Lecture Notes on Unit Conversions and Density

Unit Conversions

  • We can cancel both numbers and units during conversions.

  • When performing conversions:

    • Write down the given value with its units.
    • Leave space for conversion factors.
    • Ensure units cancel properly.
    • Example: Converting feet to inches requires arranging the conversion factor so that 'feet' cancels out.

  • If you cannot cancel the starting unit, the setup is incorrect.

Metric System Conversions

  • Example: Converting nanometers (nm) to meters (m).
    • Need to cancel 'nm' and introduce 'm'.
    • 1 nm=10−9 m1 \text{ nm} = 10^{-9} \text{ m}

Exact Conversions

  • Within the same system (English or metric), conversions are exact.
    • Examples: feet to inches, quarts to gallons (English system), metric prefixes (metric system).
    • Prefixes in the metric system denote exact relationships.

English to Metric Conversions

  • Conversions between English and metric systems are necessary but not always memorized due to historical reasons (e.g., battles between England and France).

  • Resources:

    • Look up conversion factors (Google or reference tables).
    • Page 41 of the textbook contains conversion factors.

  • Example: Converting quarts to liters.

    • 1.00 quarts=0.946 liters1.00 \text{ quarts} = 0.946 \text{ liters}
    • These conversions involve significant figures.

Exact Conversion Agreements

  • International agreements exist for certain exact conversions (established around 1921).

Setting Up Conversions

  • Always set up conversions the same way to ensure accuracy.
  • Use exact numbers/definitions whenever possible.

Density

  • Density is a physical property.
  • For solids, density is commonly expressed in grams per cubic centimeter (gcm3)\left( \frac{\text{g}}{\text{cm}^3} \right).
  • For liquids, density is commonly expressed in grams per milliliter (gmL)\left( \frac{\text{g}}{\text{mL}} \right).
  • Example densities:
    • Water: 0.997gmL0.997 \frac{\text{g}}{\text{mL}}

Density Calculations

  • Density is calculated as mass per unit volume.

  • Example: Olive oil with a mass of 18.4 grams and a volume of 20 milliliters.

    • Density=MassVolume=18.4 g20 mL=0.92gmL\text{Density} = \frac{\text{Mass}}{\text{Volume}} = \frac{18.4 \text{ g}}{20 \text{ mL}} = 0.92 \frac{\text{g}}{\text{mL}}

Conversion Factor Flipping

  • Any conversion factor can be flipped (inverted).
  • Example: 1 mL=0.92 g of oil1 \text{ mL} = 0.92 \text{ g of oil}, this can be written as 1 mL0.92 g of oil\frac{1 \text{ mL}}{0.92 \text{ g of oil}}

Example Density Values

  • Lead: Approximately 11.3gcm311.3 \frac{\text{g}}{\text{cm}^3}

Temperature Scales

  • Celsius scale:

    • Freezing point of water: 0 degrees Celsius.
    • Boiling point of water: 100 degrees Celsius.

  • A certain number of divisions on the Celsius scale equals a different number of divisions on another scale (implied Fahrenheit).

Lab Information

  • Lab books are required.
  • Students will work in teams.
  • Lab exercises involve multiple sections and questions.
  • Taking notes is recommended, even if the lab book is unavailable.