5.85 g of NaCl are dissolved in 90 g of water. The mole fraction of NaCl is-

Options

A. 0.1
B. 0.2
C. 0.3
D. 0.0196

Answer

To find the mole fraction of NaCl when 5.85 g of NaCl is dissolved in 90 g of water, we can follow these steps:

### Step 1: Calculate the number of moles of NaCl
The formula to calculate the number of moles is:

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

- The molar mass of NaCl (sodium chloride) can be calculated as follows:
- Sodium (Na) = 23 g/mol
- Chlorine (Cl) = 35.5 g/mol
- Molar mass of NaCl = 23 + 35.5 = 58.5 g/mol

Now, substituting the values:

\[ \text{Number of moles of NaCl} = \frac{5.85 \, \text{g}}{58.5 \, \text{g/mol}} \approx 0.1 \, \text{moles} \]

### Step 2: Calculate the number of moles of water (H2O)
The molar mass of water can be calculated as follows:
- Hydrogen (H) = 1 g/mol (2 H atoms in H2O)
- Oxygen (O) = 16 g/mol
- Molar mass of H2O = 2(1) + 16 = 18 g/mol

Now, substituting the values:

\[ \text{Number of moles of H2O} = \frac{90 \, \text{g}}{18 \, \text{g/mol}} = 5 \, \text{moles} \]

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

\[ \text{Total moles} = \text{moles of NaCl} + \text{moles of H2O} = 0.1 + 5 = 5.1 \, \text{moles} \]

### Step 4: Calculate the mole fraction of NaCl
The mole fraction (X) of NaCl is given by the formula:

\[ X_{\text{NaCl}} = \frac{\text{moles of NaCl}}{\text{total moles}} \]

Substituting the values:

\[ X_{\text{NaCl}} = \frac{0.1}{5.1} \approx 0.0196 \]

### Final Answer
The mole fraction of NaCl is approximately **0.0196**.

---