The mole fraction of water in 20% of aqueous hydrogen peroxide solution by mass is

Options

A. `0.2`
B. `0.8`
C. `0.883`
D. `0.117`

Explanation

To find the mole fraction of water in a 20% aqueous hydrogen peroxide solution by mass, we can follow these steps:

### Step-by-Step Solution:

1. **Assume the Total Mass of the Solution**:
Let the total mass of the solution be \( x \) grams.

2. **Calculate the Mass of Hydrogen Peroxide (H2O2)**:
Since the solution is 20% hydrogen peroxide by mass, the mass of H2O2 in the solution is:
\[ \text{Mass of H2O2} = 20\% \text{ of } x = \frac{20}{100} \times x = 0.2x \text{ grams} \]

3. **Calculate the Mass of Water (H2O)**:
The remaining mass in the solution is water, which is 80% of the total mass:
\[ \text{Mass of H2O} = 80\% \text{ of } x = \frac{80}{100} \times x = 0.8x \text{ grams} \]

4. **Calculate the Number of Moles of H2O2**:
The molecular weight of H2O2 is calculated as follows:
- Hydrogen (H) has an atomic mass of 1 g/mol, and there are 2 hydrogen atoms.
- Oxygen (O) has an atomic mass of 16 g/mol, and there are 2 oxygen atoms.
\[ \text{Molecular weight of H2O2} = (2 \times 1) + (2 \times 16) = 34 \text{ g/mol} \]
Therefore, the number of moles of H2O2 is:
\[ \text{Moles of H2O2} = \frac{\text{Mass}}{\text{Molecular Weight}} = \frac{0.2x}{34} \]

5. **Calculate the Number of Moles of Water (H2O)**:
The molecular weight of water (H2O) is:
\[ \text{Molecular weight of H2O} = (2 \times 1) + (1 \times 16) = 18 \text{ g/mol} \]
Therefore, the number of moles of water is:
\[ \text{Moles of H2O} = \frac{0.8x}{18} \]

6. **Calculate the Mole Fraction of Water**:
The mole fraction of water (\( X_{H2O} \)) is given by the formula:
\[ X_{H2O} = \frac{\text{Moles of H2O}}{\text{Moles of H2O} + \text{Moles of H2O2}} \]
Substituting the values we calculated:
\[ X_{H2O} = \frac{\frac{0.8x}{18}}{\frac{0.8x}{18} + \frac{0.2x}{34}} \]
We can simplify this by canceling \( x \) from the numerator and denominator:
\[ X_{H2O} = \frac{0.8/18}{0.8/18 + 0.2/34} \]

7. **Finding a Common Denominator**:
To simplify the expression further, we can find a common denominator for the two fractions in the denominator:
\[ X_{H2O} = \frac{0.8 \cdot 34}{0.8 \cdot 34 + 0.2 \cdot 18} \]

8. **Calculating the Values**:
\[ X_{H2O} = \frac{27.2}{27.2 + 3.6} = \frac{27.2}{30.8} \]
\[ X_{H2O} \approx 0.883 \]

9. **Final Answer**:
The mole fraction of water in the solution is approximately \( 0.883 \).