To determine the molarity of the given NaCl solution, follow these steps:
### Step 1: Identify the Given Data
- Molar mass of NaCl (sodium chloride) = 58.44 g/mol
- Mass of NaCl = 87.75 g
- Volume of the solution = 500 mL
### Step 2: Convert the Volume from mL to Liters
Since 1 L = 1000 mL,
[tex]\[ 500 \, \text{mL} = 0.5 \, \text{L} \][/tex]
### Step 3: Calculate the Number of Moles of NaCl
Using the formula for moles:
[tex]\[ \text{moles of NaCl} = \frac{\text{mass of NaCl}}{\text{molar mass of NaCl}} \][/tex]
[tex]\[ \text{moles of NaCl} = \frac{87.75 \, \text{g}}{58.44 \, \text{g/mol}} \][/tex]
[tex]\[ \text{moles of NaCl} = 1.501540041067762 \, \text{mol} \][/tex]
### Step 4: Calculate the Molarity of the Solution
Molarity is defined as:
[tex]\[ \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{liters of solution}} \][/tex]
[tex]\[ \text{Molarity} = \frac{1.501540041067762 \, \text{mol}}{0.5 \, \text{L}} \][/tex]
[tex]\[ \text{Molarity} = 3.003080082135524 \, \text{M} \][/tex]
### Conclusion
The molarity of the solution is approximately 3.00 M.
Thus, the correct answer is:
3.00 M.
