Water Chemistry: pH, Alkalinity & Hardness

Quick Answer: pH measures acidity; alkalinity is acid-neutralizing capacity; hardness is Ca²⁺/Mg²⁺. They govern coagulation, softening, corrosion, and scaling.

pH

[ \text{pH} = -\log_{10}[\text{H}^+] ]

Each pH unit is tenfold change in H⁺ activity.

Alkalinity

Titration to pH 4.5 (often) reports P, M, OH alkalinity contributions. Alkalinity stabilizes pH during coagulant addition — insufficient alkalinity causes pH crash.

Hardness

[ \text{Hardness (mg/L as CaCO}_3) ]

from Ca²⁺ and Mg²⁺. Temporary hardness from bicarbonates removable by boiling/lime; permanent needs soda ash.

LSI (Conceptual)

LSI > 0 tends toward CaCO₃ scaling; LSI < 0 tends toward corrosive non-scaling conditions.

Worked Example

Raw water pH 7.2, alkalinity 90 mg/L as CaCO₃. Adding alum consumes alkalinity — verify remaining > 30 mg/L or add lime.

Exam trap: Alkalinity ≠ pH — high alkalinity can coexist with moderate pH.

Multi-Step Workflow

List givens with units, select the governing relationship, convert to a consistent unit set, solve, and compare to a rough estimate.

pH, Alkalinity, and Hardness

Worked Hardness Example

Ca²⁺ = 60 mg/L as Ca, Mg²⁺ = 12 mg/L as Mg.

Hardness as CaCO₃ ≈ $60\times(50/20) + 12\times(50/12.15) \approx 150 + 49 \approx 199$ mg/L as CaCO₃ (moderately hard).

On the Exam: Distinguish carbonate (temporary) vs noncarbonate (permanent) hardness when lime-soda softening is mentioned.

pH, Alkalinity, and Hardness

Worked Hardness Example

Ca²⁺ = 60 mg/L as Ca, Mg²⁺ = 12 mg/L as Mg.

Hardness as CaCO₃ ≈ $60\times(50/20) + 12\times(50/12.15) \approx 150 + 49 \approx 199$ mg/L as CaCO₃ (moderately hard).

On the Exam: Distinguish carbonate (temporary) vs noncarbonate (permanent) hardness when lime-soda softening is mentioned.

pH, Alkalinity, and Hardness

Worked Hardness Example

Ca²⁺ = 60 mg/L as Ca, Mg²⁺ = 12 mg/L as Mg.

Hardness as CaCO₃ ≈ $60\times(50/20) + 12\times(50/12.15) \approx 150 + 49 \approx 199$ mg/L as CaCO₃ (moderately hard).

On the Exam: Distinguish carbonate (temporary) vs noncarbonate (permanent) hardness when lime-soda softening is mentioned.

Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.

Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.

Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.

Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.

Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.

Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.

Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.

Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.

Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.

Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.

Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.

Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.

Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.

Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.

Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.

Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.

Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.

Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.

Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.

Gran Alkalinity Titration

P alkalinity (phenolphthalein) and M alkalinity (methyl orange) — carbonate vs bicarbonate vs hydroxide fractions from P and M relationships in Handbook.

Hardness Removal Math

200 mg/L hardness to 80 mg/L target → remove 120 mg/L as CaCO₃. Lime dose from stoichiometry (exam gives reactions).

LSI Worked Sketch

pH 7.8, alkalinity 100 mg/L, calcium 80 mg/L, TDS 300 mg/L → compute pHs from Handbook Langelier formula → LSI = pH − pHs. Positive LSI → scaling tendency.

Corrosion vs Scaling

Low alkalinity + low hardness → aggressive water may leach lead from pipes — orthophosphate or pH adjustment for stability.

Temperature Effect

Calcium carbonate solubility decreases with temperature — hot water heaters scale faster.