CO is a pollutant produced due to incomplete combustion of butane . One mole of butane requires 6.5 moles of `O_2` for complete combustion. If 6 moles of oxygen are available , then number of moles of CO produced will be

Explanation

To solve the problem of how many moles of CO are produced from the incomplete combustion of butane (C₄H₁₀) when only 6 moles of O₂ are available, we can follow these steps:

### Step 1: Understand the Complete Combustion Reaction
The complete combustion of butane can be represented by the following balanced equation:
\[ C_4H_{10} + 6.5 O_2 \rightarrow 4 CO_2 + 5 H_2O \]
This indicates that 1 mole of butane requires 6.5 moles of oxygen to produce carbon dioxide and water.

### Step 2: Determine the Reaction for Incomplete Combustion
In the case of incomplete combustion, carbon monoxide (CO) is produced instead of carbon dioxide (CO₂). The balanced equation for the incomplete combustion of butane can be represented as:
\[ C_4H_{10} + O_2 \rightarrow CO + H_2O \]
We need to balance this equation based on the available oxygen.

### Step 3: Calculate the Oxygen Requirement for Incomplete Combustion
When we have 6 moles of O₂ available, we need to determine how many moles of CO can be produced.

### Step 4: Balancing the Incomplete Combustion Reaction
Let’s balance the incomplete combustion reaction:
1. Assume we have \( x \) moles of CO produced.
2. The balanced equation will look like this:
\[ C_4H_{10} + y O_2 \rightarrow x CO + H_2O \]
3. For carbon, we need 4 carbon atoms, so we will have \( x = 4 \) (4 moles of CO).
4. For hydrogen, butane has 10 hydrogen atoms, so we will produce 5 moles of water:
\[ C_4H_{10} + y O_2 \rightarrow 4 CO + 5 H_2O \]
5. Now, we count the oxygen atoms:
- From 4 CO, we get \( 4 \times 1 = 4 \) oxygen atoms.
- From 5 H₂O, we get \( 5 \times 1 = 5 \) oxygen atoms.
- Total oxygen needed = \( 4 + 5 = 9 \) oxygen atoms.
- Therefore, \( y = \frac{9}{2} = 4.5 \) moles of O₂.

### Step 5: Determine the Limiting Reactant
Since we only have 6 moles of O₂ available, we can use the stoichiometry to find out how much CO can be produced:
- If 4.5 moles of O₂ are needed to produce 4 moles of CO, we can set up a proportion:
\[ \frac{4.5 \text{ moles O}_2}{4 \text{ moles CO}} = \frac{6 \text{ moles O}_2}{x \text{ moles CO}} \]

### Step 6: Solve for x (moles of CO)
Cross-multiplying gives:
\[ 4.5x = 6 \times 4 \]
\[ 4.5x = 24 \]
\[ x = \frac{24}{4.5} = \frac{240}{45} = \frac{16}{3} \approx 5.33 \text{ moles of CO} \]

### Final Answer
Thus, the number of moles of CO produced from the incomplete combustion of butane with 6 moles of O₂ available is approximately **5.33 moles**.

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