When 4 gm of a mixture of `NaHCO_(3)` and NaCl is heated , 0.66 gm `CO_(2)` gas is evolved . Determine the percentage composition (by mass) of the original mixture.

Answer

To determine the percentage composition of the original mixture of NaHCO₃ and NaCl, we can follow these steps:

### Step 1: Write the decomposition reaction of NaHCO₃
When sodium bicarbonate (NaHCO₃) is heated, it decomposes according to the following reaction:
\[ 2 \text{NaHCO}_3 \rightarrow \text{Na}_2\text{CO}_3 + \text{CO}_2 + \text{H}_2\text{O} \]

### Step 2: Calculate the molar mass of NaHCO₃
The molar mass of NaHCO₃ can be calculated as follows:
- Sodium (Na): 23 g/mol
- Hydrogen (H): 1 g/mol
- Carbon (C): 12 g/mol
- Oxygen (O): 16 g/mol × 3 = 48 g/mol

Adding these together:
\[ \text{Molar mass of NaHCO}_3 = 23 + 1 + 12 + 48 = 84 \text{ g/mol} \]

### Step 3: Calculate the molar mass of CO₂
The molar mass of CO₂ is calculated as:
- Carbon (C): 12 g/mol
- Oxygen (O): 16 g/mol × 2 = 32 g/mol

Adding these together:
\[ \text{Molar mass of CO}_2 = 12 + 32 = 44 \text{ g/mol} \]

### Step 4: Relate the mass of CO₂ produced to the mass of NaHCO₃
From the reaction, 2 moles of NaHCO₃ produce 1 mole of CO₂. Therefore, the mass of CO₂ produced can be related to the mass of NaHCO₃:
- 2 moles of NaHCO₃ (168 g) produce 1 mole of CO₂ (44 g).

Using the mass of CO₂ evolved (0.66 g), we can find the mass of NaHCO₃ that decomposed:
\[ \text{Mass of NaHCO}_3 = \frac{168 \text{ g}}{44 \text{ g}} \times 0.66 \text{ g} = 2.52 \text{ g} \]

### Step 5: Calculate the percentage of NaHCO₃ in the mixture
The total mass of the mixture is 4 g. The percentage of NaHCO₃ can be calculated as:
\[ \text{Percentage of NaHCO}_3 = \left( \frac{2.52 \text{ g}}{4 \text{ g}} \right) \times 100 = 63\% \]

### Step 6: Calculate the percentage of NaCl in the mixture
Since the mixture consists of NaHCO₃ and NaCl, the percentage of NaCl can be found by subtracting the percentage of NaHCO₃ from 100%:
\[ \text{Percentage of NaCl} = 100\% - 63\% = 37\% \]

### Final Result
- Percentage of NaHCO₃: **63%**
- Percentage of NaCl: **37%**

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