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 state of carbon in \( C_3O_2 \)

1. **Write the equation for the oxidation states**:
- Let the oxidation state of carbon be \( x \).
- The oxidation state of oxygen is \(-2\).
- The compound is neutral, so the sum of the oxidation states must equal zero.

\[ 3x + 2(-2) = 0 \]

2. **Simplify the equation**:
\[ 3x - 4 = 0 \]

3. **Solve for \( x \)**:
\[ 3x = 4 \implies x = \frac{4}{3} \]

Thus, the average oxidation number of carbon in \( C_3O_2 \) is \( +\frac{4}{3} \).

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

1. **Write the equation for the oxidation states**:
- Let the oxidation state of carbon be \( y \).
- The oxidation state of magnesium is \( +2 \).
- There are 2 magnesium atoms, so their total contribution is \( 2(+2) = +4 \).
- The compound is neutral, so the sum of the oxidation states must equal zero.

\[ 2(+2) + 3y = 0 \]

2. **Simplify the equation**:
\[ 4 + 3y = 0 \]

3. **Solve for \( y \)**:
\[ 3y = -4 \implies y = -\frac{4}{3} \]

Thus, the average oxidation number of carbon in \( Mg_2C_3 \) is \( -\frac{4}{3} \).

### Final Answer:
The average oxidation numbers of carbon in \( C_3O_2 \) and \( Mg_2C_3 \) are respectively \( +\frac{4}{3} \) and \( -\frac{4}{3} \).

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