Soap Titration and a Family's Water Choice
A Grade 11 student at a school near Bishoftu is asked to advise her family on which of three water sources to use. She collects samples from a hand-dug well, a nearby river, and a rainwater storage tank. Using a 25 mL measuring cylinder, she adds the same soap solution drop by drop to each sample, shakes ten times, and records the number of drops needed before a lather that lasts 30 seconds appears: rainwater 4 drops, well water 18 drops, river water 27 drops. She then boils 25 mL of the well and river samples for ten minutes, cools them, and repeats the test: well water 17 drops, river water 26 drops. Her father notes that the kettle at home is coated with a hard white deposit. Her younger brother says they should use the rainwater for everything because it needed only 4 drops, while her mother prefers the river because it is free and always available.
1. What does the titration show about the hardness of the three sources, and what does the boiling test reveal about the type of hardness in the well and river samples?
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More drops mean more soap was used up before lather formed, because Ca²⁺ and Mg²⁺ ions react with soap to form an insoluble scum. The ranking is therefore river (27) > well (18) > rainwater (4), so rainwater is the softest.
Boiling removes only temporary hardness, because calcium hydrogencarbonate decomposes: Ca(HCO₃)₂ → CaCO₃(s) + CO₂ + H₂O, taking Ca²⁺ out of solution. Well water fell only from 18 to 17 drops and river water from 27 to 26. A one-drop change is about the size of normal hand-titration error, so the honest conclusion is that boiling removed almost nothing measurable: both sources are dominated by permanent hardness (sulfates and chlorides), which boiling cannot remove.
The kettle scale is consistent with some temporary hardness, but the titration does not show it clearly. To settle the point she should boil a larger volume for longer, or measure the mass of deposit, rather than relying on a one-drop difference.
2. A classmate points out that the river sample was tested with a different brand of soap from the other two. How does this affect the conclusion, and what should be done?
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It breaks the comparison. The drop count depends on the soap itself: different brands differ in fatty-acid chain length, concentration and additives, so a drop of one solution does not neutralise the same amount of Ca²⁺ as a drop of another. The river figure of 27 cannot be placed on the same scale as 18 and 4, so the ranking 'river is hardest' is not yet supported.
The problem is not equally serious for every comparison. Rainwater (4) differs so greatly from the other two that the ranking at the soft end probably survives any reasonable soap difference. The well-versus-river comparison, however, is exactly where the change occurred, and 18 versus 27 is close enough to be reversed by a stronger soap.
The fix is procedural, not statistical: prepare one large batch of soap solution, label it, and use it for every sample, including a repeat of the river sample. She should also standardise shaking (same number of shakes, same tube), same sample volume, same temperature, and have a second student read the endpoint to check consistency.
3. Recommend a water source for drinking and a source for washing, justifying each with the evidence given and stating what further testing is needed.
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For washing, the softest source wins: rainwater at 4 drops will lather with far less soap and leave no scum on clothes. The well is a workable second choice; the river is the worst, since it consumes the most soap and its turbidity after rain will also stain fabric.
For drinking, hardness is not the main hazard, so the titration alone cannot decide. Low hardness does not mean safe: harvested rainwater can pick up contamination from the roof and tank, and its low mineral content can make it corrosive. River water is the highest risk because turbidity after rain carries suspended solids and possibly pathogens. The well is the most practical drinking source, but only after testing.
Further tests needed: microbial indicators (total and faecal coliforms), turbidity, pH, nitrate, and fluoride. She should ask the district water office rather than relying on home tests, because a hand-dug well near a river is vulnerable to surface contamination.
Practical plan: rainwater for washing; well water for drinking after chlorination or boiling and after laboratory testing; river water only for cleaning or irrigation, and only after settling and filtration.