To find the molarity of the solution, we need to follow a series of steps involving the concepts of moles and molarity. Here is a detailed, step-by-step solution:
1. Identify Given Information:
- Mass of NaCl (solute): 87.75 grams
- Molar mass of NaCl: 58.44 g/mol
- Volume of the solution: 500 milliliters (mL)
2. Convert the Volume of the Solution from Milliliters to Liters:
Since molarity ([tex]\(M\)[/tex]) is defined in terms of liters, we need to convert the volume from milliliters to liters.
[tex]\[
\text{Volume of solution} = 500 \, \text{mL} = \frac{500}{1000} \, \text{L} = 0.500 \, \text{L}
\][/tex]
3. Calculate the Number of Moles of NaCl:
To determine the number of moles, we use the molar mass of NaCl. The number of moles ([tex]\(n\)[/tex]) can be calculated using the formula:
[tex]\[
\text{moles of NaCl} = \frac{\text{mass of NaCl}}{\text{molar mass of NaCl}}
\][/tex]
Substituting the given values:
[tex]\[
\text{moles of NaCl} = \frac{87.75 \, \text{g}}{58.44 \, \text{g/mol}} \approx 1.5015 \, \text{moles}
\][/tex]
4. Calculate the Molarity of the Solution:
Molarity ([tex]\(M\)[/tex]) is defined as the number of moles of solute per liter of solution. Using the formula:
[tex]\[
\text{Molarity} = \frac{\text{moles of solute}}{\text{liters of solution}}
\][/tex]
Substituting the values we have:
[tex]\[
\text{Molarity} = \frac{1.5015 \, \text{moles}}{0.500 \, \text{L}} = 3.003 \, \text{M}
\][/tex]
So, the molarity of the solution is approximately [tex]\(3.00\, \text{M}\)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{3.00 \, \text{M}} \][/tex]
This matches the given correct result from the question:
[tex]\[
(1.501540041067762, 3.003080082135524)
\][/tex]
The answer closest to the calculated molarity is [tex]\(3.00 \, \text{M}\)[/tex].
