The mass of NaCl required to prepare 0.3 m aqueous solution in 1kg water is

Options

A. 17.5g
B. 15g
C. 13g
D. 14.5g

Explanation

To find the mass of NaCl required to prepare a 0.3 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 question, we have:
- Molality (m) = 0.3 m
- 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):
\[ \text{Number of moles of NaCl} = m \times \text{Mass of solvent in kg} \]
Substituting the known values:
\[ \text{Number of moles of NaCl} = 0.3 \, \text{m} \times 1 \, \text{kg} = 0.3 \, \text{moles} \]

### Step 4: Calculate the mass of NaCl
To find the mass of NaCl, we use the formula:
\[ \text{Mass} = \text{Number of moles} \times \text{Molar mass} \]
The molar mass of NaCl is approximately 58.5 g/mol. Therefore:
\[ \text{Mass of NaCl} = 0.3 \, \text{moles} \times 58.5 \, \text{g/mol} \]
Calculating this gives:
\[ \text{Mass of NaCl} = 17.55 \, \text{g} \]

### Step 5: Round to appropriate significant figures
Since we are dealing with significant figures, we can round 17.55 g to 17.5 g.

### Final Answer
The mass of NaCl required to prepare a 0.3 m aqueous solution in 1 kg of water is **17.5 grams**.

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