Sodium oxide reacts with water to produce sodium hydroxide. 20.0 g of sodium oxide is dissolved in 500 mL of water. Neglecting the change in volume, the concentration of the resulting NaOH solution is _______ `xx 10^(-1)M`. (Nearest integer)
[Atomic mass `: a = 23.0, O = 16.0, H = 1.0`]

Answer

To solve the problem, we need to find the concentration of sodium hydroxide (NaOH) produced when 20.0 g of sodium oxide (Na2O) is dissolved in 500 mL of water. Let's go through the steps systematically.

### Step-by-Step Solution:

1. **Write the Reaction**:
Sodium oxide reacts with water to form sodium hydroxide:
\[ \text{Na}_2\text{O} + \text{H}_2\text{O} \rightarrow 2 \text{NaOH} \]

2. **Calculate the Molar Mass of Sodium Oxide (Na2O)**:
- Sodium (Na) has an atomic mass of 23.0 g/mol.
- Oxygen (O) has an atomic mass of 16.0 g/mol.
- Molar mass of Na2O = \(2 \times 23.0 + 16.0 = 46.0 + 16.0 = 62.0 \, \text{g/mol}\)

3. **Calculate the Number of Moles of Sodium Oxide**:
Using the formula:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \]
- Mass of Na2O = 20.0 g
- Molar mass of Na2O = 62.0 g/mol
\[ \text{Number of moles of Na2O} = \frac{20.0 \, \text{g}}{62.0 \, \text{g/mol}} \approx 0.3226 \, \text{mol} \]

4. **Determine the Moles of NaOH Produced**:
From the balanced equation, 1 mole of Na2O produces 2 moles of NaOH:
\[ \text{Number of moles of NaOH} = 2 \times \text{Number of moles of Na2O} = 2 \times 0.3226 \approx 0.6452 \, \text{mol} \]

5. **Calculate the Concentration of NaOH**:
Concentration (Molarity, M) is defined as:
\[ \text{Concentration (M)} = \frac{\text{Number of moles of solute}}{\text{Volume of solution in liters}} \]
- Volume of solution = 500 mL = 0.500 L
\[ \text{Concentration of NaOH} = \frac{0.6452 \, \text{mol}}{0.500 \, \text{L}} \approx 1.2904 \, \text{M} \]

6. **Express the Concentration in the Required Format**:
To express this in the form of \(xx \times 10^{-1} \, \text{M}\):
\[ 1.2904 \, \text{M} = 12.904 \times 10^{-1} \, \text{M} \]
Rounding to the nearest integer gives us:
\[ \text{Nearest integer} = 13 \]

### Final Answer:
The concentration of the resulting NaOH solution is \( \boxed{13} \).