10g `CaCO_(3)` is completely decomposed to X and CaO. X is passed into an aquesous solution containg one mole of sodium carbonate. What is the number of moles of moles sodium bicarbonte formed?
Molar mass: `CaCO_(3)(100), Na_(2)CO_(3)(106), NaHCO_(3)(84)`

Answer

To solve the problem step by step, we will follow the decomposition of calcium carbonate and its reaction with sodium carbonate to find the number of moles of sodium bicarbonate formed.

### Step 1: Decompose Calcium Carbonate
The decomposition reaction of calcium carbonate (CaCO₃) is as follows:

\[ \text{CaCO}_3 \rightarrow \text{CaO} + \text{CO}_2 \]

### Step 2: Calculate Moles of CaCO₃
First, we need to calculate the number of moles of CaCO₃ in 10 grams. The molar mass of CaCO₃ is 100 g/mol.

\[ \text{Moles of CaCO}_3 = \frac{\text{mass}}{\text{molar mass}} = \frac{10 \text{ g}}{100 \text{ g/mol}} = 0.1 \text{ moles} \]

### Step 3: Determine Moles of CO₂ Produced
From the decomposition reaction, we see that 1 mole of CaCO₃ produces 1 mole of CO₂. Therefore, 0.1 moles of CaCO₃ will produce:

\[ \text{Moles of CO}_2 = 0.1 \text{ moles} \]

### Step 4: Reaction with Sodium Carbonate
Now, we have 1 mole of sodium carbonate (Na₂CO₃) in the solution. The reaction between CO₂ and sodium carbonate to form sodium bicarbonate (NaHCO₃) is as follows:

\[ \text{Na}_2\text{CO}_3 + \text{CO}_2 + \text{H}_2\text{O} \rightarrow 2 \text{NaHCO}_3 \]

### Step 5: Calculate Moles of NaHCO₃ Formed
From the balanced equation, we see that 1 mole of Na₂CO₃ reacts with 1 mole of CO₂ to produce 2 moles of NaHCO₃. Since we have 0.1 moles of CO₂ from the decomposition of CaCO₃, we can determine how much NaHCO₃ is produced:

\[ \text{Moles of NaHCO}_3 = 2 \times \text{Moles of CO}_2 = 2 \times 0.1 = 0.2 \text{ moles} \]

### Final Answer
The number of moles of sodium bicarbonate (NaHCO₃) formed is **0.2 moles**.

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