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

Options

A. 0.3
B. 0.05
C. 0.7
D. 0.95

Answer

To find the mole fraction of the solvent in an aqueous solution of NaOH with a molality of 3, we can follow these steps:

### Step 1: Understand the definition of molality
Molality (m) is defined as the number of moles of solute per kilogram of solvent. In this case, the solute is NaOH and the molality is given as 3.

### Step 2: Calculate the number of moles of solute
Given that the molality of the NaOH solution is 3, this means there are 3 moles of NaOH in 1 kg (1000 grams) of solvent.

- Moles of NaOH (solute) = 3 moles

### Step 3: Determine the mass and molar mass of the solvent
The solvent in this case is water. The mass of the solvent is given as 1000 grams (1 kg).

- Molar mass of water (H₂O) = 2(1) + 16 = 18 g/mol

### Step 4: Calculate the number of moles of solvent
Using the formula for moles:
\[ \text{Moles of solvent} = \frac{\text{mass of solvent}}{\text{molar mass of solvent}} \]

Substituting the values:
\[ \text{Moles of solvent} = \frac{1000 \text{ g}}{18 \text{ g/mol}} \approx 55.55 \text{ moles} \]

### Step 5: Calculate the mole fraction of the solvent
The mole fraction of the solvent (water) can be calculated using the formula:
\[ \text{Mole fraction of solvent} = \frac{\text{moles of solvent}}{\text{moles of solute} + \text{moles of solvent}} \]

Substituting the values:
\[ \text{Mole fraction of solvent} = \frac{55.55}{3 + 55.55} = \frac{55.55}{58.55} \approx 0.95 \]

### Final Answer
The mole fraction of the solvent in the aqueous solution of NaOH is approximately **0.95**.

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