Average oxidation number of carbon in `C_3O_2,Mg_2C_3` are respectively.

Options

A. `-4//3,+4//3`
B. `+4//3,-4//3`
C. `-2//3,+2//3`
D. `-2//3,+4//3`

Answer

To find the average oxidation number of carbon in the compounds \( C_3O_2 \) and \( Mg_2C_3 \), we will follow these steps:

### Step 1: Determine the oxidation number of carbon in \( C_3O_2 \)

1. Let the oxidation number of carbon be \( x \).
2. In \( C_3O_2 \), there are 3 carbon atoms and 2 oxygen atoms.
3. The oxidation number of oxygen is typically \(-2\).
4. The total oxidation number for the oxygen in the compound is \( 2 \times (-2) = -4 \).
5. Since the compound is neutral, the sum of the oxidation numbers must equal 0:
\[ 3x + (-4) = 0 \]
6. Rearranging the equation gives:
\[ 3x = +4 \]
7. Solving for \( x \):
\[ x = \frac{4}{3} \]

### Step 2: Determine the oxidation number of carbon in \( Mg_2C_3 \)

1. Let the oxidation number of carbon in \( Mg_2C_3 \) be \( y \).
2. In \( Mg_2C_3 \), there are 2 magnesium atoms and 3 carbon atoms.
3. The oxidation number of magnesium is typically \( +2 \).
4. The total oxidation number for the magnesium in the compound is \( 2 \times (+2) = +4 \).
5. Again, since the compound is neutral, the sum of the oxidation numbers must equal 0:
\[ 2(+2) + 3y = 0 \]
6. Rearranging the equation gives:
\[ 4 + 3y = 0 \]
7. Solving for \( y \):
\[ 3y = -4 \quad \Rightarrow \quad y = -\frac{4}{3} \]

### Final Results

- The average oxidation number of carbon in \( C_3O_2 \) is \( +\frac{4}{3} \).
- The average oxidation number of carbon in \( Mg_2C_3 \) is \( -\frac{4}{3} \).

### Summary

The average oxidation numbers of carbon in \( C_3O_2 \) and \( Mg_2C_3 \) are respectively:
\[ \frac{4}{3}, -\frac{4}{3} \]