3.65 grams of HCl is disolved in 16.2 grams of water. The mole fraction of HCl in the resulting solution is

Options

A. 0.4
B. 0.3
C. 0.2
D. 0.1

Explanation

To find the mole fraction of HCl in the solution, we will follow these steps:

### Step 1: Calculate the number of moles of HCl
We can calculate the number of moles using the formula:

\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]

Given:
- Mass of HCl = 3.65 g
- Molar mass of HCl = 1 (H) + 35.5 (Cl) = 36.5 g/mol

Now, substituting the values:

\[ \text{Number of moles of HCl} = \frac{3.65 \, \text{g}}{36.5 \, \text{g/mol}} \approx 0.1 \, \text{mol} \]

### Step 2: Calculate the number of moles of water
Using the same formula for water:

Given:
- Mass of water = 16.2 g
- Molar mass of water (H2O) = 2(1) + 16 = 18 g/mol

Now, substituting the values:

\[ \text{Number of moles of water} = \frac{16.2 \, \text{g}}{18 \, \text{g/mol}} \approx 0.9 \, \text{mol} \]

### Step 3: Calculate the total number of moles in the solution
Now, we can find the total number of moles:

\[ \text{Total number of moles} = \text{Number of moles of HCl} + \text{Number of moles of water} = 0.1 + 0.9 = 1.0 \, \text{mol} \]

### Step 4: Calculate the mole fraction of HCl
The mole fraction of HCl (denoted as \(X_{\text{HCl}}\)) is given by:

\[ X_{\text{HCl}} = \frac{\text{Number of moles of HCl}}{\text{Total number of moles}} \]

Substituting the values we calculated:

\[ X_{\text{HCl}} = \frac{0.1}{1.0} = 0.1 \]

### Final Answer
The mole fraction of HCl in the resulting solution is **0.1**.

---