The valancy of carbons is generally `4`, but its oxidation state may be `-4, -2, 0, +2, -1`, etc. In the compounds containing `C, H`, and `O`, the oxidation number of `C` is calculated as
Oxidation number of `C= (2n_(O)-n_(H))/(n_(C ))`
Where `n_(O), n_(H)` and `n_(C )` are the numbers of oxygen, hydrogen, and carbons, atoms, respectively.
In which of the following compounds is the oxidation state of `C` a fraction?

Options

A. `CO`
B. `CO_(2)`
C. Carbon suboxide
D. All

Explanation

To solve the problem, we will calculate the oxidation state of carbon in each of the given compounds using the provided formula:

**Oxidation number of C = (2n(O) - n(H)) / n(C)**

Where:
- n(O) = number of oxygen atoms
- n(H) = number of hydrogen atoms
- n(C) = number of carbon atoms

Let's analyze each compound step by step:

### Step 1: Analyze CO (Carbon Monoxide)
- n(O) = 1 (1 oxygen atom)
- n(H) = 0 (no hydrogen atoms)
- n(C) = 1 (1 carbon atom)

Using the formula:
\[ \text{Oxidation number of C} = \frac{2 \times 1 - 0}{1} = \frac{2}{1} = 2 \]
**Hint:** Check the number of atoms in the compound carefully.

### Step 2: Analyze CO2 (Carbon Dioxide)
- n(O) = 2 (2 oxygen atoms)
- n(H) = 0 (no hydrogen atoms)
- n(C) = 1 (1 carbon atom)

Using the formula:
\[ \text{Oxidation number of C} = \frac{2 \times 2 - 0}{1} = \frac{4}{1} = 4 \]
**Hint:** Remember that the number of hydrogen atoms can be zero in some compounds.

### Step 3: Analyze C3O2 (Carbon Suboxide)
- n(O) = 2 (2 oxygen atoms)
- n(H) = 0 (no hydrogen atoms)
- n(C) = 3 (3 carbon atoms)

Using the formula:
\[ \text{Oxidation number of C} = \frac{2 \times 2 - 0}{3} = \frac{4}{3} \]
**Hint:** Pay attention to the number of carbon atoms, as it can affect the result significantly.

### Conclusion
After calculating the oxidation states of carbon in each compound:
- In CO, the oxidation state of carbon is +2.
- In CO2, the oxidation state of carbon is +4.
- In C3O2, the oxidation state of carbon is \( \frac{4}{3} \), which is a fraction.

Thus, the compound in which the oxidation state of carbon is a fraction is **C3O2 (Carbon Suboxide)**.

**Final Answer:** The correct option is **C (C3O2)**.