Question

The density of 'x' M solution ('x' molar) of NaOH is \(1.12 \, \text{g/mL}\). While in molality, the concentration of the solution is \(3 \, \text{m}\) (3 molal). Then x is:
Given: Molar mass of NaOH is \(40 \, \text{g/mol}\)

• A. 3.5
• B. 3
• C. 3.8
• D. 2.8

Answer 1

The Correct Option is B

We know the relationship between molality and molarity:
\[\text{Molality} = \frac{1000 \times M}{1000 \times d - M \times (\text{Molar mass of solute})}\]
Substituting the values:
\[3 = \frac{1000 \times x}{1000 \times 1.12 - x \times 40}\]
Rearranging:
\[3 \times (1000 \times 1.12 - x \times 40) = 1000 \times x\]
Simplify:
\[3 \times 1120 - 120x = 1000x\]
\[3360 = 1120x\]
Solving:
\[x = 3\]
Thus, the molarity of the solution is 3.0 M.

Answer 2

To determine the molarity (\(x\)) of the NaOH solution, we need to relate molarity and molality using the density of the solution. The given molality is \(3 \, \text{m}\), meaning there are 3 moles of NaOH per kilogram of the solvent (water), and the density of the solution is \(1.12 \, \text{g/mL}\).

1. Calculate the mass of the solution:
   • The density of the solution implies that \(1 \, \text{mL}\) of solution weighs \(1.12 \, \text{g}\).
2. Consider a total solution of \(1000 \, \text{mL}\) to find its mass:
   • Mass of solution = \(1.12 \, \text{g/mL} \times 1000 \, \text{mL} = 1120 \, \text{g}\).
3. Determine the mass of NaOH in the solution:
   • Molality (\(3 \, \text{m}\)) means 3 moles of NaOH per 1000 g of water.
   • Mass of water = \(1120 \, \text{g} - \text{mass of NaOH}\).
   • If \(m\) is the mass of NaOH, \(1000 \, \text{g} - m\) of water also needs to allow for 3 moles of NaOH.
4. Relation for NaOH:
   • Moles of NaOH = \(\frac{m}{40} = 3\) (since molar mass of NaOH is \(40 \, \text{g/mol}\)), leading to \(m = 3 \times 40 = 120 \, \text{g}\).
5. Mass of the water is therefore \(1000 \, \text{g} - 120 \, \text{g} = 880 \, \text{g} = 0.88 \, \text{kg}\).
6. Calculate the molarity (\(x\)):
   • Moles of solute (NaOH) in \(1120 \, \text{g} \, \text{solution}\) = 3 moles (as calculated).
   • Molarity \((x) = \frac{\text{moles of solute}}{\text{liters of solution}} = \frac{3}{1} = 3 \, \text{M}\).

Hence, the molarity of the given solution is \(x = 3\).