Overview
This lecture focused on significant figures, dimensional analysis, and applying both in complex unit conversion and chemistry word problems.
Significant Figures & Calculations
- Always count the correct number of significant figures (sigfigs) based on the measurement with the fewest sigfigs.
- Exact conversions do not limit the number of sigfigs; measured values do.
- Round final answers to match the least number of sigfigs used in calculations.
Dimensional Analysis & Unit Conversions
- Convert units by multiplying by conversion factors set up so units cancel.
- When converting metric units, often convert through the base unit (e.g., deciliter → liter → microliter).
- Cube (or square) conversion factors when converting volume or area units.
- For percentages, use the percent value over 100 as a conversion factor.
Worked Examples
- 0.00275 deciliters to microliters: Convert deciliters to liters, then liters to microliters using known metric conversions.
- Density conversion (g/mL to lb/ft³): Convert mass units from grams to pounds, then convert volume units from mL (cm³) to ft³, using cubed conversion factors.
- Weight on Jupiter: Multiply Earth weight by the ratio (Jupiter gravity as percent/100) using sigfigs from the input numbers.
- Irregular Object in Graduated Cylinder: Calculate total volume by adding initial water volume to object’s volume (found via density as a conversion factor).
- Alloy Mass Percent Problem: Set up equations using mass conservation and density, solve for unknown mass via substitution, and calculate percent composition.
- Acre-Foot to Liters: Use provided conversion factors to systematically convert acre-feet to liters, cubing where necessary, and applying all given unit relationships.
- Galena Ore Problem: Reverse-calculate needed ore by accounting for ore composition, percent composition of galena, extraction efficiency, and final lead volume/mass needed.
Key Terms & Definitions
- Significant Figures (Sigfigs) — Digits in a measurement that convey meaningful information about its precision.
- Dimensional Analysis — A problem-solving method using conversion factors to change units.
- Density — Mass per unit volume, typically in g/cm³ or g/mL.
- Conversion Factor — A ratio that expresses how many of one unit are equal to another unit.
- Mass Percent — The fraction of a component’s mass in a mixture, multiplied by 100%.
- Extraction Efficiency — The percentage of a substance successfully extracted from a source.
Action Items / Next Steps
- Practice similar dimensional analysis and sigfig problems to solidify skills.
- Review calculator functions for operations like cubing, using scientific notation, and order of operations.
- Complete any assigned textbook problems involving multi-step unit conversions and percent composition calculations.