When methane is burnt in oxygen to produce `CO_(2) and H_(2)O` Find the Change in oxidation number of carbon?

Explanation

To find the change in oxidation number of carbon when methane (CH₄) is burnt in oxygen to produce carbon dioxide (CO₂) and water (H₂O), we can follow these steps:

### Step 1: Write the balanced chemical equation for the reaction.
The combustion of methane can be represented as:
\[ \text{CH}_4 + 2\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O} \]

### Step 2: Determine the oxidation number of carbon in methane (CH₄).
In methane (CH₄):
- The oxidation number of hydrogen (H) is +1.
- Let the oxidation number of carbon (C) be \( x \).
- The equation for the oxidation number can be set up as follows:
\[ x + 4(+1) = 0 \]
\[ x + 4 = 0 \]
\[ x = -4 \]
Thus, the oxidation number of carbon in methane is -4.

### Step 3: Determine the oxidation number of carbon in carbon dioxide (CO₂).
In carbon dioxide (CO₂):
- The oxidation number of oxygen (O) is -2.
- Let the oxidation number of carbon (C) be \( y \).
- The equation for the oxidation number can be set up as follows:
\[ y + 2(-2) = 0 \]
\[ y - 4 = 0 \]
\[ y = +4 \]
Thus, the oxidation number of carbon in carbon dioxide is +4.

### Step 4: Calculate the change in oxidation number.
The change in oxidation number can be calculated using the formula:
\[ \text{Change in oxidation number} = \text{Final oxidation number} - \text{Initial oxidation number} \]
Substituting the values we found:
\[ \text{Change} = (+4) - (-4) \]
\[ \text{Change} = +4 + 4 = 8 \]

### Conclusion:
The change in oxidation number of carbon when methane is burnt in oxygen to produce carbon dioxide and water is **8**.

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