0.2 g of an organic compound contains C, H and O. On combustion , it yields 0.15 g `CO_2` and 0.12 h g `H_2O` . The percentage of C, H and O respectively is

Options

A. `C = 15% , H = 20% , O = 65%`
B. `C = 10% , H = 8.2% , O = 81.8%`
C. `C = 12.2% , H = 8.8% , O = 79%`
D. `C = 20% , H = 6.66% , O = 73.34%`

Answer

To solve the problem, we will follow these steps:

### Step 1: Calculate the mass of Carbon (C) in the organic compound.
1. We know that the mass of CO₂ produced is 0.15 g.
2. The molar mass of CO₂ is 44 g/mol (12 g/mol for C and 32 g/mol for 2 O).
3. The mass of Carbon in CO₂ can be calculated using the ratio of the molar mass of Carbon to the molar mass of CO₂:
\[ \text{Mass of C} = \left( \frac{12 \, \text{g/mol}}{44 \, \text{g/mol}} \right) \times 0.15 \, \text{g} \]
\[ \text{Mass of C} = 0.04091 \, \text{g} \]

### Step 2: Calculate the mass of Hydrogen (H) in the organic compound.
1. We know that the mass of H₂O produced is 0.12 g.
2. The molar mass of H₂O is 18 g/mol (2 g/mol for 2 H and 16 g/mol for O).
3. The mass of Hydrogen in H₂O can be calculated using the ratio of the molar mass of Hydrogen to the molar mass of H₂O:
\[ \text{Mass of H} = \left( \frac{2 \, \text{g/mol}}{18 \, \text{g/mol}} \right) \times 0.12 \, \text{g} \]
\[ \text{Mass of H} = 0.01333 \, \text{g} \]

### Step 3: Calculate the mass of Oxygen (O) in the organic compound.
1. The total mass of the organic compound is given as 0.2 g.
2. We can find the mass of Oxygen by subtracting the mass of Carbon and Hydrogen from the total mass:
\[ \text{Mass of O} = 0.2 \, \text{g} - (\text{Mass of C} + \text{Mass of H}) \]
\[ \text{Mass of O} = 0.2 \, \text{g} - (0.04091 \, \text{g} + 0.01333 \, \text{g}) = 0.14576 \, \text{g} \]

### Step 4: Calculate the percentage of each element (C, H, O).
1. Percentage of Carbon:
\[ \text{Percentage of C} = \left( \frac{\text{Mass of C}}{\text{Total mass}} \right) \times 100 \]
\[ \text{Percentage of C} = \left( \frac{0.04091 \, \text{g}}{0.2 \, \text{g}} \right) \times 100 = 20.45\% \]

2. Percentage of Hydrogen:
\[ \text{Percentage of H} = \left( \frac{\text{Mass of H}}{\text{Total mass}} \right) \times 100 \]
\[ \text{Percentage of H} = \left( \frac{0.01333 \, \text{g}}{0.2 \, \text{g}} \right) \times 100 = 6.66\% \]

3. Percentage of Oxygen:
\[ \text{Percentage of O} = 100\% - (\text{Percentage of C} + \text{Percentage of H}) \]
\[ \text{Percentage of O} = 100\% - (20.45\% + 6.66\%) = 72.89\% \]

### Final Result:
The percentages of C, H, and O in the organic compound are approximately:
- Carbon (C): 20.45%
- Hydrogen (H): 6.66%
- Oxygen (O): 72.89%