Mole fraction of solvent in aqueous solution of naoh having molality of 3 is

General
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mole fraction of solvent in aqueous solution of naoh having molality of 3 is

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Mole fraction of solvent in aqueous solution of NaOH having molality of 3 is

Answer:
To determine the mole fraction of the solvent (water) in an aqueous solution of NaOH with a molality of 3, we need to follow these steps:

  1. Understanding Molality and Mole Fraction:

    • Molality (m): Molality is defined as the number of moles of solute per kilogram of solvent. In this case, the molality is 3, which means there are 3 moles of NaOH per kilogram of water.
    • Mole Fraction: The mole fraction of a component (in this case, water) in a solution is the ratio of the number of moles of that component to the total number of moles of all components in the solution.

  2. Calculating Moles of Solute and Solvent:

    • Since the molality is 3, we have 3 moles of NaOH (solute).
    • We are considering 1 kilogram of water, which corresponds to approximately 55.51 moles of water because the molar mass of water (H₂O) is about 18.015 g/mol.

  3. Total Moles in Solution:

    • Total moles in solution ( = ) moles of NaOH ( + ) moles of water

      \text{Total moles} = 3 \, (\text{moles of NaOH}) + 55.51 \, (\text{moles of water}) = 58.51 \, (\text{moles})

  4. Calculating Mole Fraction of Solvent (Water):

    • The mole fraction of water (solvent) ( X_{\text{solvent}} ) can be calculated using the formula:

      X_{\text{solvent}} = \frac{\text{moles of solvent}}{\text{total moles in solution}}

    • Substitute the values:

      X_{\text{solvent}} = \frac{55.51}{58.51}

  5. Final Calculation:

    • Simplify the fraction:

      X_{\text{solvent}} = \frac{55.51}{58.51} \approx 0.949

Therefore, the mole fraction of the solvent (water) in an aqueous solution of NaOH with a molality of 3 is approximately 0.949.