Equivalent weight of carbon in `CO` and `CO_(2)` are in the ratio of:

Options

A. (a)`1:1`
B. (b)`1:2`
C. (c )`2:1`
D. (d)`1:4`

Answer

To find the ratio of the equivalent weight of carbon in carbon monoxide (CO) and carbon dioxide (CO₂), we can follow these steps:

### Step 1: Determine the valency of carbon in CO
- In CO, we can denote the oxidation state of carbon as \( x \).
- The oxidation state of oxygen is \(-2\).
- Since CO is a neutral molecule, we can set up the equation:
\[ x + (-2) = 0 \]
- Solving for \( x \):
\[ x = +2 \]
- Therefore, the valency of carbon in CO is 2.

### Step 2: Determine the valency of carbon in CO₂
- In CO₂, we again denote the oxidation state of carbon as \( x \).
- The oxidation state of each oxygen atom is \(-2\) (and there are two oxygen atoms).
- Setting up the equation for CO₂:
\[ x + 2(-2) = 0 \]
- Solving for \( x \):
\[ x - 4 = 0 \implies x = +4 \]
- Thus, the valency of carbon in CO₂ is 4.

### Step 3: Calculate the equivalent weight of carbon in CO
- The equivalent weight is given by the formula:
\[ \text{Equivalent weight} = \frac{\text{Atomic weight}}{\text{Valency}} \]
- The atomic weight of carbon is 12.
- Therefore, the equivalent weight of carbon in CO is:
\[ \text{Equivalent weight in CO} = \frac{12}{2} = 6 \]

### Step 4: Calculate the equivalent weight of carbon in CO₂
- Using the same formula for CO₂:
- The valency of carbon in CO₂ is 4.
- Thus, the equivalent weight of carbon in CO₂ is:
\[ \text{Equivalent weight in CO₂} = \frac{12}{4} = 3 \]

### Step 5: Find the ratio of the equivalent weights
- Now, we can find the ratio of the equivalent weights of carbon in CO and CO₂:
\[ \text{Ratio} = \frac{\text{Equivalent weight in CO}}{\text{Equivalent weight in CO₂}} = \frac{6}{3} = 2:1 \]

### Conclusion
The ratio of the equivalent weight of carbon in CO to that in CO₂ is \( 2:1 \).

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