131 lecture 1 slides = 27

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Lecture 1

Copyright © 2009 Charles Hicks1

Professor Hicks General Chemistry (CHE131)

scientific notationscientists describe things very large/smalldiameter earth = 12000000 metersdiameter atom = 0.00000000011 meters

Copyright © 2009 Charles Hicks

more conveniently expressed in scientific notation (without so many zeros) asdiameter earth = 1.2 x 107 metersdiameter atom = 1.1 x 10-10 meters

scientific notation

diameter earth = 1.2 x 107 meters

diameter earth = 12000000 meters

7 decimal places


number between 1 and 10

decimal places abbreviated as powers of 10

numbers larger than 10 have positive powers of 10

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scientific notation

= 1 1 x 10-10 meters

diameter atom = 0.00000000011 meters

10 decimal places


1.1 x 10 meters

number between 1 and 10

decimal places abbreviated as powers of 10

numbers smaller 1 have

negative exponents

SI units used in science


Some common units are not SI units• centimeters • Celsius degree• grams – convenient unit in

student lab also popular with

metric butnot SI units


student lab also popular with street level drug dealers

• SI unit of kilogram used in chemical industry and popular with drug kingpins

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prefix multipliers

• words used instead of 10something

Example: kilo means 103 so5 7 kilometer = 5 7 x 103 meters


5.7 kilometer = 5.7 x 103 meters


On the exam it will be given to you like this

Example: Express 250 kilometers in scientific notation without prefixes.

250 kilometers1) move 2 decimal places left 102


2.5 x 102 kilometers

2) replace prefix with number

2.5 x 102 x103 meters

3) simplify exponents

2.5 x 105 meters

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• Example: Express 0.0000537 seconds in microseconds.

0.0000537 secondsneed to express answer as something x 10-6 seconds

1) insert the factor 106 x10-6 = 1here’s the trick!


1) insert the factor 106 x10 6 = 1

0.0000537 × 106 × 10-6 seconds

2) combine thesedecimal movesright 6 places

3) rewrite 10-6 as micro

53.7 microseconds

here’s the trick!



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• units are like apples and oranges

≠ any number of

Units


1 inch ≠ any number! kilograms

• things with different types of units cannot be equal

Units

• always write every quantity with its associated unit

• always include units in your calculationsd th ki d f ti it


- you can do the same kind of operations on units as you can with numbers

cm × cm = cm2

cm + cm = cmcm ÷ cm = 1

- using units as a guide to problem solving is called dimensional analysis

conversion factors and units• converting one unit into another often involves ratios

called conversion factors

• conversion factors come from Equivalence Statements( i )


(equations)1 inch = 2.54 cm can give two factors

divide both sides by 1 inch or divide both sides by 2.54 cm

in1 cm54.21 = 1

cm54.2in0.1 = multiplying by either factor is

equivalent to multiplying by 1

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using conversion factorsselect conversion factors so that the old unit

cancels and is replaced by the new desired unit


unit newunit oldunit newunit old =×

conversion factor

equivalent to multiplying by 1

Example: Convert 0.299 pounds to grams

g 453.59

1 lb = 453.59 gramslook at equations you have involving pounds and grams

lb 1.0

gives 2 conversion factors

pick the conversion factor thatwill cancel the old unit and has new unit on top


lb1.0g 136lb 1.0

g 453.59lb 0.299 =×quantity in old unit conversion factor

cancels old unitquantity in new unit

g 453.59

Example: Convert 1.76 yd to centimeters1 yd = 0.9141 m1 m = 100 cm

cm001m0.9141d

yd m cm

look at equations you have involving yards and cm

yards can be converted to meters thenmeters converted to centimeters


cm 161m 1cm 001

yd 1m 0.9141yd .761 =××

quantity in old unit

conversion factors quantity in new unit

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Example: Convert 125 decimeters into meters.

1 meter = 1 meter

1 decimeter = 1 x 10-1 meter

you will have this table for the exam


gives 2 possible conversion factors

1 decimeter

1 x 10-1 meters

1 x 10-1 meters

1 decimeter

125 decimeters

old unit

x1 x 10-1 meters

1 decimeter

conversion factor

= 12.5 meters

new units

Example: Convert 235 nanometers into micrometers.

1 meter = 1 meter

1 nanometer = 1 x 10-9 meter

1 meter = 1 meter

1 micrometer = 1 x 10-6 meter

gives 2 possible conversion factors gives 2 possible conversion factors

tip 2: When converting between units with prefixesuse two conversion factors: one to go to the un-prefixed unit and one to go to the new prefixed unit.e.g. in this case nanometers meters micrometers


gives 2 possible conversion factors gives 2 possible conversion factors

1 nanometer

1 x 10-9 meters

1 x 10-9 meters

1 nanometer

1 micrometer

1 x 10-6 meters

1 x 10-6 meters

1 micrometer

235 nanometers

old unit

x 1 x 10-9 meters

1 nanometer

1 micrometer

1 x 10-6 metersx

conversion factors

= 0.235 micrometers

Derived Units• units built up from base units are called derived units

• can be multiplied or divided- “per” means division of units

derived unit


3) pressure unit “pounds per square inch”pounds

inch2

1) all formulas for area involve two length dimensions multiplied meter * meter meter2 or m2

2) units of velocity “miles per hour” mileshour

area rectangle =l*w area circle = πr2 area triangle = ½b*h

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Example: Convert 2.11 yard3 to meters3

2.11 yard3x

1 meter

1.0936 yard

3

2 11 yard3 13 meter3

tip 3: conversion factors for units of area or volume can be derived by writing downthe conversion factor for the base unit oflength and squaring or cubing it


2.11 yard3 x1.09363 yard3

2.11 yard3 x1 meter3

1.3079 yard3= 1.61 meter3

or 1.61 m3

understanding conversion factors for area/volume

area = 1 decimeter squaredor 1 dm2

1 decimeter

1 decimeterarea = 1 meter squaredor 1 m2

(deci = 10-1)


1 meter

1 meter

even though a decimeter is1/10 the length of a meter it would require 100 square decimeters to cover 1 m2

1 decimeter = 10-1 meter1 dm2 = 10-2 m2

or 100 dm2 = 1 m2

Converting base units within a derived unit

the SI unit of energy is the derived units called the Joule.

1 Joule = 1kg*m2

sec2

• any part of a derived unit can be convertedas if it was a base unit alone


sec

x1000 g

1 kg=

kg*m2

sec20.251 251 g*m2

sec2

units of Joules

conversionfactor for

kg to g

new derivedunits has grams

instead of kg

Example: Convert 0.251 joules into units of g*m2/sec2 .

it is as if we just converted

kg into grams

kg g

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4 quarts = 1 gallon16 ounces = 1 pound6.02 x 10 23 amu = 1.0 gram2 pints = 1 quart


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131 lecture 1 slides = 27

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