CHEM3120 · Environmental and Analytical Chemistry
Aqueous Chemistry: Water Properties & Hardness
Lecture 17 opens Block 3 of CHEM3120 with the chemistry of natural waters: hardness from Ca2+ and Mg2+ expressed as a CaCO3 equivalent, Henry's-law gas solubility (dissolved O2, N2, CO2), and the oxygen-demand measures COD and BOD. These are quantitative Part A short-answer favourites and part of Prof. Kepert's examinable Block 3 list, so the calculations here are high-value.
What this chapter covers
- 01Global water distribution: ~97% oceans, only ~0.5% accessible freshwater
- 02Hardness from divalent Ca2+ and Mg2+, expressed as mg/L CaCO3 equivalent
- 03Soap scum: precipitation (e.g. calcium stearate) once the ion product exceeds Ksp
- 04Henry's law [X(aq)] = kH · P(X) for dissolved O2, N2, CO2 and volatile pollutants
- 05Dissolved oxygen and its temperature dependence
- 06Chemical oxygen demand (COD) by dichromate titration; electron bookkeeping to O2 equivalent
- 07Biological oxygen demand (BOD) and eutrophication effects on dissolved gases and pH
Dissolved oxygen from Henry's law
- +1Apply Henry's law [O2(aq)] = kH · P(O2) = 1.3×10^-3 mol L^-1 atm^-1 × 0.21 atm = 2.73×10^-4 mol/L.
- +1Convert moles/L to mass/L using the molar mass: 2.73×10^-4 mol/L × 32.0 g/mol = 8.74×10^-3 g/L.
- +1Express in mg/L: 8.74×10^-3 g/L × 1000 mg/g = 8.7 mg/L.
Key terms
- Water hardness
- The concentration of divalent Ca2+ and Mg2+ in water, conventionally reported as an equivalent mass of CaCO3 (mg/L); high hardness precipitates soap and forms scale.
- CaCO3 equivalent
- A common basis for reporting hardness: each mole of divalent hardness ion is counted as one mole of CaCO3 (molar mass 100 g/mol) so different ions can be summed on one scale.
- Henry's law
- [X(aq)] = kH · P(X): at fixed temperature the dissolved concentration of a gas is proportional to its partial pressure; kH decreases as temperature rises.
- Dissolved oxygen (DO)
- The concentration of O2 dissolved in water (mg/L); essential for aquatic life and set by Henry's law, temperature and biological demand.
- Chemical oxygen demand (COD)
- The oxygen equivalent of the oxidisable matter in a water sample, measured by dichromate (Cr2O7^2-) titration and converted through electron bookkeeping to an O2 equivalent.
- Biological oxygen demand (BOD)
- The oxygen consumed by micro-organisms degrading organic matter in water; high BOD depletes dissolved oxygen and stresses aquatic ecosystems.
Aqueous Chemistry: Water Properties & Hardness FAQ
How do I express water hardness as a CaCO3 equivalent?
Convert the mass of each divalent ion (Ca2+, Mg2+) to moles, add the moles together, then re-express that total as CaCO3 by multiplying by 100 g/mol and dividing by the sample volume. The key idea is that hardness is a mole count of divalent ions on a common CaCO3 scale — you never simply add the milligrams of Ca2+ and Mg2+ together, because they have different molar masses.
Why does warm water hold less dissolved oxygen?
Because the Henry's-law constant for O2 decreases as temperature rises. Since [O2(aq)] = kH · P(O2) and P(O2) in air is roughly fixed, a smaller kH means a lower equilibrium dissolved-oxygen concentration. That is why warm, slow or thermally polluted water is more prone to oxygen stress, and why summer conditions can push dissolved oxygen below what fish need.
What is the difference between COD and BOD?
Both measure the oxygen demand of a water sample, but by different means. COD (chemical oxygen demand) uses a strong chemical oxidant, dichromate, and captures essentially all oxidisable matter, converted to an O2 equivalent via electron bookkeeping. BOD (biological oxygen demand) measures the oxygen that micro-organisms actually consume degrading the sample over time, so it reflects the biodegradable fraction. COD is faster and usually higher; BOD is more biologically meaningful.
Can AI help me with the water-chemistry calculations in CHEM3120?
Yes. Sia can walk you through a hardness or Henry's-law calculation step by step, check your COD electron bookkeeping, and explain the temperature dependence of dissolved oxygen — all in the short-answer style this Block 3 material uses. It explains the method and checks your reasoning; it does not do graded assessment for you, and University of Sydney academic-integrity rules apply.
Exam move
This is a quantitative, high-value block on Prof. Kepert's examinable Block 3 list, so secure the three routines: hardness as a CaCO3 equivalent (mass → moles → sum → ×100 ÷ volume), Henry's law for dissolved gases (mind the kH units and the temperature trend), and COD electron bookkeeping from a dichromate titration. Work each as one clean chain with units carried through, and always add a one-line physical interpretation (hard vs soft water, oxygen stress). Because these calculation types recur in weekly quizzes and Part A, rehearse them across the semester rather than in STUVAC. The final is closed-book with a formula sheet provided, so practise speed and accuracy. Confirm the exam date and permitted materials on Canvas.
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