Hydrogen and oxygen combine to form `H_(2)O_(2)` and `H_(2)O` containing `5.93 %` and `11.2%` hydrogen respectively. The data illustrates

Options

A. Law of conservation of mass
B. Law of constant proportion
C. Law of reciprocal proportions
D. Law of multiple proportions

Explanation

To solve the question, we will analyze the percentages of hydrogen in the compounds \( H_2O_2 \) and \( H_2O \) and determine which law of chemical proportions they illustrate.

### Step 1: Calculate the mass percentages of hydrogen in \( H_2O_2 \) and \( H_2O \)

1. **For \( H_2O_2 \)**:
- The molar mass of \( H_2O_2 \) is \( 2(1) + 2(16) = 34 \, g/mol \).
- The mass percentage of hydrogen in \( H_2O_2 \) is given as \( 5.93\% \).

2. **For \( H_2O \)**:
- The molar mass of \( H_2O \) is \( 2(1) + 16 = 18 \, g/mol \).
- The mass percentage of hydrogen in \( H_2O \) is given as \( 11.2\% \).

### Step 2: Convert mass percentages to a simple ratio

1. **Convert percentages to mass ratios**:
- For \( H_2O_2 \):
- Hydrogen: \( 5.93 \, g \)
- Oxygen: \( 100 - 5.93 = 94.07 \, g \)
- For \( H_2O \):
- Hydrogen: \( 11.2 \, g \)
- Oxygen: \( 100 - 11.2 = 88.8 \, g \)

### Step 3: Establish a ratio of hydrogen to oxygen

1. **Calculate the ratio of hydrogen to oxygen**:
- For \( H_2O_2 \):
- Ratio of \( H:O = 5.93:94.07 \)
- For \( H_2O \):
- Ratio of \( H:O = 11.2:88.8 \)

### Step 4: Simplify the ratios

1. **Simplify the ratios**:
- For \( H_2O_2 \):
- \( 5.93:94.07 \) simplifies to approximately \( 1:15.85 \)
- For \( H_2O \):
- \( 11.2:88.8 \) simplifies to approximately \( 1:7.93 \)

### Step 5: Compare the ratios

1. **Determine the ratio of hydrogen in both compounds**:
- The ratio of hydrogen in \( H_2O_2 \) to hydrogen in \( H_2O \) can be expressed as:
- \( \frac{5.93}{11.2} \) which gives us a ratio of approximately \( 0.529 \).

### Step 6: Identify the law illustrated

1. **Identify the law of multiple proportions**:
- The ratios of the masses of hydrogen that combine with a fixed mass of oxygen (from both compounds) demonstrate that the amounts of hydrogen that combine with the same amount of oxygen are in a simple ratio.
- This illustrates the **Law of Multiple Proportions**, which states that when two elements combine to form more than one compound, the ratios of the masses of one element that combine with a fixed mass of the other element are in simple whole number ratios.

### Conclusion

The data illustrates the **Law of Multiple Proportions**.