10L of hard water required 5.6g of lime for removing hardness. Hence temperorary hardness in ppm of `CaCO_(3)` is:

Options

A. 1000
B. 2000
C. 100
D. 1

Answer

To determine the temporary hardness of hard water in ppm of calcium carbonate (CaCO₃), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
- Volume of hard water = 10 L
- Mass of lime (CaO) required = 5.6 g

2. **Convert Volume of Hard Water to Milliliters**:
- Since 1 L = 1000 mL,
- Therefore, 10 L = 10 × 1000 mL = 10,000 mL.

3. **Determine the Molar Mass of Calcium Oxide (CaO)**:
- Molar mass of CaO = 40 (Ca) + 16 (O) = 56 g/mol.

4. **Calculate the Number of Moles of Calcium Oxide**:
- Number of moles of CaO = Mass / Molar mass = 5.6 g / 56 g/mol = 0.1 mol.

5. **Determine the Reaction with Calcium Bicarbonate**:
- The reaction of CaO with calcium bicarbonate (Ca(HCO₃)₂) produces calcium carbonate (CaCO₃).
- The stoichiometry of the reaction indicates that 1 mole of CaO will produce 1 mole of CaCO₃.

6. **Calculate the Moles of Calcium Carbonate Produced**:
- Therefore, moles of CaCO₃ produced = moles of CaO = 0.1 mol.

7. **Calculate the Mass of Calcium Carbonate Produced**:
- Molar mass of CaCO₃ = 40 (Ca) + 12 (C) + 48 (O₃) = 100 g/mol.
- Mass of CaCO₃ = Number of moles × Molar mass = 0.1 mol × 100 g/mol = 10 g.

8. **Determine the Mass of CaCO₃ in 1 mL of Hard Water**:
- Since 10 g of CaCO₃ is produced in 10,000 mL of hard water,
- Mass of CaCO₃ per mL = 10 g / 10,000 mL = 0.001 g/mL.

9. **Calculate the Mass of CaCO₃ in 1,000,000 mL (1,000 L)**:
- To find the mass in 1,000,000 mL (which is 1,000 L), we multiply the mass per mL by 1,000,000 mL:
- Mass of CaCO₃ in 1,000,000 mL = 0.001 g/mL × 1,000,000 mL = 1,000 g.

10. **Convert to ppm**:
- Since ppm (parts per million) is equivalent to mg/L, and we have 1,000 g in 1,000 L, we can express this as:
- 1,000 g = 1,000,000 mg.
- Therefore, the temporary hardness in ppm of CaCO₃ = 1,000,000 mg / 1,000 L = 1,000 ppm.

### Final Answer:
The temporary hardness of the hard water in ppm of CaCO₃ is **1,000 ppm**.

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