Molarity Practice Problems

Introduction

This tutorial will guide you through the process of calculating molarity, which is a fundamental concept in chemistry that measures the concentration of a solution. Understanding how to determine the molarity of a solution is essential for various applications, including laboratory experiments and industrial processes.

Step 1: Understanding Molarity

• Molarity (M) is defined as the number of moles of solute per liter of solution.
• The formula is:

  Molarity = Moles of solute / Liters of solution
  

• Distinguish between solute and solvent:
  • Solute: The substance being dissolved (e.g., salt).
  • Solvent: The substance doing the dissolving (e.g., water).
  • Together, they form a solution.

Step 2: Calculating Molarity from Moles and Volume

Example 1: Sodium Chloride Solution

• Given: 0.25 moles of sodium chloride in 300 mL of solution.
• Convert 300 mL to liters:

  300 mL / 1000 = 0.3 L
  

• Calculate molarity:

  Molarity = 0.25 moles / 0.3 L ≈ 0.83 M
  

Step 3: Converting Grams to Moles

Example 2: Sodium Hydroxide in Solution

• Given: 60 grams of sodium hydroxide (NaOH) in 250 mL of solution.
• Find the molar mass of NaOH:
  • Sodium (Na) = 22.99 g/mol
  • Oxygen (O) = 16.00 g/mol
  • Hydrogen (H) = 1.01 g/mol
  • Total = 40 g/mol (approximate).
• Convert grams to moles:

  Moles of NaOH = 60 g / 40 g/mol = 1.5 moles
  

• Convert 250 mL to liters:

  250 mL / 1000 = 0.25 L
  

• Calculate molarity:

  Molarity = 1.5 moles / 0.25 L = 6 M
  

Step 4: Working with Milligrams and Molarity

Example 3: Potassium Iodide Solution

• Given: 700 mg of potassium iodide (KI) in 200 mL of solution.
• Convert milligrams to grams:

  700 mg / 1000 = 0.7 g
  

• Find the molar mass of KI:
  • Potassium (K) = 39.1 g/mol
  • Iodine (I) = 126.9 g/mol
  • Total = 166 g/mol.
• Convert grams to moles:

  Moles of KI = 0.7 g / 166 g/mol ≈ 0.0042 moles
  

• Convert 200 mL to liters:

  200 mL / 1000 = 0.2 L
  

• Calculate molarity:

  Molarity = 0.0042 moles / 0.2 L = 0.021 M
  

Step 5: Concentration of Ions in a Compound

Example 4: Aluminum Sulfate

• Given: 0.30 M of aluminum sulfate (Al2(SO4)3).
• Identify the ions:
  • Aluminum (Al) = 2 per formula unit.
  • Sulfate (SO4) = 3 per formula unit.
• Calculate concentration:
  • Aluminum:

    0.30 M × 2 = 0.60 M
    

  • Sulfate:

    0.30 M × 3 = 0.90 M
    

Step 6: Finding Mass from Molarity

Example 5: Ammonium Chloride Solution

• Given: 250 mL of 0.75 M ammonium chloride (NH4Cl).
• Convert to liters:

  250 mL / 1000 = 0.25 L
  

• Calculate moles:

  Moles = 0.75 moles/L × 0.25 L = 0.1875 moles
  

• Find molar mass of NH4Cl:
  • Nitrogen (N) = 14.01 g/mol
  • Hydrogen (H) = 1.008 g/mol × 4 = 4.032 g/mol
  • Chlorine (Cl) = 35.45 g/mol
  • Total ≈ 53.49 g/mol.
• Convert moles to grams:

  Mass = 0.1875 moles × 53.49 g/mol ≈ 10.03 g
  

Step 7: Finding Volume from Mass and Molarity

Example 6: Potassium Nitrate Solution

• Given: 8.5 g of potassium nitrate (KNO3) for a 0.15 M solution.
• Find molar mass of KNO3:
  • Potassium (K) = 39.1 g/mol
  • Nitrogen (N) = 14.01 g/mol
  • Oxygen (O) = 16 g/mol × 3 = 48 g/mol
  • Total ≈ 101.1 g/mol.
• Convert grams to moles:

  Moles = 8.5 g / 101.1 g/mol ≈ 0.084 moles
  

• Use molarity to find volume:

  Volume (L) = Moles / Molarity = 0.084 moles / 0.15 M ≈ 0.56 L
  

• Convert to mL:

  Volume (mL) = 0.56 L × 1000 = 560 mL
  

Conclusion

Understanding how to calculate molarity is crucial in chemistry. Whether you need to find the concentration of a solution, convert grams to moles, or determine the required mass for a specific molarity, these steps will provide a strong foundation. Practice these calculations with different compounds to enhance your skills and confidence in working with solutions.