`10 L` of hard water required `0.56 g` of lime `(CaO)` for removing hardness. Hence, temporary hardness in ppm (part per million `10^(6)`) of `CaCO_(3)` is:

Options

A. 100
B. 200
C. 10
D. 20

Explanation

To calculate the temporary hardness of water in parts per million (ppm) of CaCO₃, we can follow these steps:

### Step 1: Understand the relationship between CaO and CaCO₃
When lime (CaO) is added to hard water, it reacts with bicarbonate ions (HCO₃⁻) to form calcium carbonate (CaCO₃). The reaction can be summarized as:
\[ \text{CaO} + \text{H}_2\text{O} + \text{CO}_2 \rightarrow \text{CaCO}_3 + \text{H}_2\text{O} \]

From the stoichiometry of the reaction, we know that 1 mole of CaO produces 1 mole of CaCO₃.

### Step 2: Calculate the moles of CaO used
First, we need to find the number of moles of CaO used. The molar mass of CaO is approximately 56 g/mol.
\[ \text{Moles of CaO} = \frac{\text{mass of CaO}}{\text{molar mass of CaO}} = \frac{0.56 \, \text{g}}{56 \, \text{g/mol}} = 0.01 \, \text{mol} \]

### Step 3: Calculate the moles of CaCO₃ produced
Since 1 mole of CaO produces 1 mole of CaCO₃, the moles of CaCO₃ produced will also be 0.01 mol.

### Step 4: Calculate the mass of CaCO₃ produced
Now, we can calculate the mass of CaCO₃ produced using its molar mass (approximately 100 g/mol):
\[ \text{Mass of CaCO}_3 = \text{moles of CaCO}_3 \times \text{molar mass of CaCO}_3 = 0.01 \, \text{mol} \times 100 \, \text{g/mol} = 1 \, \text{g} \]

### Step 5: Calculate the concentration in ppm
To find the concentration in ppm, we need to know how many grams of CaCO₃ are present in 1 million milliliters (1 million mL) of water. Since we have 1 g of CaCO₃ in 10 L (or 10,000 mL), we can scale this up to find out how much would be in 1,000,000 mL:
\[ \text{Concentration in ppm} = \left( \frac{\text{mass of CaCO}_3 \text{ in g}}{\text{volume of water in L}} \right) \times 10^6 \]
\[ = \left( \frac{1 \, \text{g}}{10 \, \text{L}} \right) \times 10^6 \]
\[ = \left( \frac{1 \, \text{g}}{10,000 \, \text{mL}} \right) \times 10^6 = 100 \, \text{ppm} \]

### Final Answer
The temporary hardness in ppm of CaCO₃ is **100 ppm**.

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