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 need to analyze the three oxides: carbon dioxide (CO₂), carbon monoxide (CO), and tricarbon dioxide (C₃O₂).

### Step-by-Step Solution:

1. **Understand the Law of Multiple Proportions**:
The law 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 small whole number ratios.

2. **Identify the Oxides**:
We have three oxides of carbon:
- Carbon Dioxide (CO₂)
- Carbon Monoxide (CO)
- Tricarbon Dioxide (C₃O₂)

3. **Calculate the Masses of Oxygen in Each Compound**:
- For **CO₂**:
- 1 mole of CO₂ contains 1 mole of carbon (12 g) and 2 moles of oxygen (32 g).
- For **CO**:
- 1 mole of CO contains 1 mole of carbon (12 g) and 1 mole of oxygen (16 g).
- For **C₃O₂**:
- 1 mole of C₃O₂ contains 3 moles of carbon (36 g) and 2 moles of oxygen (32 g).

4. **Compare the Ratios of Oxygen**:
- **CO₂ and CO**:
- Mass of oxygen in CO₂ = 32 g
- Mass of oxygen in CO = 16 g
- Ratio = 32:16 = 2:1 (Whole number ratio)

- **CO and C₃O₂**:
- Mass of oxygen in CO = 16 g
- Mass of oxygen in C₃O₂ = 32 g
- Ratio = 32:16 = 2:1 (Whole number ratio)

- **CO₂ and C₃O₂**:
- Mass of oxygen in CO₂ = 32 g
- Mass of oxygen in C₃O₂ = 32 g
- Ratio = 32:32 = 1:1 (Whole number ratio)

5. **Determine Which Pair Does Not Follow the Law**:
- All ratios calculated above are whole numbers. However, the pair **CO₂ and C₃O₂** has a ratio of 1:1, which indicates that the same mass of oxygen is involved in both compounds, thus not demonstrating the law of multiple proportions effectively.

### Conclusion:
Among the pairs of oxides, the pair **CO₂ and C₃O₂** does not adhere to the law of multiple proportions in a meaningful way since they involve the same mass of oxygen.