Which of the following pair of compounds illustrate the law of multiple proportions?

Options

A. `SO_(2)` and `SO_(3)`
B. `NO_(2)` and `N_(2) O`
C. `MgO` and `Mg(OH)_(2)`
D. `NO` and `N_(2)O_(5)`

Answer

To determine which pairs of compounds illustrate the law of multiple proportions, we need to follow these steps:

### Step 1: Understand the Law of Multiple Proportions
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 will be in the ratio of small whole numbers.

### Step 2: Identify the Compounds in Each Option
We will analyze the given pairs of compounds to see if they consist of only two elements and if they form more than one compound.

1. **SO2 and SO3**:
- Both compounds consist of sulfur (S) and oxygen (O).
- They represent two different compounds formed by the same elements.

2. **NO2 and N2O**:
- Both compounds consist of nitrogen (N) and oxygen (O).
- They represent two different compounds formed by the same elements.

3. **MgO and Mg(OH)2**:
- These compounds consist of magnesium (Mg), oxygen (O), and hydrogen (H).
- Since Mg(OH)2 contains three elements, it does not follow the law of multiple proportions.

4. **NO and N2O5**:
- Both compounds consist of nitrogen (N) and oxygen (O).
- They represent two different compounds formed by the same elements.

### Step 3: Conclusion
From the analysis:
- **SO2 and SO3** (Option 1) follow the law of multiple proportions.
- **NO2 and N2O** (Option 2) follow the law of multiple proportions.
- **MgO and Mg(OH)2** (Option 3) do not follow the law of multiple proportions.
- **NO and N2O5** (Option 4) follow the law of multiple proportions.

Thus, the pairs that illustrate the law of multiple proportions are:
- SO2 and SO3
- NO2 and N2O
- NO and N2O5

### Final Answer
The pairs of compounds that illustrate the law of multiple proportions are:
1. SO2 and SO3
2. NO2 and N2O
3. NO and N2O5