Question

Calculate the percentage by mass of carbon ethanedioic crystal C2H2O4.2H2O

Answer 1

To calculate the percentage by mass of carbon in ethanedioic acid dihydrate (C₂H₂O₄·2H₂O), we first need to determine the molar mass of the compound.

### Step 1: Calculate the Molar Mass of C₂H₂O₄·2H₂O

1. **Calculate the molar mass of C₂H₂O₄:**
- Carbon (C): 12.01 g/mol × 2 = 24.02 g/mol
- Hydrogen (H): 1.008 g/mol × 2 = 2.016 g/mol
- Oxygen (O): 16.00 g/mol × 4 = 64.00 g/mol

Total for C₂H₂O₄:
\[
24.02 + 2.016 + 64.00 = 90.036 \text{ g/mol}
\]

2. **Calculate the molar mass of 2H₂O:**
- Each water molecule (H₂O) has:
- Hydrogen (H): 1.008 g/mol × 2 = 2.016 g/mol
- Oxygen (O): 16.00 g/mol = 16.00 g/mol
- Total for H₂O = 2.016 + 16.00 = 18.016 g/mol

For 2H₂O:
\[
18.016 \text{ g/mol} × 2 = 36.032 \text{ g/mol}
\]

### Step 2: Total Molar Mass of C₂H₂O₄·2H₂O

Adding both parts together:
\[
\text{Total Molar Mass} = 90.036 \text{ g/mol (C₂H₂O₄)} + 36.032 \text{ g/mol (2H₂O)} = 126.068 \text{ g/mol}
\]

### Step 3: Calculate the Mass Percentage of Carbon

1. **Mass of carbon in the formula:**
From C₂H₂O₄, there are 2 moles of carbon:
\[
\text{Mass of Carbon} = 24.02 \text{ g/mol}
\]

2. **Calculate the percentage by mass of carbon:**
\[
\text{Percentage of Carbon} = \left( \frac{\text{Mass of Carbon}}{\text{Molar Mass of C₂H₂O₄·2H₂O}} \right) \times 100
\]
\[
\text{Percentage of Carbon} = \left( \frac{24.02}{126.068} \right) \times 100 \approx 19.05\%
\]

Therefore, the percentage by mass of carbon in ethanedioic acid dihydrate (C₂H₂O₄·2H₂O) is approximately **19.05%.**