How much mass of sodium acetate is required to make 200 mL of 0.575 molar aqueous solution?

Options

A. 10.47g
B. 9.58g
C. 11.94g
D. 41.4g

Explanation

To find the mass of sodium acetate required to make 200 mL of a 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.
To calculate the molar mass, we sum the atomic masses of all the atoms in the formula:
- Carbon (C): 2 atoms × 12.01 g/mol = 24.02 g/mol
- Hydrogen (H): 3 atoms × 1.008 g/mol = 3.024 g/mol
- Oxygen (O): 2 atoms × 16.00 g/mol = 32.00 g/mol
- Sodium (Na): 1 atom × 22.99 g/mol = 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 3: Convert the volume from mL to L.
Given volume = 200 mL. To convert to liters:
\[ \text{Volume in L} = 200 \text{ mL} \times \frac{1 \text{ L}}{1000 \text{ mL}} = 0.200 \text{ L} \]

### Step 4: Use the molarity formula to find the number of moles.
The formula for molarity (M) is:
\[ M = \frac{\text{number of moles of solute}}{\text{volume of solution in L}} \]
Rearranging gives us:
\[ \text{number of moles} = M \times \text{volume in L} \]
Substituting the values:
\[ \text{number of moles} = 0.575 \text{ mol/L} \times 0.200 \text{ L} = 0.115 \text{ moles} \]

### Step 5: Calculate the mass of sodium acetate.
Using the relationship between mass, moles, and molar mass:
\[ \text{mass} = \text{number of moles} \times \text{molar mass} \]
Substituting the values:
\[ \text{mass} = 0.115 \text{ moles} \times 82 \text{ g/mol} = 9.43 \text{ g} \]

### Step 6: Round the answer.
The mass of sodium acetate required is approximately 9.43 g.

### Final Answer:
The mass of sodium acetate required to make 200 mL of a 0.575 molar aqueous solution is approximately **9.43 grams**.

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