Rain is defined as acid rain when its pH is below about 5.6, not 7, because

pure water in equilibrium with atmospheric carbon dioxide already has a pH of about 5.6

the pH scale is defined relative to rainwater

below pH 5.6 ammonia can no longer neutralise it

sulphuric acid is always present in cloud water

Which of the following lower the equilibrium concentration of dissolved oxygen in a water body? Select all that apply.

A higher altitude of the water body

A rise in the partial pressure of oxygen above the water

A higher altitude of the water body

Assertion (A): A reaction with a negative standard Gibbs energy change has an equilibrium constant greater than one. Reason (R): ΔG° = −RT ln K. Choose the correct option.

Both A and R are true, and R is the correct explanation of A

Both A and R are true, but R is not the correct explanation of A

A pesticide degrades in soil by first-order kinetics with a half-life of 30 days. What fraction of the applied amount remains after 90 days?

0%, since three half-lives complete the decay

Environmental Chemistry I: The Classification of Elements, Stoichiometry, Gibbs Energy and Chemical Potential, Kinetics and Equilibria, the Solubility of Gases in Water, the Carbonate System, Hydrocarbons and Radioisotopes

Unit II opens with the fundamentals of environmental chemistry, the working tools for every later calculation about pollutants. This chapter takes the classification of elements and why some metals are toxic; stoichiometry, including carbon dioxide and sulphur dioxide from fuel and the theoretical oxygen demand of an organic waste; Gibbs energy, chemical potential and the link between ΔG° and the equilibrium constant; kinetics, including first-order decay, half-lives and temperature correction; chemical equilibria and solubility products; the solubility of gases in water under Henry's law; the carbonate system, alkalinity and the pH of natural rain; the saturated, unsaturated and aromatic hydrocarbons; and radioisotopes and decay. Each topic is worked with the numbers the examiner sets.

1. The classification of elements and why some are toxic

The modern periodic law, based on Moseley's work of 1913, states that the properties of elements are periodic functions of their atomic numbers, refining Mendeleev's table of 1869, which was ordered by atomic mass. The table is divided into s-, p-, d- and f-blocks by the orbital being filled, and into metals, non-metals and metalloids (boron, silicon, germanium, arsenic, antimony, tellurium), whose intermediate properties matter environmentally because arsenic and selenium behave as neither simple metals nor non-metals. Biologically, elements fall into major nutrients (C, H, O, N, P, S, K, Ca, Mg), micronutrients or trace elements needed in small amounts (Fe, Mn, Zn, Cu, Mo, B, Cl, Ni, and Se and Co for animals), and elements with no known beneficial role that are toxic at low concentration (Hg, Cd, Pb). Several essential elements, selenium and copper among them, become toxic above a narrow range.

Why mercury, cadmium and lead are so toxic is explained by Pearson's hard and soft acids and bases (1963). Soft metal ions, large and easily polarised, such as Hg²⁺ and Cd²⁺ (with Pb²⁺ borderline), bind strongly to soft donor atoms, above all the sulphur of the thiol (–SH) groups in proteins and enzymes, and so inactivate them; hard ions such as Ca²⁺ and Mg²⁺ prefer oxygen donors. The same principle guides treatment: sulphide precipitation and thiol-bearing chelating agents remove soft metals.

2. Stoichiometry and the units of concentration

Stoichiometry is the arithmetic of balanced equations: moles react in whole-number ratios, and masses follow from molar masses. Burning methane, CH₄ + 2O₂ → CO₂ + 2H₂O, turns 16 g of methane into 44 g of carbon dioxide, so 1 kg of methane gives 44 ÷ 16 = 2.75 kg of CO₂. Every tonne of carbon burnt gives 44 ÷ 12 ≈ 3.67 t of CO₂, the factor used to convert carbon emissions to carbon dioxide. For sulphur, S + O₂ → SO₂ turns 32 g of sulphur into 64 g of SO₂, so a tonne of coal with 1% sulphur, that is 10 kg of sulphur, releases 20 kg of SO₂ if all of it burns.

The theoretical oxygen demand (ThOD) of an organic compound is the oxygen needed to oxidise it completely, from its balanced equation. For glucose, C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O, 180 g of glucose needs 6 × 32 = 192 g of oxygen, so a solution of 300 mg/L glucose has a ThOD of 300 × 192 ÷ 180 = 320 mg/L. The measured COD approaches the ThOD for most organics, while the BOD is lower because microbes convert part of the carbon into new cells rather than oxidising it.

Unit	Meaning	Use
mg/L	Milligrams of solute per litre of solution; equal to ppm by mass in dilute water	Water and wastewater
ppm and ppb (by volume)	Parts of gas per million or billion parts of air by volume (or moles)	Gaseous air pollutants
µg/m³	Micrograms of pollutant per cubic metre of air	Air-quality standards and particulate matter
Molarity and normality	Moles, or gram-equivalents, per litre	Titrations and reagent preparation

Gaseous concentrations convert between the two air units through the molar volume, 24.45 L at 25 °C and 1 atm (22.4 L at 0 °C): µg/m³ = ppm × molar mass × 1000 ÷ 24.45. So 0.1 ppm of sulphur dioxide (molar mass 64) is 0.1 × 64 × 1000 ÷ 24.45 ≈ 262 µg/m³. Particulate matter has no molar mass and is always reported by mass per volume.

3. Gibbs energy, chemical potential, kinetics and chemical equilibria

Whether a reaction can proceed is decided by the change in Gibbs energy, ΔG = ΔH − TΔS: a reaction is spontaneous when ΔG is negative, at equilibrium when it is zero and non-spontaneous when it is positive. The standard change fixes the equilibrium constant, ΔG° = −RT ln K, so a negative ΔG° means K > 1 and the products are favoured; at 25 °C every factor of ten in K is worth about 5.7 kJ/mol. Away from equilibrium, ΔG = ΔG° + RT ln Q, where Q is the reaction quotient. The chemical potential of a substance, μ, is its partial molar Gibbs energy, μ = μ° + RT ln a, where a is its activity. Substances move from high to low chemical potential, and at equilibrium a substance has the same chemical potential in every phase; this is the thermodynamic basis of the partitioning of a pollutant between air, water, soil and fat.

Thermodynamics says whether; kinetics says how fast. The rate law gives the order of a reaction. For a first-order reaction, which describes radioactive decay, the die-off of bacteria and, approximately, the degradation of many pesticides and the exertion of BOD, C = C₀e^(−kt) and the half-life is t½ = 0.693 ÷ k, independent of the starting concentration. A pesticide with a 30-day half-life therefore falls to a half after 30 days, a quarter after 60 and an eighth, 12.5%, after 90. For zero order C = C₀ − kt, and for second order 1/C = 1/C₀ + kt. Rate rises with temperature according to the Arrhenius equation, k = A e^(−Ea/RT); environmental engineers use the simpler k_T = k₂₀ θ^(T−20), with θ about 1.047 for BOD.

At equilibrium the forward and reverse rates are equal and the concentrations are constant; Le Chatelier's principle predicts that a system shifts to oppose any imposed change. For a sparingly soluble salt the solubility product governs dissolution: for calcite, CaCO₃ ⇌ Ca²⁺ + CO₃²⁻, Ksp is about 3.3 × 10⁻⁹ at 25 °C. When the ion product exceeds Ksp the salt precipitates, which is how lime softening removes hardness and why hydroxide and sulphide precipitation remove heavy metals. The ion product of water, Kw = [H⁺][OH⁻] = 10⁻¹⁴ at 25 °C, makes neutral water pH 7 at that temperature only.

⚠️ A first-order half-life does not depend on how much you start with

Doubling the initial concentration of a first-order pollutant does not double the time it takes to halve; it adds exactly one half-life to the time needed to reach any given low level. A half-life that changes with concentration signals a zero- or second-order process.

4. The solubility of gases in water and the carbonate system

Henry's law states that the concentration of a gas dissolved in a liquid at equilibrium is proportional to its partial pressure above the liquid: C = KH × p. Gas solubility therefore rises with pressure and falls with temperature and salinity. Fresh water saturated with air at sea level holds about 14.6 mg/L of oxygen at 0 °C, about 9.1 mg/L at 20 °C and about 8.3 mg/L at 25 °C; water at high altitude, where pressure is lower, holds less. This is why warm effluents and summer conditions stress aquatic life, and why oxygen, being only sparingly soluble, is so easily depleted by organic waste. Carbon dioxide is far more soluble than oxygen, and it also reacts with water.

The carbonate system is the set of equilibria that controls the pH of most natural waters: CO₂(g) ⇌ CO₂(aq); CO₂(aq) + H₂O ⇌ H₂CO₃; H₂CO₃ ⇌ H⁺ + HCO₃⁻ (pK₁ = 6.35 at 25 °C); and HCO₃⁻ ⇌ H⁺ + CO₃²⁻ (pK₂ = 10.33). Below pH 6.35 dissolved CO₂ (H₂CO₃*) dominates, between 6.35 and 10.33 bicarbonate dominates, and above 10.33 carbonate dominates; natural waters, usually between pH 6.5 and 8.5, are therefore bicarbonate systems. Pure water in equilibrium with the atmosphere's CO₂ has a pH of about 5.6, which is why rain is defined as acid rain only below pH 5.6, not below 7.

Alkalinity is the acid-neutralising capacity of water: alkalinity = [HCO₃⁻] + 2[CO₃²⁻] + [OH⁻] − [H⁺], expressed as mg/L of CaCO₃. It is measured by titration with standard acid, first to the phenolphthalein end point near pH 8.3 (phenolphthalein alkalinity, from hydroxide and half the carbonate) and then to the methyl-orange end point near pH 4.5 (total alkalinity). Alkalinity as CaCO₃ = (mL of titrant × normality × 50,000) ÷ mL of sample, so if 100 mL of sample needs 12 mL of 0.02 N sulphuric acid to reach the methyl-orange end point and none to the phenolphthalein end point, the total alkalinity is 120 mg/L, all bicarbonate. The same chemistry drives ocean acidification: the oceans absorb about a quarter of emitted CO₂, and surface-ocean pH has fallen by about 0.1 unit since pre-industrial times, an increase of roughly a quarter in hydrogen-ion concentration because the scale is logarithmic, which lowers the carbonate available to corals and shell-forming organisms.

🎯 Why 50,000 in the alkalinity formula

The equivalent weight of CaCO₃ is 100 ÷ 2 = 50 g, that is 50,000 mg per equivalent. Multiplying the equivalents of acid used (mL × N ÷ 1000) by 50,000 mg and dividing by the sample volume in litres (mL ÷ 1000) gives mg/L as CaCO₃; the two factors of 1000 cancel. Hardness is expressed the same way.

5. Saturated and unsaturated hydrocarbons, and radioisotopes

Class	General formula and bonding	Environmental significance
Alkanes (saturated)	CnH2n+2; single C–C bonds only	Relatively unreactive; methane is a potent greenhouse gas with an atmospheric lifetime of about a decade
Alkenes (unsaturated)	CnH2n; at least one C=C double bond	Highly reactive with OH radicals and ozone; key precursors of photochemical smog
Alkynes (unsaturated)	CnH2n−2; a C≡C triple bond	Acetylene from combustion and welding
Aromatics	Benzene rings with delocalised electrons	Benzene is a human carcinogen; polycyclic aromatic hydrocarbons such as benzo[a]pyrene come from incomplete combustion

Radioisotopes are unstable nuclides that decay by emitting alpha particles (helium nuclei, stopped by paper or skin but dangerous if inhaled or ingested), beta particles (electrons, stopped by a few millimetres of aluminium) or gamma rays (penetrating electromagnetic radiation, reduced by lead or concrete). Decay is first order: N = N₀ (½)^(t ÷ t½). Iodine-131, with a half-life of about 8 days, falls to 12.5% after 24 days; caesium-137 (about 30 years) and strontium-90 (about 29 years) persist for decades after a reactor accident or weapons test, strontium because it substitutes for calcium in bone. Radon-222 (3.8 days), from the uranium-238 decay series, is the largest natural source of radiation dose indoors. Carbon-14 (about 5,730 years) dates organic material, tritium (about 12.3 years) dates young groundwater, and uranium-238 (about 4.47 billion years) and potassium-40 (about 1.25 billion years) date rocks.

Key takeaways

Soft metal ions such as Hg²⁺ and Cd²⁺ bind the thiol groups of enzymes, which is why they are toxic at low concentration; selenium and copper are essential but toxic above a narrow range.
Stoichiometry gives 2.75 kg CO₂ per kg of methane, 3.67 t CO₂ per t of carbon, 2 kg SO₂ per kg of sulphur and the ThOD of an organic waste; µg/m³ = ppm × M × 1000 ÷ 24.45 at 25 °C.
ΔG = ΔH − TΔS and ΔG° = −RT ln K decide direction and extent; first-order processes have t½ = 0.693 ÷ k, independent of concentration.
Henry's law makes gas solubility rise with pressure and fall with temperature and salinity; the carbonate system (pK₁ 6.35, pK₂ 10.33) makes natural waters bicarbonate-dominated and unpolluted rain about pH 5.6.
Alkanes are saturated and relatively inert, alkenes are reactive smog precursors and aromatics include carcinogens; radioisotopes decay by first-order kinetics, from 8-day iodine-131 to 30-year caesium-137.

Practice questions (10)

Attempt each one before opening the answer. Every explanation names the tempting wrong option as well as the right one, because that is where marks are lost.

How many kilograms of carbon dioxide are produced by the complete combustion of 1 kg of methane (C = 12, H = 1, O = 16)? Give the answer to two decimal places.
Numerical answer — type the value.
Show answer
Answer: 2.75
CH₄ + 2O₂ → CO₂ + 2H₂O, so 16 g of methane gives 44 g of CO₂, and 1 kg gives 44 ÷ 16 = 2.75 kg. The factor 44 ÷ 12 = 3.67 applies per kilogram of carbon, not per kilogram of methane, whose mass includes hydrogen.
What is the theoretical oxygen demand, in mg/L, of a solution containing 300 mg/L of glucose (C₆H₁₂O₆)?
Numerical answer — type the value.
Show answer
Answer: 320
C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O: 180 g of glucose needs 192 g of O₂. So 300 mg/L needs 300 × 192 ÷ 180 = 320 mg/L. Using one mole of O₂ per mole of glucose, or forgetting that each O₂ is 32 g, gives answers far too small.
In the carbonate system at 25 °C, bicarbonate (HCO₃⁻) is the dominant species
1. only at exactly pH 7
2. below pH 6.35
3. above pH 10.33
4. between pH 6.35 and pH 10.33
Show answer
Answer: D — between pH 6.35 and pH 10.33
The two pK values bound the bicarbonate field: below pK₁ (6.35) dissolved CO₂ dominates and above pK₂ (10.33) carbonate dominates. Most natural waters lie between pH 6.5 and 8.5 and so are bicarbonate systems; pH 7 has no special role in the carbonate equilibria.
Rain is defined as acid rain when its pH is below about 5.6, not 7, because
1. pure water in equilibrium with atmospheric carbon dioxide already has a pH of about 5.6
2. the pH scale is defined relative to rainwater
3. below pH 5.6 ammonia can no longer neutralise it
4. sulphuric acid is always present in cloud water
Show answer
Answer: A — pure water in equilibrium with atmospheric carbon dioxide already has a pH of about 5.6
Dissolved CO₂ forms carbonic acid, and at present atmospheric levels the equilibrium pH of pure water is about 5.6. Only acidity beyond that, mainly from sulphuric and nitric acids formed from SO₂ and NOx, counts as acid rain.
Which of the following lower the equilibrium concentration of dissolved oxygen in a water body? Select all that apply.
1. A rise in water temperature
2. A rise in the partial pressure of oxygen above the water
3. A higher altitude of the water body
4. A rise in salinity
Show answer
Answer: A — A rise in water temperature; C — A higher altitude of the water body; D — A rise in salinity
Gas solubility falls as temperature and salinity rise, and at altitude the lower atmospheric pressure lowers the partial pressure of oxygen. By Henry's law a higher partial pressure raises, not lowers, the dissolved concentration.
Assertion (A): A reaction with a negative standard Gibbs energy change has an equilibrium constant greater than one. Reason (R): ΔG° = −RT ln K. Choose the correct option.
1. Both A and R are true, and R is the correct explanation of A
2. Both A and R are true, but R is not the correct explanation of A
3. A is true, but R is false
4. A is false, but R is true
Show answer
Answer: A — Both A and R are true, and R is the correct explanation of A
Both are true and R explains A: if ΔG° is negative, ln K = −ΔG° ÷ RT is positive, so K > 1 and products are favoured at equilibrium. The sign of ΔG° says nothing about speed, which is a question of kinetics.
A pesticide degrades in soil by first-order kinetics with a half-life of 30 days. What fraction of the applied amount remains after 90 days?
1. 12.5%
2. 25%
3. 33.3%
4. 0%, since three half-lives complete the decay
Show answer
Answer: A — 12.5%
Ninety days is three half-lives, so (½)³ = 1/8 = 12.5% remains. A first-order process never reaches zero in a finite number of half-lives; 33.3% comes from wrongly assuming a linear loss of one-third per period.
A 100 mL water sample shows no phenolphthalein alkalinity and needs 12 mL of 0.02 N H₂SO₄ to reach the methyl-orange end point. What is its total alkalinity in mg/L as CaCO₃?
Numerical answer — type the value.
Show answer
Answer: 120
Alkalinity = (mL × N × 50,000) ÷ mL of sample = (12 × 0.02 × 50,000) ÷ 100 = 120 mg/L as CaCO₃. With zero phenolphthalein alkalinity the whole of it is bicarbonate alkalinity.
Which of the following radioisotopes are correctly matched with their approximate half-lives? Select all that apply.
1. Iodine-131: about 8 days
2. Carbon-14: about 5,730 years
3. Caesium-137: about 8 days
4. Radon-222: about 1,600 years
Show answer
Answer: A — Iodine-131: about 8 days; B — Carbon-14: about 5,730 years
Iodine-131 (about 8 days) and carbon-14 (about 5,730 years) are correct. Radon-222 has a half-life of only about 3.8 days; 1,600 years is radium-226, its parent. Caesium-137 lasts about 30 years, which is why it persists after reactor accidents.
Hydrocarbons with the general formula CnH2n+2, containing only single carbon-carbon bonds, are
1. alkanes
2. aromatic hydrocarbons
3. alkynes
4. alkenes
Show answer
Answer: A — alkanes
CnH2n+2 is the saturated alkane series, from methane to octane and beyond. Alkenes (CnH2n) have a double bond and alkynes (CnH2n−2) a triple bond, which is why they are far more reactive in smog chemistry; aromatics contain benzene rings.