1 g of a mixture of `NaHCO_(3)` and `Na_(2)CO_(3)` is heated to `150^(@)C`. The volume of the `CO_(2)` produced at STP is 112.0 mL. Calculate the percentage of `Na_(2)CO_(3)` in the mixture `(Na=23, C=12, O=16)`

Options

A. 20
B. 46
C. 84
D. 16

Explanation

To solve the problem, we need to find the percentage of sodium carbonate (Na₂CO₃) in a mixture of sodium bicarbonate (NaHCO₃) and sodium carbonate (Na₂CO₃) based on the volume of carbon dioxide (CO₂) produced when the mixture is heated.

### Step-by-Step Solution:

1. **Identify the Reaction**:
When sodium bicarbonate (NaHCO₃) is heated, it decomposes as follows:
\[ 2 \, \text{NaHCO}_3 \, (s) \rightarrow \text{Na}_2\text{CO}_3 \, (s) + \text{CO}_2 \, (g) + \text{H}_2\text{O} \, (g) \]
Sodium carbonate (Na₂CO₃) does not decompose upon heating.

2. **Calculate Moles of CO₂ Produced**:
The volume of CO₂ produced at STP is given as 112.0 mL. At STP, 1 mole of gas occupies 22.4 L (or 22400 mL). Thus, we can calculate the moles of CO₂:
\[ \text{Moles of CO}_2 = \frac{\text{Volume of CO}_2}{\text{Molar Volume at STP}} = \frac{112.0 \, \text{mL}}{22400 \, \text{mL/mol}} = 0.005 \, \text{mol} \]

3. **Relate Moles of CO₂ to Moles of NaHCO₃**:
From the decomposition reaction, 2 moles of NaHCO₃ produce 1 mole of CO₂. Therefore, the moles of NaHCO₃ that decomposed can be calculated as:
\[ \text{Moles of NaHCO}_3 = 2 \times \text{Moles of CO}_2 = 2 \times 0.005 \, \text{mol} = 0.010 \, \text{mol} \]

4. **Calculate the Mass of NaHCO₃**:
The molar mass of NaHCO₃ is:
\[ \text{Molar Mass of NaHCO}_3 = 23 + 1 + 12 + (3 \times 16) = 84 \, \text{g/mol} \]
Therefore, the mass of NaHCO₃ is:
\[ \text{Mass of NaHCO}_3 = \text{Moles} \times \text{Molar Mass} = 0.010 \, \text{mol} \times 84 \, \text{g/mol} = 0.84 \, \text{g} \]

5. **Calculate the Mass of Na₂CO₃ in the Mixture**:
The total mass of the mixture is 1 g. Thus, the mass of Na₂CO₃ can be calculated as:
\[ \text{Mass of Na}_2\text{CO}_3 = \text{Total Mass} - \text{Mass of NaHCO}_3 = 1 \, \text{g} - 0.84 \, \text{g} = 0.16 \, \text{g} \]

6. **Calculate the Percentage of Na₂CO₃ in the Mixture**:
The percentage of Na₂CO₃ in the mixture is given by:
\[ \text{Percentage of Na}_2\text{CO}_3 = \left( \frac{\text{Mass of Na}_2\text{CO}_3}{\text{Total Mass}} \right) \times 100 = \left( \frac{0.16 \, \text{g}}{1 \, \text{g}} \right) \times 100 = 16\% \]

### Final Answer:
The percentage of Na₂CO₃ in the mixture is **16%**.