To find the molality of a solution, we need to use the following formula:
[tex]\[ \text{Molality} (m) = \frac{\text{moles of solute}}{\text{mass of solvent in kilograms}} \][/tex]
Given:
- Moles of NaOH (solute) = 2.3 moles
- Mass of water (solvent) = 400.0 grams
Step-by-Step Solution:
1. Convert the mass of the solvent (water) from grams to kilograms:
[tex]\[ \text{mass of water in kg} = \frac{400.0 \, \text{grams}}{1000} = 0.400 \, \text{kg} \][/tex]
2. Calculate the molality:
[tex]\[ \text{Molality} (m) = \frac{\text{moles of NaOH}}{\text{mass of water in kg}} = \frac{2.3 \, \text{moles}}{0.400 \, \text{kg}} \][/tex]
3. Perform the division:
[tex]\[ \text{Molality} (m) = \frac{2.3}{0.400} = 5.75 \, \text{mol/kg} \][/tex]
Therefore, the molality of the solution is [tex]\( 5.75 \, \text{mol/kg} \)[/tex].
