⟵ 03 The Solvent (Problem Set) · Contents · 04 The Power of Hydrogen ⟶
The Solvent: Answer Key
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Suspended solids are particles physically carried in water (silt, clay, bacteria) - typically 2–100 microns. Dissolved solids are ions and molecules that interact with water at the molecular level, held in solution by hydration shells - typically a few nanometers. Conventional filters cannot catch dissolved ions because they are far smaller than filter pore sizes and are electrostatically bound to water.
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Dissolution involves three energetic terms. Lattice energy is the cost of pulling a crystal apart. Hydration energy is the payoff released when water stabilizes the separated species. Entropy is the wildcard: dispersion tends to favor dissolution, while solvent ordering can oppose it. Gibbs free energy combines these effects and tells you whether dissolution is favored.
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Sodium chloride has a manageable lattice cost, sufficient hydration payoff, and favorable entropy as the separated ions disperse through solution. That combination makes dissolution favorable under normal conditions. Calcium carbonate has a much higher lattice cost because calcium and carbonate bind strongly in a stable crystal structure. Water can hydrate the separated ions, but the payoff is often conditional and not enough to overcome the strength of the lattice, especially as temperature, pH, calcium, alkalinity, and carbon dioxide shift the balance toward solid scale.
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Dissolved ions are charge carriers. More ions means more current and higher conductivity, making it a fast, continuous proxy for TDS. Its limitation: conductivity measures total ionic load but not which ions are present. Two waters at the same conductivity can behave very differently - one may scale, the other may corrode.
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TDS ≈ 0.7 × 1,450 = 1,015 ppm.
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3.5% × 10,000 = 35,000 ppm.
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Water mass: 1,000 gal × 8.34 lb/gal = 8,340 lb. Weight of resulting solution = 8,340 lb + 5 lb = 8,345 lb. ppm increase: (5 lb / 8,345 lb) × (1,000,000) ≈ 599 ppm.
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The error is a factor of 1,000 (1 mS/cm = 1,000 µS/cm). The technician’s TDS estimate would be 1,000 times too low. This could lead to severe under-blowdown - the system would concentrate far beyond safe limits while the spreadsheet shows acceptable chemistry.
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Tower B faces far greater scaling risk. Sodium chloride is highly soluble across all normal conditions (manageable lattice cost, sufficient hydration, and favorable dispersion). Calcium bicarbonate, when concentrated and heated, shifts toward calcium carbonate precipitation - a salt with high lattice energy and inverse solubility. Identical conductivity means identical total ionic load, but the identity of the ions determines whether the water scales, corrodes, or behaves benignly.
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Surface water moves quickly over rock, giving minerals little time to dissolve, but it picks up physical debris (silt, clay, organic matter) along the way. Groundwater percolates slowly through geological formations over years or decades, giving ample contact time for minerals to dissolve. The rock itself acts as a natural filter, removing suspended particles during the slow descent. The result: high TDS, low turbidity.
⟵ 03 The Solvent (Problem Set) · Contents · 04 The Power of Hydrogen ⟶