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, we have a molality of 3, which means there are 3 moles of NaOH dissolved in 1 kg (1000 g) of water.

### Step 2: Calculate the moles of solute (NaOH)
From the problem, we know that:
- Moles of NaOH (solute) = 3 moles

### Step 3: Calculate the moles of solvent (water)
To find the moles of water, we use the formula:
\[ \text{Moles of solvent} = \frac{\text{mass of solvent (g)}}{\text{molar mass of solvent (g/mol)}} \]
The molar mass of water (H₂O) is approximately 18 g/mol. Given that we have 1000 g of water:
\[ \text{Moles of water} = \frac{1000 \, \text{g}}{18 \, \text{g/mol}} \approx 55.55 \, \text{moles} \]

### Step 4: Calculate the total number of moles
Now we can calculate the total number of moles in the solution:
\[ \text{Total moles} = \text{Moles of solute} + \text{Moles of solvent} = 3 + 55.55 = 58.55 \, \text{moles} \]

### Step 5: Calculate the mole fraction of the solvent
The mole fraction of the solvent (water) is calculated using the formula:
\[ \text{Mole fraction of solvent} = \frac{\text{Moles of solvent}}{\text{Total moles}} = \frac{55.55}{58.55} \]
Calculating this gives:
\[ \text{Mole fraction of solvent} \approx 0.95 \]

### Final Answer
The mole fraction of the solvent in the aqueous solution of NaOH with a molality of 3 is approximately **0.95**.

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