Mole fraction of solute in 1 mole aqueous solution is

Options

A. 1.77
B. 0.177
C. 0.0177
D. 0.0344

Explanation

To find the mole fraction of solute in a 1 mole aqueous solution, we can follow these steps:

### Step 1: Understand the Definition of Mole Fraction
Mole fraction (x) of a component in a solution is defined as the ratio of the number of moles of that component to the total number of moles of all components in the solution.

### Step 2: Identify the Components
In this case, we have:
- Solute (1 mole)
- Solvent (water)

### Step 3: Calculate the Moles of Solvent (Water)
Since we have 1 mole of solute, we need to calculate the number of moles of water in the solution.

1. The mass of water in the solution is typically taken as 1000 g (1 kg).
2. The molar mass of water (H₂O) is 18 g/mol.

Using the formula for moles:
\[ \text{Number of moles of water} (n_2) = \frac{\text{mass of water}}{\text{molar mass of water}} = \frac{1000 \, \text{g}}{18 \, \text{g/mol}} \approx 55.56 \, \text{moles} \]

### Step 4: Calculate the Total Moles in the Solution
Now, we can find the total number of moles in the solution:
\[ \text{Total moles} = n_1 + n_2 = 1 \, \text{mole (solute)} + 55.56 \, \text{moles (water)} = 56.56 \, \text{moles} \]

### Step 5: Calculate the Mole Fraction of the Solute
Now we can calculate the mole fraction of the solute (x₁):
\[ x_1 = \frac{n_1}{n_1 + n_2} = \frac{1}{1 + 55.56} = \frac{1}{56.56} \approx 0.0177 \]

### Conclusion
Thus, the mole fraction of the solute in a 1 mole aqueous solution is approximately 0.0177.

### Final Answer
The mole fraction of the solute in a 1 mole aqueous solution is approximately **0.0177**.

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