Butyric acid contains only C, H and O. A 4.24 mg sample of butyric acid is completely burnt. It gives 8.45 mg of carbon dioxide and 3.46 mg of water. What is the mass percentage of each element in butyric acid?

Answer

To find the mass percentage of each element (C, H, and O) in butyric acid from the given data, we can follow these steps:

### Step 1: Calculate the mass of carbon in butyric acid
1. We know that when butyric acid is burned, it produces carbon dioxide (CO₂). The mass of carbon in CO₂ can be calculated using the ratio of the molar masses of carbon and carbon dioxide.
2. The molar mass of CO₂ = 44 g/mol (12 g/mol for C + 32 g/mol for O).
3. The mass of carbon in 8.45 mg of CO₂ can be calculated as:
\[ \text{Mass of C} = \left(\frac{12 \text{ mg}}{44 \text{ mg}}\right) \times 8.45 \text{ mg} = 2.304 \text{ mg} \]

### Step 2: Calculate the mass of hydrogen in butyric acid
1. When butyric acid is burned, it also produces water (H₂O). The mass of hydrogen in water can be calculated using the ratio of the molar masses of hydrogen and water.
2. The molar mass of H₂O = 18 g/mol (2 g/mol for H + 16 g/mol for O).
3. The mass of hydrogen in 3.46 mg of H₂O can be calculated as:
\[ \text{Mass of H} = \left(\frac{2 \text{ mg}}{18 \text{ mg}}\right) \times 3.46 \text{ mg} = 0.384 \text{ mg} \]

### Step 3: Calculate the mass of oxygen in butyric acid
1. The mass of oxygen can be determined by subtracting the masses of carbon and hydrogen from the total mass of the butyric acid sample.
2. The total mass of butyric acid = 4.24 mg.
3. Therefore, the mass of oxygen is:
\[ \text{Mass of O} = 4.24 \text{ mg} - (2.304 \text{ mg} + 0.384 \text{ mg}) = 1.552 \text{ mg} \]

### Step 4: Calculate the mass percentages of each element
1. **Mass percentage of carbon**:
\[ \text{Percentage of C} = \left(\frac{2.304 \text{ mg}}{4.24 \text{ mg}}\right) \times 100 = 54.30\% \]

2. **Mass percentage of hydrogen**:
\[ \text{Percentage of H} = \left(\frac{0.384 \text{ mg}}{4.24 \text{ mg}}\right) \times 100 = 9.06\% \]

3. **Mass percentage of oxygen**:
\[ \text{Percentage of O} = 100 - (54.30\% + 9.06\%) = 36.64\% \]

### Final Results
- Mass percentage of Carbon (C) = 54.30%
- Mass percentage of Hydrogen (H) = 9.06%
- Mass percentage of Oxygen (O) = 36.64%

---