How much mass of sodium acetate is required to make 180 mL of 0.575 molar aqueous solution?

Options

A. 8.58g
B. 10.5g
C. 13.4g
D. 16g

Explanation

To find the mass of sodium acetate required to make 180 mL of a 0.575 molar aqueous solution, we can follow these steps:

### Step 1: Write 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:
\[ \text{Molar mass of sodium acetate} = 24.02 + 3.024 + 32.00 + 22.99 = 82.034 \text{ g/mol} \approx 82 \text{ g/mol} \]

### Step 3: Convert volume from mL to L
The volume of the solution is given as 180 mL. We need to convert this to liters:
\[ 180 \text{ mL} = 180 \times 10^{-3} \text{ L} = 0.180 \text{ L} \]

### Step 4: Use the molarity formula to find the number of moles
The molarity (M) is defined as the number of moles of solute per liter of solution:
\[ \text{Molarity} = \frac{\text{Number of moles}}{\text{Volume in L}} \]
Rearranging this formula to find the number of moles:
\[ \text{Number of moles} = \text{Molarity} \times \text{Volume in L} \]
Substituting the values:
\[ \text{Number of moles} = 0.575 \text{ mol/L} \times 0.180 \text{ L} = 0.1035 \text{ moles} \]

### Step 5: Calculate the mass of sodium acetate required
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:
\[ \text{Mass} = 0.1035 \text{ moles} \times 82 \text{ g/mol} = 8.487 \text{ g} \approx 8.49 \text{ g} \]

### Final Answer
The mass of sodium acetate required to make 180 mL of a 0.575 molar aqueous solution is approximately **8.49 grams**.

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