MATH and Methods

1. MATH and Methods Lesson 1 – SI Units and Dimensional Analysis

2. Chemistry: The Central Science Chemistry is the science that investigates and explains the structure and properties of matter. Seeks to explain the submicroscopic events that lead to macroscopic observations Introduction to Chemistry(not in notes)

3. Branches of Chemistry(not in notes)

4. SI Units (Le SystémeInternationale) Scientists need to report data that can be reproduced by other scientists. They need standard units of measurement. Units of measurement Standard Units • A standard unit is a defined unit in a system of measurement • There are seven standard units in SI.

5. SI Units

6. Derived units of measurement • A derived unit is any unit based off one or more SI units In other words: a derived unit is a created unit as opposed to a natural occurrence The main derived units used in this class are volume and density.

7. Volume • Volume = the amount of space occupied by a substance • Volume can be found mathematically • (Vrect. prism= L*W*H) • Volume can also be measured by water displacement • By definition 1 cm3 = 1 mL

8. Density • Density = amount of mass per unit of volume • D=m/v • Units for mass are grams • Units for volume can either be mL or cm3 • Remember 1ml = 1 cm3 • Many known densities are listed in your reference packet, these will be useful throughout the semester.

10. Why do we use the metric system? Advantages Simple to use Easy to convert from one unit to another Dimensional Analysis (coming soon!) Universal – used worldwide By all scientists to communicate By all industrialized nations Except United States

11. Unit Equalities – Some examples • 1 meter = 1000 mm • 1L = 1000 mL • 1 km = 1000 m • 1 mole = 6.022 x 10²³ particles (e.g. atoms, molecules, ions, etc.) • 1 kg = 1000 g • 1 day = 24 hours • All unit equalities can be turned into conversion factors.

12. Dimensional Analysis Process for converting between units. The Unit Equality (1 km = 1000 m) becomes the Conversion Factor: 1 km or 1000 m 1000 m 1 km

13. Using Dimensional Analysis • Multiply the starting unit by the conversion factor. • Example: Convert 4.6 m to km 4.6 m x 1 km = 0.0046 km 1000 m • If you use your conversion factors properly, the units you started with should cancel

14. Examples • Convert between the following measurements using dimensional analysis (show your conversion factors): • 1.) 2.34 mg x ___________ = g • 2.) .98 mol x ________________= atoms • 3.) 1,098 mL x _________ = L • 4.) 5 km x _______ x ________ = cm 1 g 0.00234 1000 mg 6.022 x 1023 atoms 5.9 x 1023 1 mol 1 L 1.098 1000 mL 100 cm 1000 m 500,000 1 km 1 m

15. Multiple Unit Dimensional Analysis • Convert 455 km/hr to m/s • Convert 6.67 g/mL to mg/L • Convert 45.0 m/s to mm/hr 455 km/hr x 1000 m/1 km x 1 hr/60 min x 1 min/60 s = 126 m/s 6.67 g/mL x 1000 mg/1 g x 1000 mL/1 L = 6,670,000 mg/L 45.0 m/s x 1000 mm/1 m x 60 s/1 min x 60 min/1 hr = 162,000,000 mm/hr

16. (Honors) Converting Cubed Units Express 4563 mm³ in m³ Express 35.6 mol/m³ in atoms/cm³ 4563 mm3 x (1m/1000 mm)3 = 4.563 x 10-6 m3 35.6 mol/m3 x 6.022 x 1023 atoms/mol x (1m/100 cm)3 = 2.14 x 1019 atoms/cm3