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 third element, the masses of the first two elements that combine with a fixed mass of the third element are in the ratio of small whole numbers.

### Step-by-Step Solution:

1. **Identify the Compounds Formed:**
- Carbon (C) combines with Hydrogen (H) to form Methane (CH₄).
- Carbon (C) combines with Oxygen (O) to form Carbon Dioxide (CO₂).

2. **Determine the Molar Masses:**
- For Methane (CH₄):
- Atomic mass of Carbon (C) = 12 g/mol
- Atomic mass of Hydrogen (H) = 1 g/mol
- Total mass of Hydrogen in CH₄ = 4 × 1 = 4 g
- Therefore, the total mass of CH₄ = 12 (C) + 4 (H) = 16 g.

- For Carbon Dioxide (CO₂):
- Atomic mass of Carbon (C) = 12 g/mol
- Atomic mass of Oxygen (O) = 16 g/mol
- Total mass of Oxygen in CO₂ = 2 × 16 = 32 g
- Therefore, the total mass of CO₂ = 12 (C) + 32 (O) = 44 g.

3. **Apply the Law of Reciprocal Proportions:**
- According to the law, the ratio of the masses of Hydrogen and Oxygen that combine with a fixed mass of Carbon should be compared.
- We have:
- Mass of Hydrogen (from CH₄) = 4 g
- Mass of Oxygen (from CO₂) = 32 g

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

5. **Final Answer:**
- Therefore, the ratio of Hydrogen to Oxygen by mass that combines is 1:8.