When a sample of Baking soda is strongly ignited in a crucible it suffered a loss in weight of 3.1 g. The mass of baking soda is

Options

A. 16.8 g
B. 8.4 g
C. 11.6 g
D. 4.2 g

Explanation

To solve the problem of determining the mass of baking soda that suffered a loss in weight of 3.1 g when strongly ignited, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Chemical Formula of Baking Soda:**
- Baking soda is chemically known as sodium bicarbonate, and its formula is NaHCO₃.

2. **Understand the Decomposition Reaction:**
- When sodium bicarbonate is heated, it decomposes into sodium carbonate (Na₂CO₃), water (H₂O), and carbon dioxide (CO₂).
- The balanced chemical equation for this reaction is:
\[ 2 \text{NaHCO}_3 \rightarrow \text{Na}_2\text{CO}_3 + \text{H}_2\text{O} + \text{CO}_2 \]

3. **Calculate Molar Masses:**
- Molar mass of NaHCO₃ (sodium bicarbonate) = 23 (Na) + 1 (H) + 12 (C) + 3*16 (O) = 84 g/mol.
- Molar mass of Na₂CO₃ (sodium carbonate) = 2*23 (Na) + 12 (C) + 3*16 (O) = 106 g/mol.
- Molar mass of H₂O (water) = 2*1 (H) + 16 (O) = 18 g/mol.
- Molar mass of CO₂ (carbon dioxide) = 12 (C) + 2*16 (O) = 44 g/mol.

4. **Determine Total Mass Loss:**
- From the balanced equation, we see that 2 moles of NaHCO₃ produce 1 mole of Na₂CO₃, 1 mole of H₂O, and 1 mole of CO₂.
- The total mass loss during the decomposition is the sum of the masses of water and carbon dioxide produced:
\[ \text{Mass loss} = \text{mass of H}_2\text{O} + \text{mass of CO}_2 = 18 \text{ g} + 44 \text{ g} = 62 \text{ g} \]

5. **Relate Mass Loss to Initial Mass of Baking Soda:**
- If 62 g of baking soda results in a loss of 3.1 g, we can set up a proportion to find the initial mass of baking soda (let's call it \( x \)):
\[ \frac{62 \text{ g}}{168 \text{ g}} = \frac{3.1 \text{ g}}{x} \]

6. **Calculate the Initial Mass of Baking Soda:**
- Cross-multiplying gives:
\[ 62x = 3.1 \times 168 \]
- Calculate \( 3.1 \times 168 = 520.8 \).
- Now, divide by 62:
\[ x = \frac{520.8}{62} \approx 8.4 \text{ g} \]

7. **Final Answer:**
- The mass of baking soda is approximately **8.4 g**.