The combining ratios of hydrogen and oxygen in water and hydrogen peroxide are `1:8` and `1:16`. Which law is illustrated in this example?

Options

A. Law of definite proportions
B. law of multiple proportions
C. law of conservation of mass
D. Gay Lussac's law of combining volume of gases.

Explanation

To solve the question regarding the combining ratios of hydrogen and oxygen in water and hydrogen peroxide, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Compounds**:
- Water (H₂O)
- Hydrogen Peroxide (H₂O₂)

2. **Determine the Mass Ratios**:
- For Water (H₂O):
- 2 grams of Hydrogen (H) combine with 16 grams of Oxygen (O).
- Therefore, the ratio of Hydrogen to Oxygen in water is 2:16 or simplified to 1:8.

- For Hydrogen Peroxide (H₂O₂):
- 2 grams of Hydrogen (H) combine with 32 grams of Oxygen (O).
- Therefore, the ratio of Hydrogen to Oxygen in hydrogen peroxide is 2:32 or simplified to 1:16.

3. **Analyze the Ratios**:
- In water, the ratio of hydrogen to oxygen is 1:8.
- In hydrogen peroxide, the ratio of hydrogen to oxygen is 1:16.

4. **Apply the Law of Multiple Proportions**:
- According to the law of multiple proportions, when two elements (in this case, hydrogen and oxygen) combine to form more than one compound, the ratios of the masses of the second element (oxygen) that combine with a fixed mass of the first element (hydrogen) will be in small whole numbers.
- Here, we can take the ratio of the masses of oxygen that combine with 1 gram of hydrogen in both compounds:
- For water: 8 grams of oxygen combine with 1 gram of hydrogen.
- For hydrogen peroxide: 16 grams of oxygen combine with 1 gram of hydrogen.
- The ratio of the masses of oxygen in these two compounds is 8:16, which simplifies to 1:2.

5. **Conclusion**:
- Since the ratio of the masses of oxygen that combine with a fixed mass of hydrogen (1 gram) is in small whole numbers (1:2), this illustrates the **Law of Multiple Proportions**.

### Final Answer:
The law illustrated in this example is the **Law of Multiple Proportions**.

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