What is the average oxidation number of carbon in acetone `(CH_3COCH_3)` ?

Answer

To find the average oxidation number of carbon in acetone (CH₃COCH₃), we will follow these steps:

### Step 1: Identify the structure of acetone
Acetone has the molecular formula CH₃COCH₃. This means it contains three carbon atoms: two in the methyl (CH₃) groups and one in the carbonyl (C=O) group.

### Step 2: Assign oxidation numbers to each carbon atom
1. **For the two CH₃ groups:**
- Each CH₃ group has one carbon atom bonded to three hydrogen atoms.
- The oxidation state of hydrogen is +1.
- For one carbon in CH₃:
\[ \text{Oxidation number} = x + 3(+1) = 0 \implies x + 3 = 0 \implies x = -3 \]
- Therefore, the oxidation number of carbon in each CH₃ group is -3.

2. **For the carbon in the carbonyl group (C=O):**
- This carbon is bonded to one oxygen atom (which has an oxidation state of -2) and one carbon atom (from the CH₃ group).
- The oxidation state of the carbonyl carbon can be calculated as follows:
\[ \text{Oxidation number} = y + (-2) + (-3) = 0 \implies y - 5 = 0 \implies y = +2 \]
- Therefore, the oxidation number of the carbon in the carbonyl group is +2.

### Step 3: Calculate the average oxidation number
- We have:
- Two carbons with an oxidation number of -3 (from the two CH₃ groups).
- One carbon with an oxidation number of +2 (from the carbonyl group).

- The total oxidation number is:
\[ \text{Total oxidation number} = 2(-3) + 1(+2) = -6 + 2 = -4 \]

- The average oxidation number of carbon in acetone is calculated by dividing the total oxidation number by the number of carbon atoms:
\[ \text{Average oxidation number} = \frac{-4}{3} = -\frac{4}{3} \]

### Final Answer
The average oxidation number of carbon in acetone (CH₃COCH₃) is \(-\frac{4}{3}\).

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