How much mass of sodium acetate is required to make 270 mL of 0.575 molar aqueous solution?

Explanation

To determine the mass of sodium acetate required to make 270 mL of a 0.575 M aqueous solution, we can follow these steps:

### Step 1: Identify the formula for molarity (M)
Molarity (M) is defined as the number of moles of solute per liter of solution. The formula is:
\[ M = \frac{\text{Number of moles of solute}}{\text{Volume of solution in liters}} \]

### Step 2: Convert the volume from mL to L
The volume of the solution is given as 270 mL. To convert this to liters:
\[ \text{Volume in liters} = \frac{270 \text{ mL}}{1000} = 0.270 \text{ L} \]

### Step 3: Calculate the number of moles of sodium acetate
Using the molarity formula, we can rearrange it to find the number of moles:
\[ \text{Number of moles} = M \times \text{Volume in liters} \]
Substituting the values:
\[ \text{Number of moles} = 0.575 \text{ M} \times 0.270 \text{ L} \]
\[ \text{Number of moles} = 0.15525 \text{ moles} \]

### Step 4: Calculate the mass of sodium acetate
To find the mass, we use the formula:
\[ \text{Mass} = \text{Number of moles} \times \text{Molar mass} \]
The molar mass of sodium acetate (C₂H₃O₂Na) is given as 82 g/mol. Therefore:
\[ \text{Mass} = 0.15525 \text{ moles} \times 82 \text{ g/mol} \]
\[ \text{Mass} = 12.74 \text{ grams} \]

### Conclusion
The mass of sodium acetate required to make 270 mL of a 0.575 M solution is approximately **12.74 grams**.

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