Particle Characteristics, Chemistry of Solutions and Thermal Pollution: 18-Env-A1 Principles of Environmental Engineering, December 2014, Q3

Question 3: Particle Characteristics, Chemistry of Solutions and Thermal Pollution (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

(i) An Engineered Train Handling Dissolved, Colloidal and Suspended Contaminants

No single unit process removes all three solids classes efficiently, because they differ by orders of magnitude in size and settling behaviour: suspended solids (roughly >1 µm) settle under gravity within a practical basin depth and time; colloidal solids (roughly 1 nm–1 µm) are too small to settle on their own timescale (Brownian motion dominates gravity) and must first be destabilized; and dissolved contaminants are not removable by any physical settling or straining process at all. A conceptual engineered design therefore chains three stages, each targeting the fraction the previous stage cannot: coagulation/flocculation (adding a coagulant, e.g. alum or ferric chloride, to neutralize colloidal surface charge and let particles collide and grow into settleable flocs — this converts the colloidal fraction into the suspended-solids category), sedimentation (gravity settling of the now-larger flocs and the naturally suspended solids in a quiescent basin sized from settling velocity and surface overflow rate), and filtration (a granular media bed removing the residual fine floc that settled too slowly to clarify, by straining, interception and adsorption onto media grains). Dissolved contaminants that partition strongly onto solids (high $K_{OC}$, Q1(ii)) are removed indirectly as they sorb onto the flocs being coagulated; genuinely dissolved species that do not sorb require a separate process (e.g. activated carbon adsorption or ion exchange) beyond this particulate-removal train.

Figure 3.1 — Conceptual particle-removal train handling all three solids classes: coagulation/flocculation converts colloidal solids (and sorbed dissolved contaminants) into settleable floc, sedimentation removes the bulk suspended/floc load, and a rapid filter polishes the residual fine solids before discharge or reuse.

(ii) Hardness of Lake Ontario Water Near the Copper Mine

Given. Divalent-cation concentrations from the water analysis, with atomic weights Ca = 40, H = 1, C = 12, O = 16 as stated (magnesium's standard atomic weight, 24.3, is assumed general knowledge since it is not on the supplied list):

Given data
Ion	Concentration	Atomic weight	Valence
$Ca^{2+}$	50 mg/L	40 (given)	2
$Mg^{2+}$	200 mg/L	24.3 (standard)	2
$Cu^{2+}$	200 mg/L	63.5 (standard)	2

Find. The total hardness of the water expressed as mg/L CaCO₃, and its qualitative classification (soft, moderately hard or hard).

Check: hardness is defined as the sum of polyvalent alkaline-earth metal cations in water, of which $Ca^{2+}$ and $Mg^{2+}$ are overwhelmingly dominant in natural waters; standard water-chemistry practice (and the fact that no atomic weight for copper was supplied on the exam's own aid-sheet list — the question statement itself also names the analysis as being for "Ca, Mg and Fe" while the data table lists $Cu^{2+}$, an internal inconsistency treated as a labelling slip) treats $Cu^{2+}$ here as a trace heavy-metal constituent reported alongside the hardness-forming ions, not as a contributor to the hardness figure itself. The calculation below therefore uses $Ca^{2+}$ and $Mg^{2+}$ only; for reference, including $Cu^{2+}$ as if it were hardness-forming would add a further 315.0 mg/L as CaCO₃, which does not change the classification.

Approach. Convert each hardness-forming ion's mass concentration to an equivalent mass concentration as $\text{CaCO}_3$ using the ratio of equivalent weights, then sum and classify against the standard hardness scale.

Equivalent weight of $\text{CaCO}_3$. Molecular weight $= 40 + 12 + 3(16) = 100\ \text{g/mol}$; with valence 2 (each $\text{CO}_3^{2-}$ neutralizes one divalent cation), $$EW_{CaCO_3} = \frac{100}{2} = 50\ \text{g/eq}.$$
Convert $Ca^{2+}$ to CaCO₃ equivalent. $EW_{Ca} = 40/2 = 20\ \text{g/eq}$, so $$H_{Ca} = 50 \times \frac{50}{20} = \boxed{125.0\ \text{mg/L as CaCO}_3}.$$
Convert $Mg^{2+}$ to CaCO₃ equivalent. $EW_{Mg} = 24.3/2 = 12.15\ \text{g/eq}$, so $$H_{Mg} = 200 \times \frac{50}{12.15} = \boxed{823.0\ \text{mg/L as CaCO}_3}.$$
Total hardness and classification. Summing the hardness-forming ions, $$H_{total} = H_{Ca} + H_{Mg} = 125.0 + 823.0 = \boxed{948.0\ \text{mg/L as CaCO}_3}.$$ Against the standard scale (<75 soft; 75–150 moderately hard; 150–300 hard; >300 very hard), 948.0 mg/L is far above the 300 mg/L threshold — the water is classified as hard (at the extreme, "very hard," end of that category), consistent with a magnesium-rich mineralized watershed near mine workings.

Quantity	Value
Hardness from $Ca^{2+}$	125.0 mg/L as CaCO₃
Hardness from $Mg^{2+}$	823.0 mg/L as CaCO₃
Total hardness	948.0 mg/L as CaCO₃
Classification	Hard (very hard)

(iii) Reducing Thermal-Pollution Effects from Power-Plant Cooling Water

A once-through cooling system that withdraws lake water, passes it through the condenser, and discharges it directly back to the lake maximizes the temperature rise and the area of the lake affected, driving all three named effects: thermal shock (organisms encountering a sudden temperature jump at the discharge point), reduced dissolved oxygen (warmer water holds less DO, compounding stress on aquatic life exactly where the discharge is warmest), and community redistribution (cold-water species avoiding the warm plume, warm-water/invasive species colonizing it). A conceptual engineered solution reduces the heat load reaching the lake before discharge rather than only managing where it enters:

The core engineering solution is a cooling tower (or a cooling pond/reservoir as a lower-cost alternative where land is available) installed on the condenser discharge, converting the plant from once-through to a recirculating cooling system: the heated water is sprayed or cascaded through the tower where evaporative and convective heat transfer to the atmosphere rejects most of the waste heat, and the cooled water is recirculated back to the condenser rather than discharged, with only a small "blowdown" stream (needed to control dissolved-solids buildup from evaporation) actually released to the lake, at a far lower flow and temperature than the original once-through discharge. This directly reduces all three effects because the temperature differential and the discharge volume driving the thermal plume are both cut. Where a cooling tower is not feasible, a diffuser outfall discharging the remaining heat load as many small, high-velocity jets across the lake's width/depth (rather than one concentrated point) does not reduce the total heat rejected but rapidly entrains additional lake water into near-field mixing, shrinking the area and shortening the exposure time above the fishery's thermal tolerance, which is a reasonable secondary/complementary measure rather than a substitute for reducing the load itself.

Concept & Theory

Topic. Physical/chemical unit processes for coupled dissolved/colloidal/suspended contaminant removal, water chemistry (hardness), and engineered mitigation of thermal pollution.

Key relations. Coagulation → sedimentation → filtration as a size-cascade removal train; hardness as CaCO₃, $H = \sum C_i \cdot (50/EW_i)$; once-through vs. recirculating (cooling-tower) cooling-water heat rejection.

Why this works. Each sub-part reduces a pollutant or impact by intercepting it as far upstream in the process as practical — converting colloids to settleable floc before they can pass through treatment untreated, correctly identifying which ions actually contribute to a regulatory parameter before summing it, and rejecting waste heat to the atmosphere before it ever reaches the receiving water rather than trying to manage its effects after discharge.

Common pitfall. Proposing filtration alone without coagulation/flocculation first (colloids pass through a filter largely unremoved without prior destabilization); including every reported cation (e.g., $Cu^{2+}$) in a hardness sum without checking whether it is actually a hardness-forming species; treating outfall diffusion as a substitute for reducing the total heat load rather than a secondary measure once the load itself has been cut.

Source. MWH’s Water Treatment: Principles and Design, coagulation/sedimentation/filtration chapters; Davis & Cornwell, Introduction to Environmental Engineering, ch. 5 (water chemistry, hardness) and ch. 9 (thermal pollution).

Question 3 of 7: Particle Characteristics, Chemistry of Solutions and Thermal Pollution

Question 3: Particle Characteristics, Chemistry of Solutions and Thermal Pollution (20 marks)

(i) An Engineered Train Handling Dissolved, Colloidal and Suspended Contaminants

(ii) Hardness of Lake Ontario Water Near the Copper Mine

(iii) Reducing Thermal-Pollution Effects from Power-Plant Cooling Water