The mass of NaCl required to prepare 0.09 m aqueous solution in 1kg water is

Options

A. 4.85g
B. 5.26g
C. 3.25g
D. 2.45g

Explanation

To solve the problem of finding the mass of NaCl required to prepare a 0.09 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 is:
\[ \text{Molality (m)} = \frac{\text{Number of moles of solute}}{\text{Mass of solvent in kg}} \]

### Step 2: Identify the given values
From the problem, we know:
- Molality (m) = 0.09 m
- Mass of solvent (water) = 1 kg

### Step 3: Set up the equation for molality
Using the definition of molality, we can rearrange the formula to find the number of moles of NaCl:
\[ \text{Number of moles of NaCl} = \text{Molality} \times \text{Mass of solvent in kg} \]
Substituting the known values:
\[ \text{Number of moles of NaCl} = 0.09 \, \text{m} \times 1 \, \text{kg} = 0.09 \, \text{moles} \]

### Step 4: Calculate the mass of NaCl
To find the mass of NaCl, we use the formula:
\[ \text{Mass of solute} = \text{Number of moles} \times \text{Molar mass} \]
The molar mass of NaCl is approximately 58.5 g/mol. Therefore:
\[ \text{Mass of NaCl} = 0.09 \, \text{moles} \times 58.5 \, \text{g/mol} \]

### Step 5: Perform the calculation
Calculating the mass:
\[ \text{Mass of NaCl} = 0.09 \times 58.5 = 5.265 \, \text{grams} \]

### Step 6: Round the answer
Rounding to two decimal places, we find:
\[ \text{Mass of NaCl} \approx 5.26 \, \text{grams} \]

### Final Answer
The mass of NaCl required to prepare a 0.09 m aqueous solution in 1 kg of water is **5.26 grams**.

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