The mole fraction of NaCl in a solution containing 1 mole of NaCl in 1000 g of water is

Options

A. `0.0177`
B. `0.001`
C. `0.5`
D. `0.244`

Explanation

To find the mole fraction of NaCl in a solution containing 1 mole of NaCl in 1000 g of water, we will follow these steps:

### Step 1: Identify the number of moles of NaCl
We are given that there is 1 mole of NaCl in the solution.
- **Moles of NaCl (n_NaCl)** = 1 mole

### Step 2: Calculate the number of moles of water (H2O)
To find the moles of water, we need to use the formula:
\[ \text{Moles of H2O} = \frac{\text{mass of H2O (in grams)}}{\text{molar mass of H2O (in g/mol)}} \]
The molar mass of water (H2O) is calculated as follows:
- Hydrogen (H) has a molar mass of approximately 1 g/mol, and there are 2 hydrogen atoms.
- Oxygen (O) has a molar mass of approximately 16 g/mol.
\[ \text{Molar mass of H2O} = (2 \times 1) + 16 = 18 \text{ g/mol} \]
Now, we can calculate the moles of water:
\[ \text{Moles of H2O} = \frac{1000 \text{ g}}{18 \text{ g/mol}} \approx 55.56 \text{ moles} \]

### Step 3: Calculate the total number of moles in the solution
Now we can find the total number of moles in the solution:
\[ \text{Total moles} = n_{NaCl} + n_{H2O} = 1 + 55.56 \approx 56.56 \text{ moles} \]

### Step 4: Calculate the mole fraction of NaCl
The mole fraction of NaCl (x_NaCl) is given by the formula:
\[ x_{NaCl} = \frac{n_{NaCl}}{n_{NaCl} + n_{H2O}} \]
Substituting the values we have:
\[ x_{NaCl} = \frac{1}{1 + 55.56} = \frac{1}{56.56} \approx 0.0177 \]

### Final Answer:
The mole fraction of NaCl in the solution is approximately **0.0177**.

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