Lecture Notes: Chemistry Problem Solving and Measurements

Introduction

• Extra practice problems available for every chapter.
• Encouraged to use other resources for practice (Chem 101, textbooks).
• Worked examples in student notes and PowerPoint slides.
• Videos explain examples slowly to aid understanding.

Chapter 1: Measure, Matter, Measurements, and Problem Solving

• Focus on significant figures, dimensional analysis, and conversions.

Examples 1-5: Order of Operations and Significant Figures

Example 1

• Calculation: (4.932 x 39.47) - 3.21
• Sig Figs: 4 sig figs each.
• Steps:
  • Multiply: 194.6604 (do not round yet).
  • Subtraction: 191.45604
  • Round to 191.5 (2 decimal places due to subtraction rule).

Example 2

• Calculation: 5.982 x 0.00201
• Sig Figs: 4 sig figs (5.982), 3 sig figs (0.00201).
• Answer: 0.0120 (rounded to 3 sig figs).

Example 3

• Calculation: (4.953 + 9.20) / 11.315
• Sig Figs: 3 decimal places (addition), 4 sig figs (division).
• Answer: 1.251

Example 4

• Calculation: 5.68g + 8.32g
• Answer: 14.00g (2 decimal places).

Example 5

• Calculation: 8.672 x 10^6 / 1.376 x 10^4
• Sig Figs: 4 sig figs in both.
• Answer: 6.302 x 10^-10

Examples 6-9: Addition, Multiplication, and Division with Units

Example 6

• Calculation: 5.74cm + 0.823cm + 2.651cm
• Answer: 9.21cm

Example 7

• Calculation: 4.8L + 3.965L
• Answer: 8.8L

Example 8

• Calculation: 5.02nm x 89,665nm x 0.1nm
• Answer: 4.5 x 10^5 nm³

Example 9

• Calculation: 5.892g / 6.10ml
• Answer: 0.966g/ml (density)

Examples 10-13: Complex Operations and Unit Conversion

Example 10

• Operations with multiple divisions and additions.
• Final result rounded based on the least precise measurement.

Example 11

• Calculation: (6.404 x 2.91) / (18.7 - 17.1)
• Answer: 12 (rounded to 2 sig figs).

Example 12

• Average Calculation: Adding lengths and dividing by number of measurements.
• Answer: Final result kept to one decimal place due to least precise measurement.

Example 13

• Percentage Error Calculation
• Using subtraction, division, and multiplication to find error percentage.
• Answer: Final percentage with correct sig figs.

Examples 14-16: Unit Conversions and Significance in Calculations

Example 14

• Conversion: 1.76 picometers to centimeters.
• Answer: 1.76 x 10^-7 cm.

Example 15 & 16

• Converting between Celsius and Kelvin.
• Formulas: K = °C + 273.15
• Results: 316 K and 77 K respectively.

Examples 17-20: Practical Applications of Conversion

Example 17

• Conversion: Kilometers per liter to miles per gallon.
• Answer: 35 mpg

Example 18

• Displacement Method: Calculating volume change with added mass.
• Answer: 11.7 ml

Example 19

• Calculation: Length of aluminum foil from mass and density.
• Answer: 84 meters.

Example 20

• Density and Volume Calculation
• Scenario: Converting volume of an iceberg to mass in kilograms.
• Answer: 1.99 x 10^5 kg.

Final Examples and Practice

• Several examples focus on identifying and correcting conversion mistakes, reinforcing conceptual understanding of units and sig figs.

Key Takeaways

• Understanding significant figures and proper unit conversion is crucial.
• Always check your conversion steps for accuracy.
• Verify results with expected units and sig figs.

Conclusion

• Practice is essential for mastering chemistry problems.
• Utilize additional resources and seek help to clarify complex concepts.
• Consistent practice with these principles aids understanding of future topics in chemistry.