Mole fraction of the solute in a 1.0 molal aqueous solution is:

Options

A. 1.8
B. 0.0177
C. 0.05
D. 0.098

Explanation

To find the mole fraction of the solute in a 1.0 molal aqueous solution, 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 1.0 molal solution, which means there is 1 mole of solute in 1 kilogram of solvent (water).

### Step 2: Calculate the Number of Moles of Solvent
The solvent in this case is water. The molecular weight of water (H₂O) is approximately 18 grams per mole. Since we have 1 kilogram (1000 grams) of water, we can calculate the number of moles of water (solvent):

\[ \text{Number of moles of solvent} (n_2) = \frac{\text{mass of solvent (g)}}{\text{molecular weight of solvent (g/mol)}} = \frac{1000 \text{ g}}{18 \text{ g/mol}} \approx 55.55 \text{ moles} \]

### Step 3: Determine the Number of Moles of Solute
From the definition of molality, we know that the number of moles of solute (n₁) in a 1.0 molal solution is 1 mole.

### Step 4: Calculate the Total Number of Moles
Now, we can calculate the total number of moles in the solution:

\[ \text{Total moles} = n_1 + n_2 = 1 \text{ mole (solute)} + 55.55 \text{ moles (solvent)} = 56.55 \text{ moles} \]

### Step 5: Calculate the Mole Fraction of the Solute
The mole fraction of the solute (X₁) is given by the formula:

\[ X_1 = \frac{n_1}{n_1 + n_2} \]

Substituting the values we have:

\[ X_1 = \frac{1}{1 + 55.55} = \frac{1}{56.55} \approx 0.01768 \]

### Step 6: Round the Result
Rounding 0.01768 gives approximately 0.0177.

### Final Answer
Thus, the mole fraction of the solute in a 1.0 molal aqueous solution is approximately **0.0177**.

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