Hydroxide precipitation of metals: solubility, pH and sludge

Hydroxide precipitation is the most widely used method of removing dissolved heavy metals from industrial effluent. The achievable residual is not set by the solubility product alone: hydrolysis, amphoteric re-dissolution, the age of the solid, complexing agents and temperature all shift it. This note sets out the equilibrium model, applies it to zinc, and covers co-precipitation, the sulfide alternative, sludge production and pH control.

Technical note, RB Solutions Ltd, 22 October 2026

Solubility product and the hydrolysis ladder

For a divalent metal hydroxide in equilibrium with water, the dissolution reaction and its solubility product are:

The free metal ion is not the only dissolved species. The metal also forms soluble hydroxo complexes, described by cumulative formation constants β_i:

The total dissolved metal in equilibrium with the solid is the sum over all species [1, 2]:

Each term has a distinct slope on a plot of log M_T against pH. The free ion term falls with slope −2; the first hydroxo complex with slope −1; the neutral complex M(OH)₂(aq) is independent of pH, forming a floor that no pH adjustment can remove; and the anionic complexes M(OH)₃⁻ and M(OH)₄²⁻ rise with slopes +1 and +2. The resulting log C–pH solubility diagram is V- or U-shaped, with a pH of minimum solubility [1].

Minimum solubility

Setting dM_T/d[OH⁻] = 0 gives the condition for the minimum:

Solid phase and the solubility product bracket

Freshly precipitated hydroxides are amorphous or poorly crystalline and are more soluble than the aged or crystalline phases that form over days to weeks [1, 2]. For zinc, for example, the solubility product of amorphous Zn(OH)₂ is more than an order of magnitude higher than that of crystalline ZnO [1]. In a treatment plant with a residence time of hours, the fresh phase controls unless sludge recycle provides seed of an aged solid. A defensible design therefore carries a bracket of solubility products, from fresh to aged, rather than a single value, and claims credit for the less soluble phase only on the basis of plant evidence.

Amphoteric metals

A metal is amphoteric where its anionic hydroxo complexes become significant within the practical pH range, so that raising the pH beyond the minimum re-dissolves the precipitate. Table 1 summarises the behaviour of metals common in industrial effluent [1, 2].

A mixed-metal effluent therefore has no single ideal pH. Where the optimum ranges do not overlap, the options are a compromise set point, two-stage precipitation at different pH values, or a polishing stage such as sulfide precipitation or chelating ion exchange.

Worked example: zinc solubility and pH of minimum solubility

Stated inputs. 25 °C, ionic strength taken as zero; pK_w = 14.0 [5]; log K_sp = −15.5 for freshly precipitated amorphous Zn(OH)₂ and −16.9 for crystalline ZnO; cumulative hydrolysis constants log β₁ to log β₄ = 5.0, 11.1, 13.6 and 14.8 [1, 2]; molar mass of zinc 65.38 g mol⁻¹ [6].

Route 1: numerical scan

M_T was evaluated over pH 7.0 to 12.0 at 0.001 pH intervals using the total solubility equation. For the fresh solid the minimum is at pH 9.76, with M_T = 4.12 × 10⁻⁵ mol L⁻¹ = 2.69 mg L⁻¹ Zn.

Route 2: analytical minimum and the neutral-complex floor

Solving the minimum condition for x by bisection gives [OH⁻] = 10^−4.236 mol L⁻¹, pH 9.764, agreeing with the scan. At that pH, Zn(OH)₂(aq) accounts for 96.7 % of dissolved zinc, so M_T ≈ K_spβ₂/0.967 = 10^{(−15.5 + 11.1)}/0.967 = 4.12 × 10⁻⁵ mol L⁻¹, agreeing with route 1.

Three conclusions follow. First, the minimum is flat between about pH 9 and 10.5 but rises steeply on both sides; below pH 9 the free ion dominates, and above pH 11 zincate re-dissolution dominates. Second, the bracket between fresh and crystalline solids spans a factor of 25, larger than any effect of pH within the optimum range, so the solid phase assumption governs the predicted residual. Third, the floor is set by the neutral complex, whose formation constant is among the less certain of the hydrolysis constants; the prediction should be confirmed by bench precipitation of the actual effluent, filtered at 0.45 µm to separate dissolved from particulate metal.

Complexing agents

Ligands that form soluble complexes with the metal add terms to the mass balance and raise the total dissolved metal at every pH:

Ammonia forms ammine complexes with Cu(II), Ni(II), Zn(II) and Cd(II); because free NH₃ increases as pH rises above the pK_a of the ammonium ion, raising pH to precipitate the hydroxide simultaneously increases complexation [1, 3]. Aminopolycarboxylates such as EDTA form 1:1 complexes with transition metals that are stable enough to hold the metal in solution against hydroxide precipitation at any practical pH [3]. Citrate, tartrate, gluconate and pyrophosphate, common in plating and cleaning formulations, have similar but weaker effects. Evidence of complexation is dissolved metal, after 0.45 µm filtration, well above the equilibrium prediction for the solid present.

The design responses are segregation of the complexed stream, destruction of the ligand by oxidation, displacement of the metal by an excess of a competing cation such as iron or calcium, or precipitation with a reagent that out-competes the ligand, such as sulfide. The choice depends on the ligand, and the chemical inventory of the site is the starting point.

Co-precipitation and adsorption

Dosing iron(III) to form ferric hydroxide removes metals below their own hydroxide solubility by adsorption on the hydrous ferric oxide surface and by incorporation into the precipitate. Cation adsorption on hydrous ferric oxide rises sharply over a narrow pH range, the adsorption edge, whose position differs for each metal [7]. The ferric floc also acts as a coagulant for the fine metal hydroxide particles, improving their separation. The surface complexation model of hydrous ferric oxide allows this removal to be estimated, but bench testing remains necessary because competing ions and organic matter alter adsorption.

Sulfide precipitation compared with hydroxide precipitation

Metal sulfides are far less soluble than the corresponding hydroxides, so sulfide precipitation achieves lower residuals, operates over a wider pH range and is less affected by many complexing agents [8]. Its disadvantages are practical: the precipitate is fine and often colloidal, needing coagulation and good solids separation; excess sulfide must be controlled because hydrogen sulfide is toxic and is released at low pH; and dosing control is more demanding than pH control. Sulfide is therefore most often applied as a polishing stage after hydroxide precipitation has removed the bulk of the metal [8].

Sludge production estimate

The dry mass of metal hydroxide formed follows from stoichiometry:

To this are added the hydroxides of any iron or aluminium dosed, calcium sulfate or carbonate where lime is used, and the suspended solids in the influent. The wet volume depends on the solids concentration achieved by thickening and dewatering, which is established by test.

Worked example, stated inputs. Q = 10 m³ h⁻¹ (240 m³ d⁻¹); 50 mg L⁻¹ Zn precipitated as Zn(OH)₂ (99.39 g mol⁻¹) with NaOH (40.00 g mol⁻¹) [6]. Route 1, mass ratio: Zn(OH)₂ = 50 × 99.39/65.38 = 76.0 mg L⁻¹, and NaOH = 50 × 2 × 40.00/65.38 = 61.2 mg L⁻¹. Route 2, moles: 50/65.38 = 0.765 mmol L⁻¹ Zn; × 99.39 = 76.0 mg L⁻¹ Zn(OH)₂; × 2 × 40.00 = 61.2 mg L⁻¹ NaOH. The routes agree. Dry solids are 76.0 × 240/1000 = 18.2 kg d⁻¹. The NaOH figure covers precipitation only; neutralisation of the free acidity of the effluent is additional and is usually the larger demand.

pH control

The titration curve of a metal-bearing acid effluent is strongly non-linear: the pH rises slowly while metal precipitates and buffers the system, then steeply once precipitation is complete. A fixed-gain controller tuned for the buffered region becomes unstable in the steep region, and the reverse is sluggish [9]. Robust designs use two or more stages in series, with coarse adjustment in the first and trim in the last; adequate residence time and mixing in each stage; reagent strength matched to the turndown; and probes located where the reaction is complete. The pH set point is a temperature-dependent quantity: because pK_w rises as the water cools [5], the same pH reading corresponds to a lower hydroxide activity in winter, so set points selected in warm bench tests should be confirmed at the minimum process temperature.

Regulatory context

In England and Wales, discharges of treated effluent to surface water or groundwater require an environmental permit under the Environmental Permitting (England and Wales) Regulations 2016 [10], and discharges to a public sewer require a trade effluent consent from the sewerage undertaker under the Water Industry Act 1991 [11]. Permit and consent limits are normally expressed as total or dissolved metal concentrations, so the design must address both the equilibrium solubility and the capture of particulate metal in the solids separation stage.

References

1. Stumm, W. and Morgan, J.J. (1996) Aquatic Chemistry: Chemical Equilibria and Rates in Natural Waters, 3rd ed. New York: Wiley.
2. Baes, C.F. and Mesmer, R.E. (1976) The Hydrolysis of Cations. New York: Wiley.
3. Smith, R.M. and Martell, A.E. (2004) NIST Critically Selected Stability Constants of Metal Complexes, NIST Standard Reference Database 46, version 8. Gaithersburg: National Institute of Standards and Technology.
4. Davies, C.W. (1962) Ion Association. London: Butterworths.
5. Bandura, A.V. and Lvov, S.N. (2006) The ionization constant of water over wide ranges of temperature and density. Journal of Physical and Chemical Reference Data, 35(1), 15–30.
6. Prohaska, T. et al. (2022) Standard atomic weights of the elements 2021 (IUPAC Technical Report). Pure and Applied Chemistry, 94(5), 573–600.
7. Dzombak, D.A. and Morel, F.M.M. (1990) Surface Complexation Modeling: Hydrous Ferric Oxide. New York: Wiley.
8. Lewis, A.E. (2010) Review of metal sulphide precipitation. Hydrometallurgy, 104(2), 222–234.
9. Shinskey, F.G. (1973) pH and pION Control in Process and Waste Streams. New York: Wiley.
10. The Environmental Permitting (England and Wales) Regulations 2016, SI 2016/1154. legislation.gov.uk.
11. Water Industry Act 1991, Part IV, Chapter III (trade effluent). legislation.gov.uk.

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