Overview
This lecture focuses on the essential skill of unit conversions using dimensional analysis, emphasizing its importance for solving chemical problems and ensuring accurate calculations.
Introduction to Dimensional Analysis
- Dimensional analysis is a method to track and convert units during calculations.
- Ensures units cancel correctly, helping check the validity of solutions.
- Core skill for chemistry problem-solving, especially for first-semester calculations.
Conversion Factors and Equalities
- A conversion factor is an equality between two units (e.g., 1 inch = 2.54 cm).
- Conversion factors can be written in two ways, depending on which unit needs to cancel.
- Using conversion factors is mathematically equivalent to multiplying by one, just changing units.
Applying Conversion Factors
- To convert from cents to dollars: use 1 dollar/100 cents to cancel cents.
- To convert from dollars to cents: use 100 cents/1 dollar to cancel dollars.
- Multi-step conversions may require chaining several conversion factors (e.g., inches to yards via feet).
Metric Prefixes and Stepwise Conversions
- When converting between metric prefixes, convert to the base unit first, then to the target unit (e.g., mg → g → kg).
- Example: 573 mg = 0.573 g; then 0.573 g = 5.73 × 10⁻⁴ kg.
Handling Exponential Units
- When converting units with exponents (e.g., cm³ to m³), cube the conversion factor (100 cm = 1 m ⇒ 100³ cm³ = 1 m³).
- Always apply the exponent to both the number and the unit.
Practice Problems
- Convert between metric and US/customary units by following a logical path through available conversion factors.
- Example: 2.76 km to inches can be done via km → m → inches or km → miles → feet → inches, adjusting for significant figures.
- Example: 32.5 gallons to liters requires using quarts as an intermediary (gallons → quarts → liters).
Significant Figures
- Retain the appropriate number of significant figures based on measured values and conversion factors.
- Only round final answers and carry all significant digits through intermediate steps.
Key Terms & Definitions
- Dimensional Analysis — A technique for converting between units by tracking and canceling units through conversion factors.
- Conversion Factor — An equality expressing the relationship between two units, used in fraction form to convert units.
- Base Unit — The fundamental unit in the metric system (e.g., grams, meters).
- Significant Figures (Sig Figs) — Digits in a number that reflect the precision of a measurement.
Action Items / Next Steps
- Practice converting between various units using dimensional analysis.
- Memorize metric prefixes and their relationships.
- Review provided conversion factors, especially for metric to US unit conversions.
- Complete any assigned homework on unit conversions and dimensional analysis.