Two Water Samples, One Dropper of Soap
A village school has two water sources: a borewell (sample P) and a rooftop rain-harvesting tank (sample Q). Students take 20 mL of each, add soap solution drop by drop, shake exactly ten times after each drop and record the number of drops needed for a lather that persists for 30 seconds. Distilled water needs 1 drop, Q needs 2 drops and P needs 24 drops. With P a white curd forms before any lather appears. The same P, boiled for ten minutes, cooled and filtered, needs 8 drops. The laboratory has no burette and no EDTA, only a dropper bottle of soap solution. A parent asks whether boiling the borewell water makes it fit for the family to drink and for washing clothes. The students also notice a hard white deposit inside the kettle in which P was boiled, and that the deposit does not disappear when the kettle is rinsed with plain water.
1. Using the distilled-water value as the blank, work out how much of the hardness of P is temporary and how much is permanent. State clearly what your units mean.
Read the worked answer
The blank is 1 drop; a sample needing n drops has hardness proportional to (n - 1) dropper units per 20 mL under this exact procedure.
- Q: 2 - 1 = 1 unit, essentially soft rainwater.
- P before boiling: 24 - 1 = 23 units total.
- P after boiling: 8 - 1 = 7 units remaining.
Boiling destroyed 23 - 7 = 16 units. That portion must be the temporary hardness due to bicarbonates, because these are the only salts removed by boiling. The remaining 7 units are permanent hardness from sulphates and chlorides of calcium and magnesium, which survive boiling.
So roughly 16/23, about 70%, of P's hardness is temporary and 7/23, about 30%, is permanent. Caveat: the unit is arbitrary and defined only by this dropper, this soap and this shaking protocol. The numbers allow comparison within this experiment but should not be quoted as mg/L or as 'degrees' of hardness; a burette and a standard soap solution, or EDTA titration, would be needed for that.
2. Explain with equations why boiling softens P but does not bring it down to the distilled-water value. What is the white deposit in the kettle?
Read the worked answer
Temporary hardness is caused by calcium and magnesium hydrogencarbonates, which are soluble. On boiling they decompose and precipitate insoluble carbonates:
Ca(HCO3)2 (aq) -> CaCO3 (s) + H2O + CO2 (g) Mg(HCO3)2 (aq) -> MgCO3 (s) + H2O + CO2 (g), with some MgCO3 reacting further to Mg(OH)2 and CO2.
The precipitate is filtered off before the second titration, so the calcium and magnesium no longer consume soap. The white scale lining the kettle is mainly calcium carbonate; it does not simply rinse away because it is insoluble in water and must be removed with dilute acid or by mechanical cleaning.
Permanent hardness comes from salts such as CaSO4, MgSO4 and CaCl2, none of which decompose or precipitate on boiling. They remain in solution and still react with soap to give an insoluble scum, so the drop count falls from 24 to 8 rather than to 1. The drop count measures soap consumed by the hardness ions, not the total dissolved solid.
3. Answer the parent: is boiled borewell water safe to drink and good for washing? What treatment would remove the remaining hardness?
Read the worked answer
Boiling makes P microbiologically safer: it kills bacteria, viruses and most cysts, and it removes the temporary hardness that caused the scum. But boiling is not a chemical purification. It leaves the permanent hardness untouched, and it does nothing about dissolved nitrate, fluoride, arsenic, excess salinity or pesticide residues. Indeed, if water is boiled for a long time and some evaporates, the remaining salts become more concentrated. So the honest answer is: boiled P is safer against infection, but it is still hard water and not guaranteed chemically safe; the family should also filter it or use a tested source.
For washing, hard water wastes soap as scum and can leave grey deposits on clothes. Adding washing soda (Na2CO3) before washing precipitates the calcium and magnesium as carbonates, which softens the water; synthetic detergents work better than soap because their calcium salts are soluble and no scum forms. Rainwater Q, being nearly soft, is the better choice for washing, though it should be boiled or filtered before drinking because it was collected from a roof.