The mass of NaCl required to prepare 0.1 m aqueous solution in 1kg water is

Options

A. 5.85g
B. 4.78g
C. 2.74g
D. 3.78g

Explanation

To find the mass of NaCl required to prepare a 0.1 m aqueous solution in 1 kg of water, we can follow these steps:

### Step 1: Understand the definition of molality
Molality (m) is defined as the number of moles of solute per kilogram of solvent. The formula for molality is:
\[ m = \frac{\text{number of moles of solute}}{\text{mass of solvent in kg}} \]

### Step 2: Identify the given values
From the problem, we have:
- Molality (m) = 0.1 m
- Mass of solvent (water) = 1 kg

### Step 3: Rearrange the formula to find the number of moles of solute
Using the definition of molality, we can rearrange the formula to find the number of moles of solute:
\[ \text{number of moles of solute} = m \times \text{mass of solvent in kg} \]
Substituting the known values:
\[ \text{number of moles of NaCl} = 0.1 \, \text{m} \times 1 \, \text{kg} = 0.1 \, \text{moles} \]

### Step 4: Calculate the mass of NaCl using its molar mass
The molar mass of NaCl is approximately 58.5 g/mol. To find the mass of NaCl required, we use the formula:
\[ \text{mass of NaCl} = \text{number of moles} \times \text{molar mass} \]
Substituting the values:
\[ \text{mass of NaCl} = 0.1 \, \text{moles} \times 58.5 \, \text{g/mol} = 5.85 \, \text{g} \]

### Step 5: Conclusion
The mass of NaCl required to prepare a 0.1 m aqueous solution in 1 kg of water is **5.85 grams**.

---