This chemistry question involves key chemical concepts and calculations. The detailed solution below walks through each step, from identifying the reaction type to computing the final answer.

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a) Conclusion: Tap water is hard water because it forms scum and requires more soap to produce a lather. Boiling the tap water reduces its hardness, as indicated by the reduced amount of soap needed to form a permanent lather. This suggests the tap water contains temporary hardness.
b) Reason for scum formation: Scum was formed with unboiled tap water because hard water contains dissolved calcium and magnesium ions. These ions react with the soap (sodium stearate) to form insoluble precipitates, which are the scum. This reaction prevents the soap from forming a lather until all the hardness ions are removed.
c) Effect of using detergent instead of soap: If a detergent had been used instead of soap solution, it would have formed a lather immediately with both the unboiled tap water and the boiled tap water. Detergents do not form scum with hard water because their calcium and magnesium salts are soluble.
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a) Conclusion: Tap water is hard water because it forms scum and requires more soap to produce a lather.
This chemistry question involves key chemical concepts and calculations. The detailed solution below walks through each step, from identifying the reaction type to computing the final answer.