The mass of NaCl required to prepare 0.5 m aqueous solution in 1kg water is

Options

A. 28g
B. 29g
C. 32g
D. 25g

Explanation

To find the mass of NaCl required to prepare a 0.5 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:
\[ m = \frac{\text{Number of moles of solute}}{\text{Mass of solvent (kg)}} \]

### Step 2: Identify Given Values
From the problem, we have:
- Molality (m) = 0.5 m
- Mass of solvent (water) = 1 kg

### Step 3: Rearrange the Molality Formula
We need to find the number of moles of NaCl. Rearranging the molality formula gives us:
\[ \text{Number of moles of solute} = m \times \text{Mass of solvent (kg)} \]

### Step 4: Substitute the Known Values
Substituting the known values into the rearranged formula:
\[ \text{Number of moles of NaCl} = 0.5 \, \text{m} \times 1 \, \text{kg} = 0.5 \, \text{moles} \]

### Step 5: Calculate the Mass of NaCl
To find the mass of NaCl, we use the formula:
\[ \text{Mass of NaCl} = \text{Number of moles} \times \text{Molar mass of NaCl} \]
The molar mass of NaCl is approximately 58.5 g/mol. Thus:
\[ \text{Mass of NaCl} = 0.5 \, \text{moles} \times 58.5 \, \text{g/mol} = 29.25 \, \text{g} \]

### Step 6: Round the Answer
Since we typically round to the nearest whole number in chemistry when dealing with mass, we can say:
\[ \text{Mass of NaCl} \approx 29 \, \text{g} \]

### Final Answer
The mass of NaCl required to prepare a 0.5 m aqueous solution in 1 kg of water is **29 grams**.

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