Calculating Molarity of Solutions

Definition of Terms

• Molarity (M): Moles of solute divided by liters of solution.
• Solute: Substance dissolved in a solvent (e.g., salt in water).
• Solvent: Substance that dissolves the solute (e.g., water).
• Solution: Combination of solute and solvent.

Calculation Steps

1. Convert volume to liters: Divide milliliters by 1000.
2. Formula for Molarity: ( M = \frac{moles , of , solute}{liters , of , solution} ).

Example Calculations

Example 1: Sodium Chloride

• Problem: 0.25 moles of NaCl in 300 mL of solution.
• Solution:
  • Convert volume: ( 300, mL \to 0.3, L ).
  • Calculate molarity: ( \frac{0.25}{0.3} \approx 0.83, M ).

Example 2: Sodium Hydroxide

• Problem: 60 grams of NaOH in 250 mL.
• Solution:
  • Molar mass of NaOH: 40 g/mol.
  • Convert grams to moles: ( \frac{60}{40} = 1.5, moles ).
  • Convert volume: 250 mL \to 0.25 L.
  • Calculate molarity: ( \frac{1.5}{0.25} = 6, M ).

Example 3: Potassium Iodide

• Problem: 700 mg of KI in 200 mL.
• Solution:
  • Convert mg to grams: 700 mg \to 0.7 g.
  • Molar mass of KI: 166 g/mol.
  • Convert grams to moles: ( \frac{0.7}{166} ).
  • Convert volume: 200 mL \to 0.2 L.
  • Calculate molarity: ( \approx 0.0211, M ).

Example 4: Ethanol Solution

• Problem: 50 mL ethanol in 400 mL water.
• Solution:
  • Total volume: 450 mL \to 0.45 L.
  • Density of ethanol: 0.79 g/mL.
  • Molar mass of ethanol (C2H5OH): 46.068 g/mol.
  • Convert mL to grams and then to moles.
  • Calculate molarity: ( \approx 1.905, M ).

Advanced Examples

Aluminum Sulfate

• Concentration of Ions: Given 0.3 M Al2(SO4)3.
  • Aluminum cations: ( 0.3 \times 2 = 0.6, M ).
  • Sulfate ions: ( 0.3 \times 3 = 0.9, M ).
  • Use dissolution equation for detailed calculation.

Iron(III) Chloride

• Problem: 15 g of FeCl3 in 450 mL.
• Solution:
  • Molar mass of FeCl3: 162.2 g/mol.
  • Convert grams to moles and then to moles of Cl−.
  • Calculate molarity: ( \approx 0.617, M ).

Ammonium Chloride Mass Required

• Problem: 250 mL of 0.75 M NH4Cl.
• Solution:
  • Convert volume to liters.
  • Calculate mass using molar mass: 53.492 g/mol.
  • Answer: 10.03 g of NH4Cl.

Potassium Nitrate Volume Required

• Problem: 8.5 g KNO3 for 0.15 M solution.
• Solution:
  • Molar mass of KNO3: 101.11 g/mol.
  • Calculate volume in liters and convert to mL: ( 0.56, L \to 560, mL ).

Tips

• Molarity is always moles divided by liters.
• Always convert units as needed for consistency.
• Understand molar mass and its role in converting grams to moles.