Question 3 of 7: Particle Characteristics, Water Hardness and Thermal Pollution

Question 3: Particle Characteristics, Water Hardness 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) Biological Removal of Dissolved Solids and the Characteristics Required

Conventional biological treatment (activated sludge, trickling filters, and similar attached- or suspended-growth processes) removes dissolved solids indirectly: microorganisms metabolize dissolved organic (and some inorganic) substrates as an energy and carbon source, converting the dissolved material into new microbial cell mass and gaseous end-products (CO₂, and N₂ under denitrification), then that cell mass is removed from the water as a settleable solid in a downstream clarifier — the dissolved fraction is thereby converted into a separable particulate fraction rather than being filtered out directly. Two characteristics the dissolved solids must have to be removed effectively this way:

1. Biodegradability. The dissolved constituent must be usable by the microbial community as a carbon/energy or nutrient source (readily or at least slowly biodegradable organic matter, ammonia for nitrifiers); a dissolved solid that is biologically inert (many dissolved inorganic salts, some recalcitrant synthetic organics) passes through a biological process essentially unchanged.
2. Bioavailability (solubility and molecular accessibility). The constituent must actually be available for microbial uptake — dissolved and at a molecular size/form the organisms’ enzyme systems can act on (or that can first be hydrolyzed to that form); a compound that is chemically biodegradable in principle but bound, complexed, or present in a form the resident microbial population cannot access will not be removed at the rate the demonstrated biodegradability alone would suggest.

(ii) Hardness of Lake Superior Water Near the Salt Mine

Given. Divalent-cation concentrations from the lake-water analysis, with atomic weights $Ca=40$, $Mg=24$, $Cu=64$, $H=1$, $C=12$, $O=16$ as stated on the exam:

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

Approach. Hardness, by the Standard Methods/Sawyer–McCarty definition, is the sum of the alkaline-earth cations $Ca^{2+}$ and $Mg^{2+}$ only, each converted to an equivalent mass of CaCO₃ via the ratio of equivalent weights; $Cu^{2+}$ is a transition-metal cation supplied alongside Ca and Mg as a deliberate decoy and is not a hardness-forming ion under this definition.

1. Equivalent weight of CaCO₃. Build its molecular weight from the given atomic weights ($Ca+C+3O$), then halve for the divalent carbonate: $$MW_{CaCO_3} = 40+12+3(16) = 100\ \text{g/mol}, \qquad EW_{CaCO_3} = 100/2 = 50\ \text{g/eq}.$$
2. Equivalent weights of the cations. Equivalent weight $=$ atomic weight $\div$ valence, all three ions being divalent: $$EW_{Ca} = 40/2 = 20\ \text{g/eq}, \qquad EW_{Mg} = 24/2 = 12\ \text{g/eq}, \qquad EW_{Cu} = 64/2 = 32\ \text{g/eq}.$$
3. Convert $Ca^{2+}$ and $Mg^{2+}$ to CaCO₃ equivalents. $$H_{Ca} = 80\times\dfrac{50}{20} = 200.0\ \text{mg/L as CaCO}_3, \qquad H_{Mg} = 60\times\dfrac{50}{12} = 250.0\ \text{mg/L as CaCO}_3.$$
4. Sum for total hardness. $$\boxed{H = H_{Ca}+H_{Mg} = 200.0+250.0 = 450.0\ \text{mg/L as CaCO}_3.}$$ $Cu^{2+}$ is not included in this sum: under the Standard Methods/Sawyer–McCarty definition, hardness is specifically the Group 2 alkaline-earth pair $Ca^{2+}+Mg^{2+}$, not every polyvalent cation a water analysis happens to report. For reference only, $Cu^{2+}$ would contribute $40\times(50/32) = 62.5\ \text{mg/L as CaCO}_3$ if (incorrectly) included, giving 512.5 mg/L — a common trap, since the question deliberately supplies copper’s atomic weight alongside calcium’s and magnesium’s.
5. Classify the water. Against the standard hardness scale (0–75 soft, 75–150 moderately hard, 150–300 hard, >300 very hard), $H=450.0$ mg/L places this water in the very hard category.

(iii) Controlling Thermal Pollution from a Nuclear Plant Using a Cooling Tower

Selecting the cooling-tower option (over a cooling pond), three design criteria/operational approaches that effectively control thermal pollution to the receiving environment:

1. Size the tower’s heat-rejection (approach-temperature) capacity to the plant’s full design heat load, including summer worst-case wet-bulb temperature. A mechanical or natural-draft cooling tower must be sized so that even at the highest ambient wet-bulb temperature expected, the cooled water leaving the tower is close enough to ambient that the blowdown/discharge stream does not itself constitute a thermal-pollution source to the receiving water body.
2. Operate on a closed-loop recirculating basis rather than once-through, and control blowdown volume and temperature. Recirculating the condenser cooling water through the tower repeatedly (rather than discharging it once-through) sharply reduces both the volume and average temperature of water that must ultimately be discharged as blowdown; blowdown temperature and rate are then the parameters actually regulated and monitored against the receiving water’s thermal-mixing-zone limit.
3. Control drift and cycles of concentration to manage the discharge’s dissolved-solids load alongside its temperature. Drift eliminators limit water (and any entrained treatment chemicals) lost as fine droplets, while managing the number of concentration cycles before blowdown balances water-use efficiency against the dissolved-solids concentration of the blowdown — both are operational levers that keep the eventual thermal discharge within its permitted temperature and water-quality limits simultaneously.