Mixture of `MgCO_(3)` &`NaHCO_(3)` on strong heating gives `CO_(2)`
&`H_(2)O` in 3 : 1 mole ratio. The weight % of `NaHCO_(3)` present in the mixture is :

Options

A. 0.3
B. 0.8
C. 0.4
D. 0.5

Answer

To solve the problem, we need to analyze the decomposition reactions of sodium bicarbonate (NaHCO₃) and magnesium carbonate (MgCO₃) when heated, and then calculate the weight percentage of NaHCO₃ in the mixture based on the products formed.

### Step-by-Step Solution:

1. **Identify the Decomposition Reactions:**
- Sodium bicarbonate decomposes as follows:
\[ 2 \text{NaHCO}_3 \rightarrow \text{Na}_2\text{O} + 2 \text{CO}_2 + \text{H}_2\text{O} \]
- Magnesium carbonate decomposes as follows:
\[ \text{MgCO}_3 \rightarrow \text{MgO} + \text{CO}_2 \]

2. **Determine the Moles of Products:**
- From the sodium bicarbonate reaction, 2 moles of NaHCO₃ produce 2 moles of CO₂ and 1 mole of H₂O.
- From the magnesium carbonate reaction, 1 mole of MgCO₃ produces 1 mole of CO₂.
- Therefore, the total moles of CO₂ produced from both reactions can be expressed in terms of x (moles of NaHCO₃) and y (moles of MgCO₃):
- Total CO₂ = 2x (from NaHCO₃) + y (from MgCO₃)
- Total H₂O = x (from NaHCO₃)

3. **Set Up the Mole Ratio:**
- According to the problem, the ratio of CO₂ to H₂O is given as 3:1. Therefore, we can write:
\[ \frac{2x + y}{x} = 3 \]

4. **Solve for y in terms of x:**
- Cross-multiplying gives:
\[ 2x + y = 3x \]
- Rearranging gives:
\[ y = 3x - 2x = x \]

5. **Calculate the Weight Percent of NaHCO₃:**
- The molar mass of NaHCO₃ is 84 g/mol, and the molar mass of MgCO₃ is 100 g/mol.
- The total mass of the mixture can be expressed as:
\[ \text{Total mass} = 84x + 100y = 84x + 100x = 184x \]
- The weight percentage of NaHCO₃ in the mixture is given by:
\[ \text{Weight \% of NaHCO}_3 = \left(\frac{84x}{184x}\right) \times 100 \]
- Simplifying this gives:
\[ \text{Weight \% of NaHCO}_3 = \left(\frac{84}{184}\right) \times 100 \approx 45.65\% \]

6. **Final Answer:**
- The weight percentage of NaHCO₃ present in the mixture is approximately 45.65%, which can be rounded to 46%.