If carbon combines with hydrogen to form methane and carbon also combines with oxygen to form carbon dioxide then as per law of reciprocal proportions the ratio of hydrogen and oxygen by mass that combines should be?

Options

A. `8:1`
B. `2:1`
C. `1:8`
D. `1:2`

Answer

To solve the problem, we will use the Law of Reciprocal Proportions, which states that when two elements combine with a fixed mass of a third element, the ratio of the masses of the two elements will be the same or a simple multiple of the ratio of the masses of the two elements when they combine with the third element.

### Step-by-Step Solution:

1. **Identify the Compounds**:
- Carbon combines with hydrogen to form methane (CH₄).
- Carbon combines with oxygen to form carbon dioxide (CO₂).

2. **Determine the Masses of Elements in Each Compound**:
- For methane (CH₄):
- Mass of Carbon (C) = 12 g (1 atom of C)
- Mass of Hydrogen (H) = 4 g (4 atoms of H, since each H has an atomic mass of 1 g)
- Therefore, the mass ratio of C to H in CH₄ = 12 g : 4 g = 3 : 1.

- For carbon dioxide (CO₂):
- Mass of Carbon (C) = 12 g (1 atom of C)
- Mass of Oxygen (O) = 32 g (2 atoms of O, since each O has an atomic mass of 16 g)
- Therefore, the mass ratio of C to O in CO₂ = 12 g : 32 g = 3 : 8.

3. **Apply the Law of Reciprocal Proportions**:
- According to the law, if we take the fixed mass of Carbon (12 g) in both compounds, we can compare the masses of Hydrogen and Oxygen.
- The mass of Hydrogen that combines with 12 g of Carbon in methane is 4 g.
- The mass of Oxygen that combines with 12 g of Carbon in carbon dioxide is 32 g.

4. **Calculate the Ratio of Hydrogen to Oxygen**:
- The ratio of the masses of Hydrogen to Oxygen is:
\[ \text{Ratio} = \frac{\text{Mass of H}}{\text{Mass of O}} = \frac{4 \text{ g}}{32 \text{ g}} = \frac{1}{8}. \]

5. **Conclusion**:
- Therefore, the ratio of hydrogen to oxygen by mass that combines is \( \frac{1}{8} \).

### Final Answer:
The ratio of hydrogen and oxygen by mass that combines is \( \frac{1}{8} \).

---