Lecture Notes: Using Molarity as a Conversion Factor

Introduction

• Molarity: Measure of concentration, defined as moles of solute per liter of solution
• Objective: Using molarity as a conversion factor to switch between liters and moles

Problem 1: Converting Liters to Moles

Scenario

• Given: 3.5 L of a 1.5 M NaCl solution
• Question: How many moles of NaCl?

Process

1. Identify conversion factor: 1.5 M = 1.5 moles/L
2. Calculate:
   • Multiply: 3.5 L * 1.5 moles/L = 5.3 moles (2 sig. figs)*

Key Point

• Expand and unpack molarity to get a usable conversion factor

Problem 2: Determining Final Volume from Moles

Scenario

• Given: 4.1 moles of glucose, desire a 0.25 M solution
• Question: What volume will result?

Process

1. Identify conversion factor: 0.25 M = 0.25 moles/L
2. Calculate:
   • Flip the conversion factor: 1 L / 0.25 moles
   • Multiply: 4.1 moles * (1 L / 0.25 moles) = 16 L (2 sig. figs)*

Key Points

• Always unpack molarity first
• Sometimes need to flip the conversion factor for proper unit cancellation

Problem 3: Complex Problem with Additional Unit Conversions

Scenario

• Given: 35.0 g of FeCl3, need a 1.5 M solution
• Question: What will the solution's volume be?

Process

1. Convert grams to moles using molar mass
   • Molar mass of FeCl3 = 162.2 g/mol
   • Calculate: 35.0 g * (1 mol / 162.2 g) = 0.216 moles (3 sig. figs)
2. Convert moles to liters using molarity
   • Use 1.5 M as conversion factor: 1.5 moles / L
   • Flip if needed: 1 L / 1.5 moles
   • Calculate: 0.216 moles * (1 L / 1.5 moles) = 0.14 L (2 sig. figs)
3. Convert liters to milliliters for more practical reporting
   • 0.14 L * 1000 mL/L = 140 mL*

Key Points

• Convert given units to moles first if not directly in moles/liters
• Always report small volumes in milliliters for practicality

Problem 4: Converting Milliliters and Molarity to Grams

Scenario

• Given: 725 mL of 2.5 M NaOH solution
• Question: How many grams of NaOH are needed?

Process

1. Convert mL to L
   • 725 mL * (1 L / 1000 mL) = 0.725 L
2. Convert liters to moles using molarity
   • 2.5 M = 2.5 moles/L
   • Calculate: 0.725 L * 2.5 moles/L = 1.81 moles (2 sig. figs)
3. Convert moles to grams using molar mass
   • Molar mass of NaOH = 40 g/mol
   • Calculate: 1.81 moles * 40 g/mol = 72 g*

Key Points

• Convert volume units if needed before using molarity
• Always check if final reporting should be in grams for practical understanding

General Tips

• Unpacking Molarity: Always convert molarity to moles/L for easier use as a conversion factor.
• Flipping Conversion Factors: Check unit alignment, flip conversion factors when needed.
• Significant Figures: Maintain proper significant figures throughout calculations.

Conclusion

• These steps are foundational for performing calculations involving molarity as a conversion factor in chemistry.