Step 1: Understanding the Question:
The question presents three statements about soap and water quality and asks to evaluate which statement(s) are chemically accurate.
Step 2: Key Formula or Approach:
We analyze each statement based on the definitions of soap, hard water, and heavy water.
Step 3: Detailed Explanation:
• Statement I: Hard water contains dissolved salts of calcium and magnesium. Soap molecules (sodium or potassium salts of long-chain fatty acids) react with these calcium and magnesium ions to form insoluble, sticky precipitates called scum:
\[ 2\text{C}_{17}\text{H}_{35}\text{COONa} + \text{Ca}^{2+} \to (\text{C}_{17}\text{H}_{35}\text{COO})_2\text{Ca} \downarrow + 2\text{Na}^+ \]
This prevents the soap from forming lather or foam easily. Thus, Statement I is correct.
• Statement II: This is incorrect. Soaps are sodium or potassium salts of long-chain fatty carboxylic acids (such as stearic, palmitic, or oleic acids). It is synthetic detergents, not soaps, that are sodium salts of alkyl hydrogen sulfates or long-chain alkyl benzene sulfonic acids.
• Statement III: This is incorrect. Deuterium oxide (\(\text{D}_2\text{O}\)) is called heavy water, which is used as a moderator in nuclear reactors. "Hard water" is water that has a high concentration of dissolved calcium and magnesium minerals.
• Therefore, only Statement I is correct.
Step 4: Final Answer:
Only Statement I is correct.