If `5.85`g of `NaCl`are dissolved in`90g` of water,the moles fraction of`NaCl` is

Options

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

Explanation

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

### Step 1: Calculate the number of moles of NaCl
To find the number of moles of NaCl, we use the formula:

\[ \text{Moles of NaCl} = \frac{\text{mass of NaCl}}{\text{molar mass of NaCl}} \]

Given:
- Mass of NaCl = 5.85 g
- Molar mass of NaCl = 58.5 g/mol

Now, substituting the values:

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

### Step 2: Calculate the number of moles of water
Next, we calculate the number of moles of water using the same formula:

\[ \text{Moles of water} = \frac{\text{mass of water}}{\text{molar mass of water}} \]

Given:
- Mass of water = 90 g
- Molar mass of water = 18 g/mol

Now, substituting the values:

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

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

\[ \text{Total moles} = \text{Moles of NaCl} + \text{Moles of water} \]

Substituting the values we calculated:

\[ \text{Total moles} = 0.1 \, \text{mol} + 5 \, \text{mol} = 5.1 \, \text{mol} \]

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

\[ \text{Mole fraction of NaCl} = \frac{\text{Moles of NaCl}}{\text{Total moles}} \]

Substituting the values:

\[ \text{Mole fraction of NaCl} = \frac{0.1 \, \text{mol}}{5.1 \, \text{mol}} \approx 0.0196 \]

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

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