If 5.85 g of `NaCl` is dissolved in 90g of water, the mole fraction of solute is

Options

A. `0.0196`
B. `0.01`
C. `0.1`
D. `0.2`

Explanation

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 for calculating the number of moles is:

\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} \]

- Given mass of NaCl = 5.85 g
- Molar mass of NaCl = Atomic mass of Na (23 g/mol) + Atomic mass of Cl (35.5 g/mol) = 58.5 g/mol

Now, we can calculate the number of moles of NaCl:

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

### Step 2: Calculate the number of moles of water

Using the same formula:

- Given mass of water = 90 g
- Molar mass of water (H₂O) = 2 × Atomic mass of H (1 g/mol) + Atomic mass of O (16 g/mol) = 18 g/mol

Now, we can calculate the number of moles of water:

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

### Step 3: Calculate the mole fraction of NaCl

The mole fraction of a solute is given by:

\[ \text{Mole fraction of solute} = \frac{\text{Number of moles of solute}}{\text{Number of moles of solute} + \text{Number of moles of solvent}} \]

Substituting the values we calculated:

\[ \text{Mole fraction of NaCl} = \frac{0.1 \, \text{mol}}{0.1 \, \text{mol} + 5 \, \text{mol}} = \frac{0.1}{5.1} \]

Calculating this gives:

\[ \text{Mole fraction of NaCl} \approx 0.0196 \]

### Final Answer

The mole fraction of NaCl is approximately **0.0196**.

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