What weight of carbon dioxide gas would have evolved if 3 g of ethane is burnt in the presence of excess of air ?

Options

A. 4.4 g
B. 8.8 g
C. 0.44 g
D. 0.88 g

Answer

To determine the weight of carbon dioxide (CO₂) gas evolved when 3 g of ethane (C₂H₆) is burnt in the presence of excess air, we can follow these steps:

### Step 1: Write the balanced chemical equation for the combustion of ethane.
The balanced equation for the combustion of ethane is:
\[ 2 \text{C}_2\text{H}_6 + 7 \text{O}_2 \rightarrow 4 \text{CO}_2 + 6 \text{H}_2\text{O} \]

### Step 2: Calculate the molar mass of ethane (C₂H₆).
The molar mass of ethane is calculated as follows:
- Carbon (C) has a molar mass of approximately 12 g/mol.
- Hydrogen (H) has a molar mass of approximately 1 g/mol.

Thus, the molar mass of C₂H₆ is:
\[ (2 \times 12) + (6 \times 1) = 24 + 6 = 30 \text{ g/mol} \]

### Step 3: Calculate the number of moles of ethane in 3 g.
Using the formula:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \]
we can find the number of moles of ethane:
\[ \text{Number of moles of C}_2\text{H}_6 = \frac{3 \text{ g}}{30 \text{ g/mol}} = 0.1 \text{ moles} \]

### Step 4: Use stoichiometry to find the moles of CO₂ produced.
From the balanced equation, we see that:
- 2 moles of C₂H₆ produce 4 moles of CO₂.
- Therefore, 1 mole of C₂H₆ produces 2 moles of CO₂.

Thus, 0.1 moles of C₂H₆ will produce:
\[ 0.1 \text{ moles C}_2\text{H}_6 \times 2 \text{ moles CO}_2/\text{mole C}_2\text{H}_6 = 0.2 \text{ moles CO}_2 \]

### Step 5: Calculate the molar mass of carbon dioxide (CO₂).
The molar mass of CO₂ is calculated as follows:
- Carbon (C) has a molar mass of approximately 12 g/mol.
- Oxygen (O) has a molar mass of approximately 16 g/mol.

Thus, the molar mass of CO₂ is:
\[ 12 + (2 \times 16) = 12 + 32 = 44 \text{ g/mol} \]

### Step 6: Calculate the weight of CO₂ produced.
Using the formula:
\[ \text{Weight} = \text{Number of moles} \times \text{Molar mass} \]
we can find the weight of CO₂ produced:
\[ \text{Weight of CO}_2 = 0.2 \text{ moles} \times 44 \text{ g/mol} = 8.8 \text{ g} \]

### Final Answer:
The weight of carbon dioxide gas evolved is **8.8 g**.

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