Mole fraction of solute in aqueous solution of 30% NaOH.

Options

A. 0.16
B. 0.05
C. 0.25
D. 0.95

Answer

To find the mole fraction of solute (NaOH) in a 30% aqueous solution, we can follow these steps:

### Step 1: Understand the meaning of 30% NaOH
30% NaOH means that there are 30 grams of NaOH (solute) in 100 grams of the solution.

### Step 2: Calculate the mass of the solvent (water)
Since the total mass of the solution is 100 grams and the mass of NaOH is 30 grams, the mass of water (solvent) can be calculated as:
\[ \text{Mass of water} = \text{Total mass of solution} - \text{Mass of NaOH} = 100 \, \text{g} - 30 \, \text{g} = 70 \, \text{g} \]

### Step 3: Calculate the number of moles of NaOH
To find the number of moles of NaOH, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \]
The molar mass of NaOH can be calculated as follows:
- Molar mass of Na = 23 g/mol
- Molar mass of O = 16 g/mol
- Molar mass of H = 1 g/mol

Thus, the molar mass of NaOH = 23 + 16 + 1 = 40 g/mol.

Now, we can calculate the number of moles of NaOH:
\[ \text{Number of moles of NaOH} = \frac{30 \, \text{g}}{40 \, \text{g/mol}} = 0.75 \, \text{moles} \]

### Step 4: Calculate the number of moles of water
Next, we calculate the number of moles of water using its molar mass:
- Molar mass of H2O = 2(1) + 16 = 18 g/mol.

Now, we can find the number of moles of water:
\[ \text{Number of moles of water} = \frac{70 \, \text{g}}{18 \, \text{g/mol}} \approx 3.88 \, \text{moles} \]

### Step 5: Calculate the mole fraction of NaOH
The mole fraction of the solute (NaOH) is given by the formula:
\[ \text{Mole fraction of NaOH} = \frac{\text{Number of moles of NaOH}}{\text{Number of moles of NaOH} + \text{Number of moles of water}} \]
Substituting the values we calculated:
\[ \text{Mole fraction of NaOH} = \frac{0.75}{0.75 + 3.88} = \frac{0.75}{4.63} \approx 0.162 \]

### Final Answer
The mole fraction of NaOH in the 30% aqueous solution is approximately **0.162**.

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