280 g of a mixture containing `CH_(4) and C_(2)H_(6)` in `5:2` molar ratio is burnt in presence of excess of oxygen. Calculate total moles of `CO_(2)` produced.

Options

A. 9
B. 18
C. 7
D. 12

Answer

To solve the problem of calculating the total moles of CO₂ produced from the combustion of a mixture of CH₄ and C₂H₆, we will follow these steps:

### Step 1: Determine the composition of the mixture
Given that the mixture contains CH₄ and C₂H₆ in a molar ratio of 5:2, we can express the moles of CH₄ and C₂H₆ in terms of a variable \( x \).

Let:
- Moles of CH₄ = \( 5x \)
- Moles of C₂H₆ = \( 2x \)

### Step 2: Calculate the total mass of the mixture
The total mass of the mixture is given as 280 g. We can express the mass of each component using their molar masses:
- Molar mass of CH₄ = 16 g/mol
- Molar mass of C₂H₆ = 30 g/mol

The total mass can be expressed as:
\[ \text{Total mass} = (\text{moles of CH₄} \times \text{molar mass of CH₄}) + (\text{moles of C₂H₆} \times \text{molar mass of C₂H₆}) \]
\[ 280 = (5x \times 16) + (2x \times 30) \]

### Step 3: Set up the equation
Substituting the values, we have:
\[ 280 = 80x + 60x \]
\[ 280 = 140x \]

### Step 4: Solve for \( x \)
Now, we can solve for \( x \):
\[ x = \frac{280}{140} = 2 \]

### Step 5: Calculate moles of CH₄ and C₂H₆
Now that we have \( x \), we can find the moles of CH₄ and C₂H₆:
- Moles of CH₄ = \( 5x = 5 \times 2 = 10 \)
- Moles of C₂H₆ = \( 2x = 2 \times 2 = 4 \)

### Step 6: Write the combustion reactions
The combustion reactions for CH₄ and C₂H₆ are:
1. For CH₄:
\[ CH₄ + 2O₂ \rightarrow CO₂ + 2H₂O \]
(1 mole of CH₄ produces 1 mole of CO₂)

2. For C₂H₆:
\[ C₂H₆ + \frac{7}{2}O₂ \rightarrow 2CO₂ + 3H₂O \]
(1 mole of C₂H₆ produces 2 moles of CO₂)

### Step 7: Calculate total moles of CO₂ produced
Now, we can calculate the total moles of CO₂ produced:
- From CH₄: \( 10 \) moles of CH₄ produce \( 10 \) moles of CO₂.
- From C₂H₆: \( 4 \) moles of C₂H₆ produce \( 4 \times 2 = 8 \) moles of CO₂.

### Step 8: Total moles of CO₂
Adding the moles of CO₂ from both reactions:
\[ \text{Total moles of CO₂} = 10 + 8 = 18 \]

Thus, the total moles of CO₂ produced is **18 moles**.

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