Environmental, green and energy chemistry

Chemistry of natural waters, wastewater treatment

Water quality emerges from acid–base, redox and phase equilibria coupled to biological processes. Learn how those principles explain carbonate buffering, oxygen demand, nutrient cycling, treatment and contaminant removal.

1 Lower secondary 2 Upper secondary 3 Undergraduate 4 Advanced 5 Research

IntuitionWater chemistry links invisible equilibria to visible water quality

A stream can look clear yet carry dissolved salts, nutrients, metals, or microbes. Its chemistry reflects both natural geology and human inputs; treatment changes chemical form or separates contaminants rather than simply making matter disappear.

Follow the treatment train from screening and settling through aeration, clarification and disinfection; switch modes to trace nitrification, nitrate recycle and sludge return.

SchoolSchool level: what water carries and what treatment does

Definition: Water hardness

Hardness is mainly the combined concentration of dissolved calcium and magnesium, commonly reported as mg/L equivalent $\ce{CaCO3}$ . Temporary hardness is associated with bicarbonate; boiling can remove some by forming carbonate solids, whereas sulfate and chloride hardness generally remains.

Dissolved oxygen saturation in freshwater near 1 atm
Temperature	Approximate DO (mg/L)
0 °C	14.6
20 °C	9.1
25 °C	8.3
30 °C	7.6

Dissolved oxygen (DO) reflects the balance between reaeration, photosynthesis and biological or chemical consumption. Biochemical oxygen demand (BOD) estimates oxygen used by microbes to oxidize biodegradable matter; chemical oxygen demand (COD) measures oxidizable material by a strong chemical oxidant and is usually higher.

BOD_t=L_0\left(1-e^{-kt}\right),\qquad \mathrm{BOD}_5=L_0\left(1-e^{-5k}\right)

Example: Estimating ultimate BOD

A diluted bottle test gives a five-day BOD of 200 mg/L (as the original sample). If the first-order rate constant at 20 °C is $k=0.23\ \mathrm{d^{-1}}$ , estimate the ultimate carbonaceous demand $L_0$ .

Solution

At five days, the fraction exerted is $1-e^{-5(0.23)}=0.683$ . Thus $L_0=200/0.683\approx293\ \mathrm{mg/L}$ . This model is an estimate; nitrification, seeding, temperature and inhibition can alter a measured BOD.

UndergraduateUniversity: carbonate equilibria and alkalinity

The dissolved inorganic carbon pool is conventionally written $\ce{CO2^*}$ (dissolved $\ce{CO2}$ plus the small hydrated fraction often called $\ce{H2CO3}$ ), $\ce{HCO3^-}$ and $\ce{CO3^2-}$ . At 25 °C, approximate thermodynamic $pK_{a1}=6.35$ and $pK_{a2}=10.33$ ; apparent values shift with ionic strength and temperature.

\ce{CO2^* + H2O <=> H+ + HCO3^-}\quad K_{a1};\qquad \ce{HCO3^- <=> H+ + CO3^2-}\quad K_{a2}

Definition: Alkalinity

Alkalinity is the acid-neutralizing capacity, not the pH. For a carbonate-dominated water, total alkalinity is approximately $[\ce{HCO3^-}]+2[\ce{CO3^2-}]+[\ce{OH^-}]-[\ce{H^+}]$ , in equivalents per litre; other weak-acid systems can contribute.

Example: Carbonate speciation from alkalinity

At 25 °C a sample has pH 7.80 and total alkalinity 2.00 meq/L. Estimate total inorganic carbon, neglecting noncarbonate alkalinity.

Solution

Using the diprotic-acid distribution fractions at pH 7.80 gives $\alpha_0=0.0342$ , $\alpha_1=0.9630$ , $\alpha_2=0.00284$ . Thus $TA\approx C_T(\alpha_1+2\alpha_2)$ and $C_T\approx2.00/(0.9630+2\times0.00284)=2.06\ \mathrm{mmol/L}$ . About 1.99 mmol/L is bicarbonate; only about 0.0059 mmol/L is carbonate.

Example: Hardness as calcium carbonate

A water contains 60 mg/L $\ce{Ca^2+}$ and 12 mg/L $\ce{Mg^2+}$ . Estimate total hardness as mg/L $\ce{CaCO3}$ .

Solution

Use equivalent-weight factors: $H_T=2.497[Ca]+4.118[Mg]=2.497(60)+4.118(12)\approx199\ \mathrm{mg/L}$ as $\ce{CaCO3}$ .

UndergraduateUniversity: treatment trains and chemical removal

Conventional municipal wastewater treatment screens debris, removes grit and settleable solids, biologically oxidizes dissolved organics in an aeration basin, separates activated-sludge biomass in a secondary clarifier, and disinfects the effluent when required. Return activated sludge maintains biomass; wasting sludge controls solids retention time. Nutrient-removal trains add anoxic zones and recycle nitrate-rich mixed liquor.

F/M=\frac{Q S_0}{V X}\qquad;\qquad \theta_c=\frac{V X}{Q_wX_w+Q_eX_e}

Example: Sizing an aeration basin by F/M

A plant treats $10{,}000\ \mathrm{m^3/d}$ with influent BOD $200\ \mathrm{mg/L}$ (use this as $S_0$ for a simplified estimate). At target $F/M=0.30\ \mathrm{d^{-1}}$ and $X=2500\ \mathrm{mg/L}$ , estimate basin volume.

Solution

Convert concentrations: $200\ \mathrm{mg/L}=0.20\ \mathrm{kg/m^3}$ and $X=2.50\ \mathrm{kg/m^3}$ . Then $V=QS_0/[(F/M)X]=10{,}000(0.20)/(0.30\times2.50)\approx2{,}670\ \mathrm{m^3}$ . This simplified result implies HRT about 6.4 h; real design also uses removal targets, temperature, settling, oxygen transfer and SRT.

Coagulation destabilizes colloids by charge neutralization, adsorption and sweep capture in metal-hydroxide floc. Alum or ferric salts hydrolyse, consume alkalinity and form insoluble hydroxides; jar tests establish dose and pH because natural organic matter and water composition change the optimum. Phosphate can be precipitated or sorbed with Fe(III) or Al(III); lime promotes calcium-phosphate solids at suitable pH. Dissolved metals may be precipitated as hydroxides or sulfides, adsorbed, ion-exchanged or separated by membranes; pH must account for amphoteric redissolution and competing ligands.

Example: Nickel hydroxide precipitation estimate

For an idealized solution at 25 °C, use $K_{sp}(\ce{Ni(OH)2})=5.5\times10^{-16}$ . Estimate the minimum pH at which free nickel could be reduced to 1.0 mg/L by hydroxide precipitation.

Solution

At saturation, $K_{sp}=[\ce{Ni^2+}][\ce{OH^-}]^2$ . Here $[\ce{Ni^2+}]=0.001/58.69=1.70\times10^{-5}\ \mathrm M$ , giving $[\ce{OH^-}]=\sqrt{5.5\times10^{-16}/1.70\times10^{-5}}=5.7\times10^{-6}\ \mathrm M$ and pH $\approx8.75$ . Complexation, activity corrections, solids and amphoteric behavior can shift real treatment results.

Disinfection targets pathogens with chlorine, ozone or ultraviolet light. Chlorine forms hypochlorous acid, whose acid-base balance matters: HOCl is generally more effective than $\ce{OCl^-}$ , so increasing pH can reduce rapid disinfection. Chlorine may form disinfection by-products with natural organic matter; ozone is powerful but leaves no persistent residual, and UV inactivates microbes without a chemical residual. Select a validated process and control residual, contact time, turbidity and by-products.

AdvancedAdvanced: redox zonation and biological transformations

Redox potential is often expressed as $E_h$ (volts) or $pe=F E_h/(2.303RT)$ ; at 25 °C, $pe\approx E_h/0.05916$ . A pe–pH diagram maps thermodynamically favoured forms, but does not predict rates, microbial pathways or equilibrium in a real, heterogeneous water body.

pe=\frac{F E_h}{2.303RT}\approx\frac{E_h}{0.05916\,\mathrm{V}}\quad(25\ ^\circ\mathrm C)

As oxygen is depleted, microbes commonly use nitrate, manganese(IV) oxides, iron(III) oxides, sulfate and ultimately carbon dioxide as electron acceptors, subject to availability and kinetics. Fe(II) is often more mobile under reducing conditions; oxidation produces Fe(III) hydroxide flocs that can sorb arsenic and other trace elements. Mn(II) oxidation is often slower and may require microbial catalysis. Nitrification oxidizes ammonium through nitrite to nitrate and consumes oxygen and alkalinity; denitrification reduces nitrate to nitrogen gas under anoxic conditions and restores some alkalinity.

Biological nitrogen transformations in treatment
Process	Net description
Nitrification	$\ce{NH4+ + 2O2 -> NO3- + 2H+ + H2O}$ ; about 4.57 g $\ce{O2}$ /g ammonium-N and 7.14 g alkalinity as $\ce{CaCO3}$ /g N consumed.
Denitrification	Anoxic reduction of nitrate to $\ce{N2}$ using an electron donor; methanol is one possible donor.

References

Aquatic Chemistry: Chemical Equilibria and Rates in Natural Waters · Werner Stumm, James J. Morgan, 1996
Wastewater Engineering: Treatment and Resource Recovery · Metcalf & Eddy / AECOM; George Tchobanoglous, H. David Stensel, Ryujiro Tsuchihashi, Franklin L. Burton, 2014