Math Problem Statement

What is the molarity of 250mL of a solution containing 3.7g of sodium chloride? Answer to 2 sig fig.

Solution

To find the molarity of the solution, we use the formula:

Molarity (M)=moles of solutevolume of solution in liters\text{Molarity (M)} = \frac{\text{moles of solute}}{\text{volume of solution in liters}}

Step 1: Calculate the moles of sodium chloride (NaCl).

  1. Molar mass of NaCl:
    Sodium (Na): 22.99g/mol22.99 \, \text{g/mol}
    Chlorine (Cl): 35.45g/mol35.45 \, \text{g/mol}
    Molar mass of NaCl=22.99+35.45=58.44g/mol\text{Molar mass of NaCl} = 22.99 + 35.45 = 58.44 \, \text{g/mol}

  2. Moles of NaCl:
    Moles of NaCl=Mass of NaClMolar mass of NaCl\text{Moles of NaCl} = \frac{\text{Mass of NaCl}}{\text{Molar mass of NaCl}} Moles of NaCl=3.7g58.44g/mol0.0633mol\text{Moles of NaCl} = \frac{3.7 \, \text{g}}{58.44 \, \text{g/mol}} \approx 0.0633 \, \text{mol}

Step 2: Convert the volume of solution to liters.

Volume in liters=250mL1000=0.250L\text{Volume in liters} = \frac{250 \, \text{mL}}{1000} = 0.250 \, \text{L}

Step 3: Calculate the molarity.

Molarity (M)=Moles of NaClVolume in liters\text{Molarity (M)} = \frac{\text{Moles of NaCl}}{\text{Volume in liters}} Molarity=0.0633mol0.250L0.25M\text{Molarity} = \frac{0.0633 \, \text{mol}}{0.250 \, \text{L}} \approx 0.25 \, \text{M}

Final Answer:

The molarity of the solution is 0.25 M (to 2 significant figures).


Would you like further clarification on any step?

Here are 5 related questions for deeper understanding:

  1. How is molar mass calculated for more complex compounds?
  2. What is the difference between molarity and molality?
  3. How would the molarity change if the solution volume were halved?
  4. What would the molarity be if 10g of NaCl were used instead?
  5. How does temperature affect the molarity of a solution?

Tip: Always ensure the solution volume is converted to liters when calculating molarity!

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Math Problem Analysis

Mathematical Concepts

Molarity
Stoichiometry
Unit Conversion

Formulas

Molarity (M) = moles of solute / volume of solution in liters
Moles = mass of solute / molar mass

Theorems

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Suitable Grade Level

Grades 10-12