How much mass of sodium acetate is required to make 320 mL of 0.575 molar aqueous solution?

Options

A. 12g
B. 15g
C. 16g
D. 10g

Explanation

To find the mass of sodium acetate required to make 320 mL of a 0.575 molar aqueous solution, we can follow these steps:

### Step 1: Write down the known values
- Molarity (M) = 0.575 mol/L
- Volume of solution (V) = 320 mL = 0.320 L (convert mL to L by dividing by 1000)

### Step 2: Use the molarity formula
The formula for molarity is:
\[ \text{Molarity (M)} = \frac{\text{Number of moles of solute}}{\text{Volume of solution in liters}} \]
Rearranging this formula to find the number of moles of solute gives:
\[ \text{Number of moles} = \text{Molarity} \times \text{Volume} \]

### Step 3: Calculate the number of moles of sodium acetate
Substituting the known values into the equation:
\[ \text{Number of moles} = 0.575 \, \text{mol/L} \times 0.320 \, \text{L} = 0.184 \, \text{mol} \]

### Step 4: Calculate the molar mass of sodium acetate
The molar mass of sodium acetate (C2H3O2Na) is calculated as follows:
- Carbon (C) = 12.01 g/mol × 2 = 24.02 g/mol
- Hydrogen (H) = 1.008 g/mol × 3 = 3.024 g/mol
- Oxygen (O) = 16.00 g/mol × 2 = 32.00 g/mol
- Sodium (Na) = 22.99 g/mol × 1 = 22.99 g/mol

Adding these together:
\[ \text{Molar mass of sodium acetate} = 24.02 + 3.024 + 32.00 + 22.99 = 82.034 \, \text{g/mol} \approx 82 \, \text{g/mol} \]

### Step 5: Calculate the mass of sodium acetate required
Using the formula:
\[ \text{Mass} = \text{Number of moles} \times \text{Molar mass} \]
Substituting the values:
\[ \text{Mass} = 0.184 \, \text{mol} \times 82 \, \text{g/mol} = 15.088 \, \text{g} \]
Rounding this to two decimal places gives:
\[ \text{Mass} \approx 15.09 \, \text{g} \]

### Final Answer
The mass of sodium acetate required to make 320 mL of a 0.575 molar aqueous solution is approximately **15.09 g**.

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