Question

The density of 2 M aqueous solution of NaOH is 1.28 g/cm$^3$. The molality of the solution is [Given that molecular mass of NaOH = 40 g mol$^{-1}$]

• A. 1.20 m
• B. 1.56 m
• C. 1.67 m
• D. 1.32 m

Answer 1

The Correct Option is C

To find the molality of the 2 M aqueous solution of NaOH, we need to follow a series of logical steps. Here is the detailed solution:

1. First, understand the given terms:
   • Molarity (M) is 2 M. This means there are 2 moles of NaOH in 1 liter of solution.
   • Density of the solution is 1.28 g/cm^3, which is equivalent to 1280 g/L.
   • Molecular mass of NaOH is 40 g/mol.
2. Calculate the mass of NaOH in the solution:
   • Since molarity is 2 M, there are 2 moles of NaOH in 1 liter of solution.
   • The mass of NaOH in 1 liter = 2 moles × 40 g/mol = 80 g.
3. Calculate the mass of water in the solution:
   • Total mass of 1 liter of solution = 1280 g (from density).
   • Mass of water = Total mass of solution - Mass of NaOH = 1280 g - 80 g = 1200 g.
4. Convert mass of water to kilograms for molality calculation:
   • 1200 g of water = 1.2 kg.
5. Calculate molality (m):
   • Molality is defined as the number of moles of solute per kilogram of solvent.
   • Molality, m = \frac{\text{moles of NaOH}}{\text{mass of water in kg}} = \frac{2}{1.2} = 1.67 \, m.
6. Conclusion:
   • The molality of the solution is 1.67 m.