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

Options

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

Explanation

To find the fraction of the solute in a 1.00 m aqueous solution, we will calculate the mole fraction of the solute. Here’s a step-by-step solution:

### 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 aqueous solution, which means there is 1 mole of solute per 1 kg of solvent (water).

### Step 2: Identify the mass of the solvent
Since the solution is aqueous, the solvent is water. We have:
- Mass of solvent (water) = 1 kg = 1000 grams

### Step 3: Calculate the number of moles of the solvent
To find the number of moles of water, we use the formula:
\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molecular mass}} \]
The molecular mass of water (H₂O) is:
- Hydrogen (H) = 1 g/mol (2 atoms) + Oxygen (O) = 16 g/mol = 18 g/mol

Now, substituting the values:
\[ \text{Number of moles of water} = \frac{1000 \text{ g}}{18 \text{ g/mol}} \approx 55.56 \text{ moles} \]

### Step 4: Calculate the mole fraction of the solute
The mole fraction (χ) of the solute is calculated using the formula:
\[ \chi_{\text{solute}} = \frac{\text{Number of moles of solute}}{\text{Number of moles of solute} + \text{Number of moles of solvent}} \]
Substituting the values:
- Number of moles of solute = 1 mole
- Number of moles of solvent = 55.56 moles

Thus,
\[ \chi_{\text{solute}} = \frac{1}{1 + 55.56} = \frac{1}{56.56} \approx 0.0177 \]

### Final Answer
The fraction of the solute in a 1.00 m aqueous solution is approximately **0.0177**.

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