What is the mole fraction of the solute in a 1.00 m aqueous solution ?

Options

A. `0.0354`
B. `0.0177`
C. `0.177`
D. `1.770`

Answer

To find the mole fraction of the solute in a 1.00 m 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 1.00 m solution, which means there is 1 mole of solute in 1 kg of solvent (water).

### Step 2: Calculate the Moles of Solvent
To find the mole fraction, we need to know the number of moles of the solvent (water). The molar mass of water (H₂O) is approximately 18 g/mol. Since we have 1 kg (1000 g) of water, we can calculate the moles of water as follows:

\[ \text{Moles of water} = \frac{\text{mass of water (g)}}{\text{molar mass of water (g/mol)}} = \frac{1000 \, \text{g}}{18 \, \text{g/mol}} \approx 55.56 \, \text{moles} \]

### Step 3: Calculate Total Moles in the Solution
The total number of moles in the solution is the sum of the moles of solute and the moles of solvent:

\[ \text{Total moles} = \text{moles of solute} + \text{moles of solvent} = 1 \, \text{mole} + 55.56 \, \text{moles} = 56.56 \, \text{moles} \]

### Step 4: Calculate the Mole Fraction of the Solute
The mole fraction (X) of the solute is calculated using the formula:

\[ X_{\text{solute}} = \frac{\text{moles of solute}}{\text{total moles in solution}} = \frac{1 \, \text{mole}}{56.56 \, \text{moles}} \approx 0.0177 \]

### Step 5: Final Result
Thus, the mole fraction of the solute in a 1.00 m aqueous solution is approximately 0.0177.

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