The mole fraction of glucose `(C_(6)H_(12)O_(6))` in an aqueous binary solution is 0.1. The mass percentage of water in it, to the nearest integer, is _______.

Explanation

To find the mass percentage of water in an aqueous solution of glucose with a mole fraction of 0.1, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Mole Fraction of Water:**
Given that the mole fraction of glucose \( (C_6H_{12}O_6) \) is 0.1, we can find the mole fraction of water. The sum of the mole fractions in a solution is equal to 1.
\[ \text{Mole fraction of water} = 1 - \text{Mole fraction of glucose} = 1 - 0.1 = 0.9 \]

2. **Set Up the Mole Fraction Equation:**
The mole fraction of glucose can be expressed in terms of the number of moles of glucose and water:
\[ \text{Mole fraction of glucose} = \frac{n_{\text{glucose}}}{n_{\text{glucose}} + n_{\text{water}}} \]
Let \( n_{\text{glucose}} = 0.1 \) moles (for simplicity), then:
\[ n_{\text{water}} = \frac{0.1 \times n_{\text{glucose}}}{0.9} = \frac{0.1}{0.9} \approx 0.111 \text{ moles} \]

3. **Calculate the Mass of Glucose and Water:**
- The molar mass of glucose \( (C_6H_{12}O_6) \) is calculated as follows:
- Carbon: \( 12 \times 6 = 72 \, \text{g/mol} \)
- Hydrogen: \( 1 \times 12 = 12 \, \text{g/mol} \)
- Oxygen: \( 16 \times 6 = 96 \, \text{g/mol} \)
- Total: \( 72 + 12 + 96 = 180 \, \text{g/mol} \)

- The mass of glucose:
\[ \text{Mass of glucose} = n_{\text{glucose}} \times \text{Molar mass of glucose} = 0.1 \times 180 = 18 \, \text{g} \]

- The molar mass of water \( (H_2O) \) is:
- Hydrogen: \( 1 \times 2 = 2 \, \text{g/mol} \)
- Oxygen: \( 16 \, \text{g/mol} \)
- Total: \( 2 + 16 = 18 \, \text{g/mol} \)

- The mass of water:
\[ \text{Mass of water} = n_{\text{water}} \times \text{Molar mass of water} = 0.111 \times 18 \approx 2 \, \text{g} \]

4. **Calculate the Total Mass of the Solution:**
\[ \text{Total mass of solution} = \text{Mass of glucose} + \text{Mass of water} = 18 + 2 = 20 \, \text{g} \]

5. **Calculate the Mass Percentage of Water:**
The mass percentage of water in the solution is given by:
\[ \text{Mass percentage of water} = \left( \frac{\text{Mass of water}}{\text{Total mass of solution}} \right) \times 100 = \left( \frac{2}{20} \right) \times 100 = 10\% \]

### Final Answer:
The mass percentage of water in the solution, to the nearest integer, is **10%**.