On heating 200 g `CaCO_(3)` , CaO is obtained which will react with how much gram of water to obtain `Ca(OH)_(2)`?

Options

A. 200 g
B. 112 g
C. 36 g
D. 40 g

Explanation

To solve the problem, we need to follow these steps:

### Step 1: Calculate the molar mass of Calcium Carbonate (CaCO₃)
- Calcium (Ca) = 40 g/mol
- Carbon (C) = 12 g/mol
- Oxygen (O) = 16 g/mol (and there are 3 oxygen atoms in CaCO₃)

Molar mass of CaCO₃ = Ca + C + 3 × O = 40 + 12 + (3 × 16) = 40 + 12 + 48 = 100 g/mol

### Step 2: Calculate the amount of Calcium Oxide (CaO) produced from 200 g of CaCO₃
From the decomposition reaction:
\[ \text{CaCO}_3 \rightarrow \text{CaO} + \text{CO}_2 \]

According to the stoichiometry:
- 100 g of CaCO₃ produces 56 g of CaO.

Using a unitary method:
- 200 g of CaCO₃ will produce:
\[ \text{Mass of CaO} = \frac{56 \text{ g CaO}}{100 \text{ g CaCO}_3} \times 200 \text{ g CaCO}_3 = 112 \text{ g CaO} \]

### Step 3: Write the reaction of Calcium Oxide with Water
The reaction is:
\[ \text{CaO} + \text{H}_2\text{O} \rightarrow \text{Ca(OH)}_2 \]

### Step 4: Calculate the molar mass of Calcium Oxide (CaO)
- Molar mass of CaO = Ca + O = 40 + 16 = 56 g/mol

### Step 5: Calculate the molar mass of Calcium Hydroxide (Ca(OH)₂)
- Molar mass of Ca(OH)₂ = Ca + 2 × (O + H) = 40 + 2 × (16 + 1) = 40 + 2 × 17 = 40 + 34 = 74 g/mol

### Step 6: Determine how much water reacts with 112 g of CaO
From the stoichiometry of the reaction:
- 56 g of CaO reacts with 18 g of water.

Using a unitary method:
- To find the amount of water that reacts with 112 g of CaO:
\[ \text{Mass of water} = \frac{18 \text{ g H}_2\text{O}}{56 \text{ g CaO}} \times 112 \text{ g CaO} = \frac{18 \times 112}{56} = 36 \text{ g H}_2\text{O} \]

### Final Answer
The amount of water that reacts with 112 g of CaO is **36 grams**.

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