Step 1: Determine NaOH moles
The molar mass of sodium hydroxide (\( \text{NaOH} \)) is:
\[M_{\text{NaOH}} = 23 + 16 + 1 = 40 \, \text{g/mol}\]
The number of moles of NaOH in 10 g is:
\[\text{Moles of NaOH} = \frac{\text{Mass of NaOH}}{\text{Molar mass of NaOH}} = \frac{10 \, \text{g}}{40 \, \text{g/mol}} = 0.25 \, \text{mol}\]
Step 2: Convert solution volume to liters
Given a solution volume of 500 mL, convert it to liters:
\[\text{Volume of solution} = \frac{500 \, \text{mL}}{1000} = 0.5 \, \text{L}\]
Step 3: Compute NaOH solution molarity
Molarity (\( M \)) is moles of solute per liter of solution:
\[M = \frac{\text{Moles of NaOH}}{\text{Volume of solution in liters}} = \frac{0.25 \, \text{mol}}{0.5 \, \text{L}} = 0.5 \, \text{M}\]
Answer: The molarity of the NaOH solution is \( 0.5 \, \text{M} \). Thus, option (2) is correct.