Mass of NaCl required to prepare 0.01 m aqueous solution in 1kg water is

Options

A. 0.01 g
B. 0.584 g
C. 58.8 g
D. 5.88g

Answer

To find the mass of NaCl required to prepare a 0.01 molal 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:
\[ m = \frac{\text{moles of solute}}{\text{mass of solvent in kg}} \]

### Step 2: Identify the given values
From the question, we have:
- Molality (m) = 0.01 mol/kg
- Mass of solvent (water) = 1 kg

### Step 3: Calculate the number of moles of NaCl
Using the formula for molality, we can rearrange it to find the number of moles of solute (NaCl):
\[ \text{moles of solute} = m \times \text{mass of solvent in kg} \]
Substituting the known values:
\[ \text{moles of NaCl} = 0.01 \, \text{mol/kg} \times 1 \, \text{kg} = 0.01 \, \text{mol} \]

### Step 4: Find the molar mass of NaCl
The molar mass of NaCl (sodium chloride) is approximately:
\[ \text{Molar mass of NaCl} = 58.44 \, \text{g/mol} \]

### Step 5: Calculate the mass of NaCl required
Using the number of moles calculated in Step 3, we can find the mass of NaCl using the formula:
\[ \text{mass (w)} = \text{moles} \times \text{molar mass} \]
Substituting the values:
\[ \text{mass of NaCl} = 0.01 \, \text{mol} \times 58.44 \, \text{g/mol} = 0.5844 \, \text{g} \]

### Step 6: Round the answer
Since we are asked for the mass, we can round it to three significant figures:
\[ \text{mass of NaCl} \approx 0.584 \, \text{g} \]

### Conclusion
Thus, the mass of NaCl required to prepare a 0.01 molal aqueous solution in 1 kg of water is approximately **0.584 g**.