By which reaction formation of hard water takes place :
(a) `Ca(CH)_(2)+2HCl`
(b) `NaOH+HCl`
(c) `KOH+HCl`
(d) `NaOH+H_(2)CO_(3)`

Options

A. By only d
B. By only a
C. By a, b, c
D. By all process

Explanation

To determine which reaction leads to the formation of hard water, we need to analyze each given reaction and identify the products formed. Hard water is characterized by the presence of calcium and magnesium salts, while soft water contains sodium and potassium salts.

### Step-by-Step Solution:

1. **Identify the reactions:**
- (a) \( \text{Ca(OH)}_2 + 2 \text{HCl} \)
- (b) \( \text{NaOH} + \text{HCl} \)
- (c) \( \text{KOH} + \text{HCl} \)
- (d) \( \text{NaOH} + \text{H}_2\text{CO}_3 \)

2. **Analyze Reaction (a):**
- **Reactants:** Calcium hydroxide (\( \text{Ca(OH)}_2 \)) and hydrochloric acid (\( \text{HCl} \)).
- **Products:** The reaction produces calcium chloride (\( \text{CaCl}_2 \)) and water (\( \text{H}_2\text{O} \)).
- **Conclusion:** Since calcium chloride is a salt of calcium, this reaction produces hard water.

3. **Analyze Reaction (b):**
- **Reactants:** Sodium hydroxide (\( \text{NaOH} \)) and hydrochloric acid (\( \text{HCl} \)).
- **Products:** The reaction produces sodium chloride (\( \text{NaCl} \)) and water.
- **Conclusion:** Sodium chloride is a salt of sodium, thus this reaction produces soft water.

4. **Analyze Reaction (c):**
- **Reactants:** Potassium hydroxide (\( \text{KOH} \)) and hydrochloric acid (\( \text{HCl} \)).
- **Products:** The reaction produces potassium chloride (\( \text{KCl} \)) and water.
- **Conclusion:** Potassium chloride is a salt of potassium, hence this reaction also produces soft water.

5. **Analyze Reaction (d):**
- **Reactants:** Sodium hydroxide (\( \text{NaOH} \)) and carbonic acid (\( \text{H}_2\text{CO}_3 \)).
- **Products:** The reaction produces sodium carbonate (\( \text{Na}_2\text{CO}_3 \)) and water.
- **Conclusion:** Sodium carbonate is a salt of sodium, so this reaction results in soft water as well.

### Final Conclusion:
From the analysis, only reaction (a) produces hard water due to the formation of calcium chloride. The other reactions produce soft water.

### Answer:
The correct option is (a) \( \text{Ca(OH)}_2 + 2 \text{HCl} \).

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