Carbon combines with oxygen to form three oxides `CO_(2), CO and C_(3)O_(2)`. Among which pair of oxides does law of multiple proportions not hold true?

Options

A. `CO_(2) and CO`
B. `CO and C_(3)O_(2)`
C. `CO_(2) and C_(3)O_(2)`
D. It holds true in all cases

Answer

To determine which pair of carbon oxides does not adhere to the law of multiple proportions, we first need to understand the law itself. The law of multiple proportions states that when two elements combine to form more than one compound, the masses of one element that combine with a fixed mass of the other element can be expressed in a ratio of small whole numbers.

### Step-by-Step Solution:

1. **Identify the Compounds**: The three oxides of carbon we are considering are:
- Carbon Dioxide (CO₂)
- Carbon Monoxide (CO)
- Tricarbon Dioxide (C₃O₂)

2. **Calculate the Mass Ratios for CO₂ and CO**:
- For CO₂:
- Mass of Carbon (C) = 12 g
- Mass of Oxygen (O) = 16 g × 2 = 32 g
- Ratio of O to C = 32 g / 12 g = 2.67 (approximately)
- For CO:
- Mass of Carbon (C) = 12 g
- Mass of Oxygen (O) = 16 g
- Ratio of O to C = 16 g / 12 g = 1.33 (approximately)

3. **Calculate the Ratio of Masses of Oxygen**:
- Ratio of Oxygen in CO₂ to CO = 2.67 / 1.33 = 2 (which is a whole number)

4. **Calculate the Mass Ratios for CO and C₃O₂**:
- For C₃O₂:
- Mass of Carbon (C) = 12 g × 3 = 36 g
- Mass of Oxygen (O) = 16 g × 2 = 32 g
- Ratio of O to C = 32 g / 36 g = 0.89 (approximately)
- For CO:
- We already calculated this as 1.33.

5. **Calculate the Ratio of Masses of Oxygen**:
- Ratio of Oxygen in C₃O₂ to CO = 0.89 / 1.33 = 0.67 (approximately)

6. **Determine if the Ratios are Whole Numbers**:
- The ratio of 2 (from CO₂ and CO) is a whole number.
- The ratio of 0.67 (from CO and C₃O₂) is not a whole number.

7. **Conclusion**: The pair of oxides that does not adhere to the law of multiple proportions is **CO and C₃O₂**.

### Final Answer:
The pair of oxides among which the law of multiple proportions does not hold true is **CO and C₃O₂**.