How much mass of sodium acetate is required to make 350 mL of 0.575 molar aqueous solution?

Options

A. 14g
B. 16.5g
C. 12g
D. 13g

Explanation

To find the mass of sodium acetate required to make a 350 mL of 0.575 molar aqueous solution, we can follow these steps:

### Step 1: Write down the formula for sodium acetate
The chemical formula for sodium acetate is \( \text{C}_2\text{H}_3\text{O}_2\text{Na} \).

### Step 2: Calculate the molar mass of sodium acetate
The molar mass of sodium acetate can be 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:
\[ \text{Molar mass of sodium acetate} = 24.02 + 3.024 + 32.00 + 22.99 = 82.034 \text{ g/mol} \]
For simplicity, we can round this to 82 g/mol.

### Step 3: Convert volume from mL to L
The volume of the solution is given as 350 mL. To convert this to liters:
\[ \text{Volume in L} = 350 \text{ mL} \times \frac{1 \text{ L}}{1000 \text{ mL}} = 0.350 \text{ L} \]

### Step 4: Use the molarity formula to find the number of moles
The molarity (M) is defined as:
\[ \text{Molarity} = \frac{\text{Number of moles of solute}}{\text{Volume of solution in L}} \]
Rearranging this formula gives:
\[ \text{Number of moles} = \text{Molarity} \times \text{Volume in L} \]
Substituting the values:
\[ \text{Number of moles} = 0.575 \text{ mol/L} \times 0.350 \text{ L} = 0.20125 \text{ moles} \]

### Step 5: Calculate the mass of sodium acetate
Using the number of moles and the molar mass, we can find the mass:
\[ \text{Mass} = \text{Number of moles} \times \text{Molar mass} \]
Substituting the values:
\[ \text{Mass} = 0.20125 \text{ moles} \times 82 \text{ g/mol} = 16.5 \text{ g} \]

### Conclusion
The mass of sodium acetate required to make 350 mL of a 0.575 molar solution is **16.5 grams**.

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