Dimensional Analysis (Unit Conversions)

Conversion Factors

Exact/Defined/Counting Numbers

Warning: not all conversion factors are exact Can you think of an example of an inexact conversion factor?

Exact/Defined/Counting Numbers Warning: not all conversion factors are exact Can you think of an example of an inexact conversion factor? Conversions between metric & imperial units E.g. 1 m = … This number is rounded to 6 sig figs but goes on forever There is always uncertainty so it counts towards sig figs

Solving Unit Conversion Problems Step 1: identify the initial amount – what info are you given? Step 2: identify the unknown amount – what are you looking for? Step 3: identify the conversion factor – how are 1 & 2 related? Overall: unknown amount = initial amount x conversion factor

Example 1 How many min are there in 3480 s? Step 1: Step 2: Step 3:

Example 1 How many min are there in 3480 s? Step 1: initial = 3480 s Step 2: Step 3:

Example 1 How many min are there in 3480 s? Step 1: initial = 3480 s Step 2: unknown = min Step 3:

Example 1

How many min are there in 3480 s? Overall: unknown = initial x conversion factor

Example 1 How many min are there in 3480 s? Overall: unknown = initial x conversion factor ? = 3480 s x conversion factor Want to cancel out “s” so use the c.f. that has “s” as the denominator

Example 1

Example 2 The automobile gas tank of a Canadian tourist holds 39.5 L of gas. If 1 L of gas is equal to gal in the US (“gal” is the symbol for “gallon”), and gas is $1.26/gal in Dallas, Texas, how much will it cost the tourist to fill his gas tank in Dallas?

Example 2 Initial = Unknown = Conversion factors:

Example 2 Initial = 39.5 L Unknown = Conversion factors:

Example 2 Initial = 39.5 L Unknown = $ (cost) Conversion factors:

Example 2 Initial = 39.5 L Unknown = $ (cost) Conversion factors: L  gal: gal  $:

Example 2

Unknown = initial x c.f. x c.f.

Example 2 $ ? = 39.5 L x c.f. x c.f. First c.f. must cancel out litres Must have L in the denominator

Example 2

Tips to Avoid Rounding Errors Write only one equation for the entire question Do not round before you get the final answer Instead, write down as many digits as you can or use the memory function on your calculator (M+) This is the difference b/t right and wrong answers!

Practice Hebden p.14 # 2

SI Units The International System of Units (Le Système International d’Unités) Modernized version of the metric system used in science Any SI prefix can be used with any SI unit

SI Base Units SI Prefixes Quantity Unit name Unit Symbol Lengthmetrem Masskilogramkg VolumelitreL Timeseconds TemperatureKelvinK Amount of Substance molemol Written Prefix Prefix Symbol Equivalent Exponential megaM10 6 kilok10 3 hectoh10 2 dekada decid10 -1 centic10 -2 millim10 -3 microμ10 -6

Other Units & Equivalences 1 t = 1 tonne = 10 3 kg 1 mL = 1 cm 3 (cubic centimetres, cc) 10 3 L = 1 m 3

Derived Units A unit made by combining two or more other units Speed: km/h (kilometres per hour) Density: g/L (grams per litre)

From a 3 rd year physical chem course at UBC…

Practice Hebden p #2-40