Two Water Sources for a Highway Dhaba
A dhaba on NH-33 near Ranchi draws water from two sources: A, a deep borewell, and B, a rainwater-fed open well. A laboratory reports that 100 mL of each sample, titrated against 0.0100 M EDTA at pH 10 with Eriochrome Black T, consumed 8.0 mL (A) and 26.0 mL (B); under these conditions 1.00 mL of 0.0100 M EDTA is equivalent to 1.00 mg of CaCO₃. Both samples show zero phenolphthalein alkalinity. Total alkalinity as CaCO₃ is 40 mg/L for A and 300 mg/L for B. The owner wants to install a small boiler for tea and rice, washes utensils with bar soap, and can afford only one treatment: prolonged boiling in a storage tank (cheap to build, costly in fuel) or a small ion-exchange softener costing ₹18,000 plus salt regeneration. The health department's drinking-water limit is 200 mg/L hardness as CaCO₃; the boiler maker's ceiling for feed water is 600 mg/L.
1. Calculate the total hardness of both sources in mg/L as CaCO₃ and classify each against the drinking-water limit.
Read the worked answer
Use the given equivalence: mg CaCO₃ in the 100 mL sample = volume of EDTA × 1.00.
- Source A: 8.0 mL ≡ 8.0 mg per 100 mL = 80 mg/L (80 ppm)
- Source B: 26.0 mL ≡ 26.0 mg per 100 mL = 260 mg/L (260 ppm)
Classification on the usual scale (soft < 60; moderately hard 60–120; hard 120–180; very hard > 180): A is moderately hard, B is very hard.
Against the health department's 200 mg/L limit, A is comfortably potable, while B exceeds the limit by 30 % (60 mg/L over) and should not be used for drinking or cooking as drawn. Note also that the boiler ceiling of 600 mg/L is met by both sources - so hardness alone does not disqualify either source for the boiler, which becomes important when choosing a treatment.
2. Using the alkalinity data, decide how much of each source's hardness is temporary and predict what boiling will actually achieve. Why does the zero phenolphthalein alkalinity matter?
Read the worked answer
Carbonate (temporary) hardness = the smaller of total hardness and total alkalinity.
- A: min(80, 40) = 40 mg/L carbonate, leaving 40 mg/L permanent (Ca/Mg sulphates and chlorides)
- B: min(260, 300) = 260 mg/L carbonate, i.e. all of it, leaving 0 permanent
Zero phenolphthalein alkalinity means there is no hydroxide or carbonate alkalinity - the whole alkalinity is bicarbonate. That is exactly the form that decomposes on boiling: Ca(HCO₃)₂ → CaCO₃↓ + CO₂ + H₂O. So boiling A can remove at most 40 mg/L and the remaining 40 mg/L (sulphate/chloride hardness) survives boiling untouched; boiling B can, in principle, remove essentially all 260 mg/L.
The practical caveat matters for the judgement: boiling works only if the precipitated CaCO₃ is allowed to settle and the clear water is decanted. Stirring or drawing from the bottom re-suspends the scale, so the water can still test hard and will still spot the utensils. Boiling also costs fuel for every litre, every day.
3. Recommend a single treatment decision, comparing boiling and the ₹18,000 softener using soap consumption, boiler safety and running costs.
Read the worked answer
The two uses pull in different directions, so separate them.
Boiler: both sources are already below the maker's 600 mg/L ceiling, so the softener is not needed for boiler safety. B's 260 mg/L will scale the boiler over months rather than weeks; boiling B before feeding the boiler removes that risk at fuel cost, and is the cheaper route for the small volumes a dhaba boiler uses.
Drinking and cooking: use A. At 80 mg/L it is within the 200 mg/L limit and needs no treatment; B at 260 mg/L is over the limit and should not be used for tea or rice.
Washing utensils: here the softener earns its keep. Hardness consumes soap as insoluble calcium and magnesium stearate, roughly in proportion to hardness above a small threshold, so B wastes about 260/80 ≈ 3.2 times the soap that A does for the same wash. Against a soap bill of, say, ₹700 a month on A, B would cost roughly ₹2,200 - an avoidable ₹18,000 a year, which repays the softener in about a year.
The defensible single decision: draw cooking water from A, boil B only for the boiler, and buy the softener only if B is used for washing - otherwise add washing soda (sodium carbonate), which precipitates the same calcium at a fraction of the capital cost.