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 volumes of gases.

Answer

To determine which law is illustrated by the combining ratios of hydrogen and oxygen in water (H₂O) and hydrogen peroxide (H₂O₂), we can follow these steps:

### Step 1: Identify the Compounds and Their Ratios
- Water (H₂O) has a combining ratio of hydrogen to oxygen as 1:8.
- Hydrogen peroxide (H₂O₂) has a combining ratio of hydrogen to oxygen as 1:16.

### Step 2: Calculate the Mass of Elements in Each Compound
- For water (H₂O):
- Hydrogen: 2 atoms × 1 g/mol = 2 g
- Oxygen: 1 atom × 16 g/mol = 16 g
- Ratio of mass of hydrogen to mass of oxygen = 2 g : 16 g = 1 : 8

- For hydrogen peroxide (H₂O₂):
- Hydrogen: 2 atoms × 1 g/mol = 2 g
- Oxygen: 2 atoms × 16 g/mol = 32 g
- Ratio of mass of hydrogen to mass of oxygen = 2 g : 32 g = 1 : 16

### Step 3: Compare the Ratios
- In both compounds, we take the mass of hydrogen as a fixed amount (1 g for simplicity).
- For H₂O, 1 g of hydrogen combines with 8 g of oxygen.
- For H₂O₂, 1 g of hydrogen combines with 16 g of oxygen.

### Step 4: Establish the Ratio of Oxygen Masses
- The ratio of the masses of oxygen that combine with the same mass of hydrogen (1 g) in both compounds is:
- For H₂O: 8 g of oxygen
- For H₂O₂: 16 g of oxygen
- The ratio of these two amounts is 8:16, which simplifies to 1:2.

### Step 5: Identify the Law Illustrated
- 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) are in small whole numbers.
- Here, the ratio of the masses of oxygen (8 g and 16 g) that combine with 1 g of hydrogen is 1:2, which is a small whole number.

### Conclusion
The law illustrated by the combining ratios of hydrogen and oxygen in water and hydrogen peroxide is the **Law of Multiple Proportions**.

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