Calculate percentage of carbon in ethanol `(C_(2)H_(5)OH)`.

Options

A. 52
B. 13
C. 34
D. 90

Answer

To calculate the percentage of carbon in ethanol (C₂H₅OH), we will follow these steps:

### Step 1: Determine the molar mass of ethanol (C₂H₅OH)
- **Carbon (C)**: There are 2 carbon atoms in ethanol. The molar mass of carbon is 12 g/mol.
\[ \text{Mass of Carbon} = 2 \times 12 = 24 \text{ g/mol} \]

- **Hydrogen (H)**: There are 6 hydrogen atoms in ethanol (5 from C₂H₅ and 1 from OH). The molar mass of hydrogen is 1 g/mol.
\[ \text{Mass of Hydrogen} = 6 \times 1 = 6 \text{ g/mol} \]

- **Oxygen (O)**: There is 1 oxygen atom in ethanol. The molar mass of oxygen is 16 g/mol.
\[ \text{Mass of Oxygen} = 1 \times 16 = 16 \text{ g/mol} \]

- **Total molar mass of ethanol**:
\[ \text{Molar mass of C₂H₅OH} = \text{Mass of Carbon} + \text{Mass of Hydrogen} + \text{Mass of Oxygen} = 24 + 6 + 16 = 46 \text{ g/mol} \]

### Step 2: Calculate the percentage of carbon in ethanol
- The formula to calculate the percentage of carbon is:
\[ \text{Percentage of Carbon} = \left( \frac{\text{Mass of Carbon}}{\text{Molar Mass of Ethanol}} \right) \times 100 \]

- Plugging in the values:
\[ \text{Percentage of Carbon} = \left( \frac{24}{46} \right) \times 100 \]

### Step 3: Perform the calculation
- Calculate \( \frac{24}{46} \):
\[ \frac{24}{46} \approx 0.5217 \]

- Now multiply by 100 to get the percentage:
\[ 0.5217 \times 100 \approx 52.17\% \]

### Step 4: Round off the result
- The percentage of carbon can be approximated to:
\[ \approx 52\% \]

### Final Answer:
The percentage of carbon in ethanol (C₂H₅OH) is approximately **52%**.

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