric dissolution” is a crucial skill directly linked to: - Predicting Al toxicity in Acid Mine Drainage (AMD). - Evaluating ecological impacts of soil acidification. - Designing coagulation and precipitation processes in water treatment.

NoteWhat You Will Learn in This Tutorial
  • How to define a virtual mineral, Fix_H+, in the PHASES block to lock a solution at a specific pH.
  • How to equilibrate with Gibbsite using EQUILIBRIUM_PHASES to obtain Al solubility.
  • How to extract the activities of specific Al species (\(\mathrm{Al^{3+}, AlOH^{2+}, Al(OH)_2^+, Al(OH)_3^0, Al(OH)_4^-}\)) using SELECTED_OUTPUT.
  • How to generate an interactive solubility diagram using USER_GRAPH.

Theoretical Background: Amphoteric Dissolution

Dissolution Reactions of Gibbsite

The fundamental dissolution reaction of Gibbsite is:

\[\mathrm{Al(OH)_3(s) \rightleftharpoons Al^{3+} + 3OH^-} \quad \log K_{sp} = -34.0\]

However, in reality, Aluminum forms various hydroxyl complexes depending on the pH:

Aqueous Species Reaction Equation Dominant pH Range log K
Al³⁺ Al(OH)₃ + 3H⁺ → Al³⁺ + 3H₂O pH < 4 +8.11
AlOH²⁺ Al(OH)₃ + 2H⁺ → AlOH²⁺ + 2H₂O pH 4–5 +4.80
Al(OH)₂⁺ Al(OH)₃ + H⁺ → Al(OH)₂⁺ + H₂O pH 5–6 +1.04
Al(OH)₃° Al(OH)₃ → Al(OH)₃° pH 6–8 −0.78
Al(OH)₄⁻ Al(OH)₃ + OH⁻ → Al(OH)₄⁻ pH > 8 −0.64 (log β)

Minimum Solubility

Total dissolved Al reaches its minimum near pH 6.5, dropping to a theoretical value of roughly \(10^{-7}\) mol/L (about 0.003 mg/L). This is approximately 67 times lower than the WHO drinking water guideline (0.2 mg/L), demonstrating how effectively equilibrium with Gibbsite restricts Al concentration.

Methodology: Fixing pH with Fix_H+

To manually fix the pH of a solution in PHREEQC, we employ a classic workaround: defining a virtual mineral named Fix_H+.

💡 The Principle of Fix_H+
By defining H⁺ = H⁺, log_k = 0 in the PHASES block, this "mineral" acts as an infinite acid-base buffer. It maintains the target pH by either dissolving or precipitating H⁺ ions. Practically, it acts as an unlimited virtual reagent tank capable of supplying HCl (for acidic targets) or NaOH (for alkaline targets).
Acidic Side (pH < 7)
Fix_H+ -3 HCl 10
→ Target pH is locked at 3.
→ Up to 10 moles of HCl can be added.
→ Fix_H+ "consumes" the HCl to exactly maintain the pH.
Alkaline Side (pH > 7)
Fix_H+ -10 NaOH 10
→ Target pH is locked at 10.
→ Up to 10 moles of NaOH can be added.
→ Fix_H+ "consumes" the NaOH to exactly maintain the pH.
ImportantWatch Your Signs

In the EQUILIBRIUM_PHASES block, the syntax is:

Fix_H+   <Target_log{H+}>   <Reagent_Name>   <Reagent_Amount>

If your target is pH 3, specify log{H+} = -3. If it is pH 14, specify log{H+} = -14. Entering the wrong sign will force the pH in the opposite direction!

Full PHREEQC Code

Below is the complete input file. It steps through pH 3 to 12, calculating the Al solubility and activities of each species in equilibrium with Gibbsite at each step.

# ============================================================
#  DeepFlow #7 - Gibbsite Solubility Diagram
#  Al solubility calculation across pH 3–12 using Fix_H+
# ============================================================

PHASES
    Fix_H+
        H+ = H+
        log_k     0

# ----------------------------------------
# Define Base Solution (Dilute, near pure water)
# ----------------------------------------
SOLUTION 1
    temp      25
    pH        7
    pe        4
    units     mol/kgw
    -water    1  # kg

SAVE solution 1
END

# ==============================
# Graph and Output Definitions
# ==============================

SELECTED_OUTPUT 1
    -file             gibbsite_solubility.txt
    -reset            false
    -pH               true
    -totals           Al
    -activities       Al+3  AlOH+2  Al(OH)2+  Al(OH)3  Al(OH)4-
    -equilibrium_phases  Gibbsite

USER_GRAPH 1
    -chart_title      "Gibbsite Solubility Diagram"
    -axis_titles      pH  "log[Al] (mol/kgw)"
    -axis_scale       x_axis  3  12
    -axis_scale       y_axis  -9  -2
    -plot_concentration_vs x
    -start
    10 GRAPH_X  -LA("H+")
    20 GRAPH_Y  LOG10(TOT("Al")+1e-20),  "Total Al"
    30 GRAPH_Y  LA("Al+3"),              "Al3+"
    40 GRAPH_Y  LA("AlOH+2"),            "AlOH2+"
    50 GRAPH_Y  LA("Al(OH)2+"),          "Al(OH)2+"
    60 GRAPH_Y  LA("Al(OH)3"),           "Al(OH)3(aq)"
    70 GRAPH_Y  LA("Al(OH)4-"),          "Al(OH)4-"
    -end
END

# ==============================
# pH 3 ~ 6 (Using HCl as acid reagent)
# ==============================
USE solution 1
EQUILIBRIUM_PHASES 1
    Fix_H+    -3    HCl    10
    Gibbsite   0    10
END

USE solution 1
EQUILIBRIUM_PHASES 2
    Fix_H+    -4    HCl    10
    Gibbsite   0    10
END

USE solution 1
EQUILIBRIUM_PHASES 3
    Fix_H+    -5    HCl    10
    Gibbsite   0    10
END

USE solution 1
EQUILIBRIUM_PHASES 4
    Fix_H+    -6    HCl    10
    Gibbsite   0    10
END

# ==============================
# pH 7 ~ 12 (Using NaOH as base reagent)
# ==============================

USE solution 1
EQUILIBRIUM_PHASES 5
    Fix_H+    -7    NaOH    10
    Gibbsite   0    10
END

USE solution 1
EQUILIBRIUM_PHASES 6
    Fix_H+   -8    NaOH   10
    Gibbsite   0    10
END

USE solution 1
EQUILIBRIUM_PHASES 7
    Fix_H+   -9    NaOH   10
    Gibbsite   0    10
END

USE solution 1
EQUILIBRIUM_PHASES 8
    Fix_H+   -10    NaOH   10
    Gibbsite   0    10
END

USE solution 1
EQUILIBRIUM_PHASES 9
    Fix_H+   -11    NaOH   10
    Gibbsite   0    10
END

USE solution 1
EQUILIBRIUM_PHASES 10
    Fix_H+   -12    NaOH   10
    Gibbsite   0    10
END

Results and Visualizations

Numerical Table

Below are the theoretical values calculated using the default phreeqc.dat (Lawrence Livermore thermodynamic database).

pH log[Al]_total log{Al³⁺} log{AlOH²⁺} log{Al(OH)₂⁺} log{Al(OH)₃} log{Al(OH)₄⁻} Dominant
3 −2.11 −2.11 −5.27 −7.97 −9.71 <−13 Al³⁺
6 −6.20 −7.11 −6.27 −5.97 −9.71 −12.3 Al(OH)₂⁺
6.5 −6.98 −7.61 −6.77 −6.47 −9.71 −11.8 Minimum
8 −5.72 −9.11 −8.27 −7.97 −9.71 −10.3 Al(OH)₄⁻
10 −3.72 <−11 <−10 <−9 −9.71 −8.31 Al(OH)₄⁻

Interactive Solubility Diagram

3 4 5 6 7 8 9 10 11 12 13 14 −2 −3 −4 −5 −6 −7 −8 −9 −10 −11 pH log [Al] (mol/kgw) Min pH ≈ 6.5 ≈ 10⁻⁷ mol/L Gibbsite Precipitation Zone Total Al Al³⁺ AlOH²⁺ Al(OH)₂⁺ Al(OH)₃(aq) Al(OH)₄⁻ T = 25°C, Gibbsite Eq. Gibbsite Solubility Diagram (Al–H₂O System, 25°C)

Fig 1. Al solubility and species activities under Gibbsite equilibrium (pH 3 to 14).

Discussion

1. Mechanisms of Amphoteric Dissolution

The reason Al solubility bottoms out near pH 6.5 is due to two entirely different dissolution mechanisms dominating on the acidic and alkaline sides:

🔴 Acidic Side (pH < 6)
Dissolution via proton attack:
$\mathrm{Al(OH)_3 + 3H^+ \rightarrow \mathbf{Al^{3+}} + 3H_2O}$

For every 1 unit drop in pH, $\mathrm{Al^{3+}}$ activity increases by 1,000 times.
(Slope = −3 on the log-log scale)
🔵 Alkaline Side (pH > 8)
Dissolution via hydroxyl attack:
$\mathrm{Al(OH)_3 + OH^- \rightarrow \mathbf{Al(OH)_4^-}}$

For every 1 unit rise in pH, $\mathrm{Al(OH)_4^-}$ activity increases by 10 times.
(Slope = +1 on the log-log scale)

2. The Unique Behavior of \(\mathrm{Al(OH)_3(aq)}\)

The horizontal green dashed line representing \(\mathrm{Al(OH)_3(aq)}\) shows a constant activity (\(\approx 10^{-9.71}\) mol/L) regardless of pH. This occurs because the dissolution reaction \(\mathrm{Gibbsite \leftrightarrow Al(OH)_3(aq)}\) is a neutral reaction that does not consume or release \(\mathrm{H^+}\). Its concentration is dictated directly by its own equilibrium constant.

3. Environmental and Engineering Applications

NoteImplications for Acid Mine Drainage (AMD)

In AMD environments at pH 3–4, dissolved Al concentrations can reach tens of mg/L. When AMD is neutralized to pH 6–7, Gibbsite rapidly precipitates, dropping Al concentrations to below 0.003 mg/L. This 4- to 5-order of magnitude drop is the fundamental chemical basis for AMD neutralization treatment.

TipAlkali-Silica Reaction in Concrete

In the pore water of concrete (pH > 12), Al redissolves as \(\mathrm{Al(OH)_4^-}\). This high solubility at extreme alkalinity can accelerate the weathering of aluminosilicate minerals in aggregates. Solubility diagrams provide essential insights into these engineering challenges.

Summary

🧪
Fix_H+ Trick
Locking pH in the PHASES block.
Setting log_k = 0 is the key to creating virtual buffers.
📊
Amphoterism
Minimum solubility at pH 6.5.
Acidic → Al³⁺
Alkaline → Al(OH)₄⁻
🌍
Applications
AMD neutralization,
Soil acidification,
Water treatment design.

In this session, we employed the Fix_H+ technique to pin the pH at specific values and mapped the entire amphoteric solubility profile of Gibbsite. This exact technique can be generalized to draw solubility diagrams for iron, manganese, silica, or any other mineral system in PHREEQC.

References

Appelo, CAJ, and Dieke Postma. 2005. Geochemistry, Groundwater and Pollution. Second. Balkema, Rotterdam, p. 634.
Parkhurst, David L, and CAJ Appelo. 2013. Description of Input and Examples for PHREEQC Version 3—a Computer Program for Speciation, Batch-Reaction, One-Dimensional Transport, and Inverse Geochemical Calculations. US Geological Survey Techniques; Methods, book 6, chap. A43, 497 p.
Yamamoto, S. 1983. Method of the Groundwater Survey. Kokon Shoin, Tokyo (in Japanese), 490 p.
Yang, Heejun, T Mishima, S Katazakai, and M Kagabu. 2023. “Analytical Approach Using a Chemical Equilibrium Formula and Geochemical Modeling for Alkalinity Measurements of Small Natural Water Samples.” Applied Geochemistry 148: 105535.

Other articles in this series:

DeepFlow | Science beneath the surface