Chemistry I

1
Chapter 2

• Chemistry I
• Ms Appleby

2
Units and Measurements

• International System of Units, SI
• The metric system
• Standard in the scientific community
• Measurements are based on units of 10

3
Base Unit and SI Prefixes

• Prefix Symbol Power of 10 Numerical
  value
• Giga (G-) 109 1 billion
• Mega (M-) 106 1 million
• Kilo (k-) 103 1 thousand
• Hecto (h-) 102 1 hundred
• Deka (da-) 10 1 ten
• Deci (d-) 10-1 1 tenth
• Centi (c-) 10-2 1 hundredth
• Milli (m-) 10-3 1 thousandth
• Micro (µ-) 10-6 1 millionth
• Nano (n-) 10-9 1 billionth
• Pico (p-) 10-12 1 trillionth

4
Time

• SI unit is the second (s)
• The standard to define a second is the frequency
  of radiation given off by a cesium-133 atom
• Cesium based clocks are highly accurate
• Although a second seems like a short period of
  time, in chemistry many reactions occur in a
  fraction of a second

5
Length

• The basic SI unit is the meter (m)
• A meter stick is divided into 100 divisions
• Each division is a centimeter
• A centimeter is divided into 10 divisions
• Each division is a millimeter
• One meter is the distance light travels in a
  vacuum in 1/299,792,458 of a second

6
Mass

• Mass is the quantity of matter an object contains
• Mass is not weight, weight is a force
• The SI unit of mass is the kilogram (kg)

7
Temperature

• The degree of hotness or coldness of an object
• Nearly all substances expand with an increase in
  temperature
• Likewise they will contract with a decrease in
  temperature
• An important exception is water

8
Fahrenheit

• Used in the US to measure temperature
• Scale was devised in 1724 by a German scientist
• On this scale water freezes at 32F
• On this scale water boils at 212F

9
Celsius

• Freezing point of water is 0C
• Boiling point of water is 100C
• To convert from F to C subtract 32 and multiply
  by 5/9

10
Kelvin

• The freezing point of water is 273K
• The boiling point of water is 373K
• 0 Kelvin, or absolute zero equals
• -273C
• To convert from C to Kelvin add 273
• http//www.absolutezerocampaign.org/

11
Derived Unit

• Unit that is a combination of base units
• Speed m/s
• Volume cm3
• Density g/cm3

12
Volume

• The space occupied by an object
• The volume of an object with a regular shape is
  determined by multiplying the length x width x
  height (l x w x h) and is measured in cm3
• The volume of an irregularly shaped solid, or a
  liquid is expressed in liters (L)
• 1mL 1 cm3

13
Density

• A physical property of matter
• Defined as unit of mass per unit of volume
• Density mass/volume
• For solids the units are g/cm3
• For liquids the units are g/mL
• Density can be used to identify an unknown
  element

14
English - Metric Conversions

• Length
• 2.54 cm 1 inch
• 1 mi 5280 ft
• 1 mi 1.609 km
• Temperature Conversions
• 0C (0F - 32) x 5/9
• 0F (9/5 x 0C) 32
• K 0C 273

15
English-Metric Conversions

• Mass
• 454 g 1 lb
• 1 lb 0.453 kg

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English-Metric Conversions

• Volume
• 1 L 1.057 qt
• 1 oz 28.350 g
• 1 gal 3.785 L
• 8 oz 1 cup
• 2 cups 1 pint
• 2 pints 1 quart
• 4 quarts 1 gallon

17
Problem Solving

• Solving a problem is like taking a trip to a new
  place
• It takes planning and a knowledge of what your
  starting point is and where you want to end up

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Techniques of Problem Solving

• Identify the unknown
• Identify What is Known or Given
• Plan a Solution
• Do the calculations
• Finish Up
• Check your work!

19
Identify the Unknown

• Know what the problem is asking
• Read the problem carefully
• What will the unit of the answer be

20
Identify What is Known

• This usually includes a measurement
• Learn to recognize which information is extra

21
Plan a Solution

• Sketching a picture of the
  problem may help you see
  a relationship between the known
  and the unknown
• Break down a complex problem into simpler
  problems
• You may need to look up a conversion or a formula

22
Do The Calculations

• This may involve solving an equation
• Substituting in known quantities
• Doing arithmetic
• You may need to convert a measurement form one
  form to another
• Be sure to use relationships correctly to move
  from the given quantity to the unknown

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Finish Up

• The answer should always be expressed to the
  correct number of significant figures
• When appropriate,
  the number should
  be written in
  scientific notation

24
Check Your Work!

• Have you found what was asked for
• Check your math
• Check your units
• Does the answer
  make sense
• Is it reasonable

25
Density Webpage

• http//www.nyu.edu/pages/mathmol/textbook/density.
  html

26
Scientific Notation and Dimensional Analysis

• The Hope Diamond contains 460,000,000,000,000,000,
  000,000 atoms of carbon
• Each carbon atom has a mass of 0.00000000000000000
  000002 g.
• If you were to use these numbers to calculate the
  mass of the Hope Diamond you would find the
  zeroes get in the way and a calculator is no help

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Scientific Notation

• Used to express any number as a number between 1
  and 10 (the coefficient)
• Multiplied by 10 and raised to a power (the
  exponent)
• In scientific notation the number of carbon atoms
  in the Hope Diamond 4.6 x 1023
• The mass of one carbon atom 2 x 10-23

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Scientific Notation

• In each case the number 10 raised to an exponent
  replaced the zeroes that preceded or followed the
  nonzero numbers
• For numbers greater than 1 a positive exponent
  tells you the number of places the decimal must
  be moved to the right when converting to a whole
  number
• For numbers less than 1 a negative exponent tells
  you the number of places the decimal must be
  moved to the left

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Scientific Notation Practice Problems

• Use this site to hone your scientific notation
  skills.
• http//science.widener.edu/svb/tutorial/scinotcsn7
  .html

32
Multiplication with Exponents

• When performing multiplication with exponents, do
  the multiplication and add the exponents
• (2.68 x 10-5) x (4.40 x 10-8)
• (8.41 x 106) x (5.02 x 1012)
• (4.6 x 1023) x (2 x 10-23)

33
Division with Exponents

• When performing division, do the division and
  subtract the exponents
• (2.95 x 107) (6.28 x 1015)
• (9.21 x 10-4) (7.60 x 105)
• (4.6 x 1023) (2 x 10-23)

34
Another Look Multiplication/Division in
Scientific Notation

• http//www.regentsprep.org/Regents/math/scinot/pag
  e4.htm

35
Addition and subtraction are more complex

• There are four basic steps
• Find the number whose exponent is the smallest
  (remember, negative numbers are smaller than
  positive ones, and the "more negative" the
  number, the smaller it is).
• If the exponents of the numbers are not the same,
  change the number with the smaller exponent. Do
  this by moving the decimal point of the
  coefficient of that number to the left, and
  adding one to the exponent of that number, until
  the two exponents are equal.

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Addition and Subtraction of Exponents

• Four Basic Steps, Continued
• 3. Add or subtract the coefficients of the two
  numbers. The result is the coefficient of the
  result. The exponent is the exponent of the
  number you did not change
• 4. Put the result in standard form, if necessary

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Examples

• (3 x 10-6) - (2 x 10-7)
• The algebraically smallest exponent is -7, so we
  change the second term to match the first
• 2 x 10-7 0.2 x 10-6 The exponents are now the
  same
• (3 x 10-6) - (0.2 x 10-6)
• (3 - 0.2) x 10-6
• 2.8 x 10-6

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Example

• (9.39 x 105) (8 x 103)
• (9.39 x 105) (0.08 x 105)
• (9.39 0.08) x 105
• 9.47 x 105

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Addition and Subtraction

• 3.2 x 103 4.25 x 105
• 6.2 x 108 7.6 x 106
• 2.6 x 10-4 1.8 x 10-5
• 5.0 x 10-1 3.9 x 10-3

40
Equalities

• Which of these numbers are equal to each other?
• 5.678 x 10 3     
• 56.78 x 10 2  
• 567.8 x 10 1
• 0.5678 x 10 4    
• 0.05678 x 10 5 
• 0.005678 x 10 6

41
Conversion Factors

• Equality relationships can be written as a
  conversion factor to allow you to change from one
  unit to another
• 12 inches 1 foot
• 12 eggs 1 dozen eggs
• Anything that can be written as an equality can
  be used as a ratio
• A conversion factor must cancel one unit and
  introduce a new unit

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Conversions

• 0.044 km to meters
• 4.6 mg to grams
• 8.9 m to decimeters
• 0.107 g to centigrams
• 15 cm3 to liters
• 7.38 g to kilograms
• 6.7 s to milliseconds
• 94.5 g to micrograms

43
Conversion problems

• How many eight packs of water would you need if
  32 people each had two bottles of water?
• If Noah built his Ark 60 cubits in length, how
  long was the Ark in meters?
• A cubit is equal to 7 palms, a palm is equal to 4
  fingers, and a finger is equal to 18.75
  millimeters.

44
Conversion Problems

• Who is taller a man 1.62 m tall or a woman who
  is 56 tall?
• A 1 kg package of hamburger has a mass closest
  to 8 oz 1 lb 2 lb 10 lb
• A recipe in metric calls for 250 ml of milk. How
  much milk (in cups) should be used?
• The Greenland Ice Sheet has an area of 1.7
  million square kilometers (about the size of
  Mexico). How many square miles is this? 1 mile
  1.609 kilometer
• You are doing 65 mi/hr and you take your eyes off
  the road for just a second. How many feet do
  you travel in this time?

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Accuracy and Precision

• Measurements in the lab must be certain
• When scientist make measurements they evaluate
  the accuracy and precision of the measurements
  they make
• Accuracy is how close a measured value is to the
  accepted value
• Precision is how close are series of measurements
  are to each other

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Accuracy

• How close a single measurements comes to the
  actual value of that which is being measured
• In a dart game your closeness
• to the bulls eye is a test of
• your accuracy

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Precision

• How close several measurements are to the same
  value
• Precise measurements are reproducible

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Precision vs Accuracy

• Precision depends on more than one measurement
• Individual measurements may be either accurate or
  inaccurate
• Precision depends on the skill of the person
  taking the measurement
• Accuracy depends on the quality of the measuring
  device

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Checking the accuracy of your measurements

• The accepted value is the true or correct value
• The experimental value is the measured value
  found in the lab
• The difference between the two is the
  experimental error
• Error accepted value-experimental value

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Percent Error

• The percent error is the error divided by the
  accepted value expressed as a percentage of the
  accepted value
• error   your result - accepted value x100
                            accepted value
• This tells us how accurate we are, or how closely
  our experimental value compares to the known value

51
Calculating Error

• Example  A student measures the volume of a 2.50
  liter container to be 2.38 liters. What is the
  percent error in the student's measurement?
• Ans.      error (2.38 liters 2.5 liters) 
  x   100                                   2.50
  liters
•                          .12 liters     x   
  100                             2.50 liters
•                           .048     x   100
•                           4.8 error

52
Significant Figure Rules

• There are three rules on determining how many
  significant figures are in a number
• Non-zero digits are always significant.
• Any zeros between two significant digits are
  significant.
• A final zero or trailing zeros in the decimal
  portion ONLY are significant.

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Rule 1 Non-zero digits are always significant.

• Hopefully, this rule is rather obvious
• If you measure something and the device you use
  (ruler, thermometer, triple-beam balance, etc.)
  returns a number to you, then you have made a
  measurement decision and that ACT of measuring
  gives significance to that particular numeral (or
  digit) in the overall value you obtain
• A number like 26.38 would have four significant
  figures and 7.94 would have three

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Rule 2 Any zeros between two significant digits
are significant.

• Suppose you had a number like 406
• By the first rule, the 4 and the 6 are
  significant
• However, to make a measurement decision on the 4
  (in the hundred's place) and the 6 (in the unit's
  place), you HAD to have made a decision on the
  ten's place
• The zero is significant because there are zero
  tens

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Rule 3 A final zero or trailing zeros in the
decimal portion are significant.

• This rule causes the most difficulty
• Here are two examples of this rule with the zeros
  this rule affects in boldface
• 0.00500
• 0.03040
• Here are two more examples where the significant
  zeros are in boldface
• 2.30 x 105
• 4.500 x 1012

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Zeros that are not significant

• Zero Type 1 Space holding zeros on numbers less
  than one.
• 0.00500
• Zero Type 2 the zero to the left of the decimal
  point on numbers less than one.
• When 0.00500 is written, the very first zero (to
  the left of the decimal point) is put there to
  communicate that the decimal point is a decimal
  point

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More Zeros that are not significant

• Zero Type 3 trailing zeros in a whole number.
• 200 is considered to have only ONE significant
  figure while 25,000 has two
• The zeros are simply place holders
• Zero Type 4 leading zeros in a whole number.
• 00250 has two significant figures
• 005.00 x 104 has three

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Special Cases

• Exact numbers, such as the number of people in a
  room, have an infinite number of significant
  figures
• Exact numbers are counting up how many of
  something are present, they are not measurements
  made with instruments
• Another example of this are defined numbers, such
  as 1 foot 12 inches, there are exactly 12
  inches in one foot

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Practice Problems

• 1) 3.0800
• 2) 0.00418
• 3) 7.09 x 105
• 4) 91,600
• 5) 0.003005
• 6) 3.200 x 109
• 7) 250
• 8) 780,000,000
• 9) 0.0101
• 10) 0.00800
• http//dbhs.wvusd.k12.ca.us/webdocs/SigFigs/SigFig
  sFable.html