MATH AND METHODS Lesson 1 – SI Units and Dimensional Analysis

Introduction to Chemistry (not in notes)  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

Branches of Chemistry (not in notes) BranchArea of Emphasis Examples Organic chemistry most carbon-containing chemicalspharmaceuticals, plastics Inorganic chemistry (this class) in general, matter that does not contain carbon minerals, metals and nonmetals, semi- conductors Physical chemistry the behavior and changes of matter and the related energy changes reaction rates, reaction mechanisms Analytical chemistry components and composition of substances food nutrients, quality control Biochemistrymatter and processes of living organisms metabolism, fermentation

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

SI Units

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.

Volume  Volume = the amount of space occupied by a substance  Volume can be found mathematically  (V rect. prism = L*W*H)  Volume can also be measured by water displacement  By definition 1 cm 3 = 1 mL

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 cm 3  Remember 1ml = 1 cm 3  Many known densities are listed in your reference packet, these will be useful throughout the semester.

PrefixSymbolFactor Scientific Notation gigaG megaM kilok hectoh dekada NO prefix, use BASE UNIT (gram, liter, meter) decid1/ centic1/ millim1/ micro μ 1/ nanon1/ picop1/

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

Unit Equalities – Some examples  1 meter = 1000 mm  1L = 1000 mL  1 km = 1000 m  1 mole = x 10 ²³ particles (e.g. atoms, molecules, ions, etc.)  1 kg = 1000 g  1 shirt = $20.00  1 day = 24 hours  All unit equalities can be turned into conversion factors.

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

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

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

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 6.67 g/mL x 1000 mg/1 g x 1000 mL/1 L 45.0 m/s x 1000 mm/1 m x 60 s/1 min x 60 min/1 hr = 126 m/s = 6,670,000 mg/L = 162,000,000 mm/hr

(Honors) Converting Cubed Units Express 4563 mm³ in m³ Express 35.6 mol/m³ in atoms/cm³ 35.6 mol/m 3 x x atoms/mol x (1m/100 cm) mm 3 x (1m/1000 mm) 3 = 4.53 x m 3 = 2.14 x atoms/cm 3