Calculate the mass of CaO required to remove the hardness of 1000,000 litres of water containing 1.62 g of calcium bicarbonate per litre.

Answer

To calculate the mass of CaO required to remove the hardness of 1,000,000 liters of water containing 1.62 g of calcium bicarbonate per liter, we can follow these steps:

### Step 1: Calculate the total mass of calcium bicarbonate in the water
Given that the concentration of calcium bicarbonate (Ca(HCO₃)₂) is 1.62 g/L, we can find the total mass in 1,000,000 liters.

\[ \text{Total mass of Ca(HCO₃)₂} = \text{Concentration} \times \text{Volume} \]
\[ \text{Total mass of Ca(HCO₃)₂} = 1.62 \, \text{g/L} \times 1,000,000 \, \text{L} = 1,620,000 \, \text{g} \]

### Step 2: Calculate the molar mass of calcium bicarbonate
The molar mass of calcium bicarbonate (Ca(HCO₃)₂) can be calculated as follows:
- Calcium (Ca): 40 g/mol
- Hydrogen (H): 1 g/mol × 2 = 2 g/mol
- Carbon (C): 12 g/mol × 2 = 24 g/mol
- Oxygen (O): 16 g/mol × 6 = 96 g/mol

\[ \text{Molar mass of Ca(HCO₃)₂} = 40 + 2 + 24 + 96 = 162 \, \text{g/mol} \]

### Step 3: Calculate the number of moles of calcium bicarbonate
Using the total mass calculated in Step 1, we can find the number of moles of calcium bicarbonate.

\[ \text{Number of moles of Ca(HCO₃)₂} = \frac{\text{Total mass}}{\text{Molar mass}} = \frac{1,620,000 \, \text{g}}{162 \, \text{g/mol}} = 10,000 \, \text{mol} \]

### Step 4: Write the balanced chemical equation
The reaction for removing hardness using calcium oxide (CaO) is:

\[ \text{Ca(HCO₃)₂} + \text{CaO} \rightarrow 2 \text{CaCO₃} + \text{H₂O} \]

From the equation, we see that 1 mole of Ca(HCO₃)₂ reacts with 1 mole of CaO.

### Step 5: Calculate the mass of CaO required
Since 10,000 moles of Ca(HCO₃)₂ will require the same number of moles of CaO, we can calculate the mass of CaO needed.

First, we calculate the molar mass of CaO:
- Calcium (Ca): 40 g/mol
- Oxygen (O): 16 g/mol

\[ \text{Molar mass of CaO} = 40 + 16 = 56 \, \text{g/mol} \]

Now, we find the mass of CaO required:

\[ \text{Mass of CaO} = \text{Number of moles} \times \text{Molar mass} = 10,000 \, \text{mol} \times 56 \, \text{g/mol} = 560,000 \, \text{g} \]

### Step 6: Convert grams to kilograms
To convert grams to kilograms:

\[ \text{Mass of CaO in kg} = \frac{560,000 \, \text{g}}{1000} = 560 \, \text{kg} \]

### Final Answer
The mass of CaO required to remove the hardness of 1,000,000 liters of water is **560 kg**.

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