Ch. 2: Measurements

1
Ch. 2 Measurements Calculations

• An Introduction to Scientific Investigations

2
What is Chemistry?

• Chemistry- the study of substances and the
  changes they can undergo.
• EX a match burning, how bleach removes stains,
  why bread dough rises, etc.

3

• A) The Central Science
• Chemicals are everywhere, in everything, and
  impact many different aspects of life.
  Chemistry, therefore, is considered a central
  science. Life, as we know it, is a product of
  what Chemistry and Physics has already done.
• (ex. occupations which require chemistry
  Engineering, medical professionals, hair
  stylists, crime labs, cosmetic makers, drug
  developers, oil companies, Wine makers, Mc
  Donalds, Candy makers, Photographers )

4

• B) Why Study Chemistry?
• To help you understand the physical world around
  you. To develop skills for evaluation and
  critical thinking. Maybe even help prepare you
  for a job which requires chemistry.

5
2.1 The Scientific Method

• Scientific Method- an orderly, systematic
  approach to gather knowledge. It is a way of
  answering questions about our observable world.

6

• Steps of the Scientific Method
• Make an observation
• State the question
• Collect information
• State a hypothesis
• Design an experiment
• Make observations
• Collect, record and study data
• Draw a conclusion

7

• Making an Observation
• Notice a natural event the ball falls to the
  ground, the sky is blue, etc. This observation
  can be about almost anything! Once youve noticed
  something form a question.

8

• Forming a Hypothesis
• This should be a possible, logical, answer to the
  question about your observation. It is typically
  expressed in a cause-and-effect format. A
  scientific hypothesis must be one which requires
  and can be tested by an experiment. If it does
  not it is not scientific.

9

• Performing an Experiment
• For a hypothesis to be tested properly, you must
  design and perform an experiment which examines
  ONE variable at a time. If you have more than
  one variable the results will not be conclusive
  and very little knowledge will be gained.

10

• Interpreting the Results
• Once the experiment is complete you look at your
  data and the observations you made interpret what
  they tell you. Did you prove your hypothesis
  wrong? Did you learn anything new? (Experimental
  control)
• Quantitative- numerical values
• Qualitative- descriptive i.e. color, shape, ect.

11

• Laws and Theories
• Law- a statement of fact meant to explain, in
  concise terms, an action or set of actions. It is
  generally accepted to be true and universal, and
  can sometimes be expressed in terms of a single
  mathematical equation. THEY TELL WHAT HAPPENED.
• Theory- an explanation of a set of related
  observations or events based upon proven
  hypotheses and verified multiple times by
  detached groups of researchers. One scientist
  cannot create a theory he can only create a
  hypothesis. THEY EXPLAIN AND PREDICT EVENTS.

12
Lab Safety

• Video
• http//www.youtube.com/watch?vVRWRmIEHr3A

13
2.2 Units of Measurement

• The International System of Units
• In 1960, at a scientific conference on units held
  in France, the SI system of units were
  internationally accepted for the scientific
  community. The SI system is based on the metric
  system and we refer to these as base units.

14
BASE UNITS
Mass kilogram kg
Length meter m
Time seconds s
Count quantity mole mol
Temperature kelvin K
Electric current ampere A
Luminous intensity candela cd
15

• Meter- defined as the distance that light travels
  in a vacuum during a time interval of
  1/299,792,458 of a second.
• Mass- amount of matter in an object. 1 kg 2.2
  lbs (on earth).
• Weight - equals the force of gravity pulling on
  the object.
• ?? What changes in outer space weight or mass??
• Derived units - a combination of 2() base units
  a new unit.

16
DERIVED UNITS
Area Square meter m2
Volume Cubic meter m3
Force Newton N
Pressure Pascal Pa
Energy Joule J
Power Watt W
Voltage Volt V
Frequency Hertz Hz
Electric charge Coulomb C
17

• Area- length X width m X m m2
• Volume- the amount of space that an object
  occupies.
• Length X width X height m X m X m m3
• EXCEPTIONS
• The liter (L)- the common unit for volume. 1mL
  1cm3
• Celsius (C?)- common unit for temperature
• 1K (273 C?)

18

• Metric Prefixes
• Prefix- a word attached to the front of the base
  unit.
• The SI prefixes are base 10 and, therefore,
  increase and decrease by 10s.

19
Prefix Abbreviation Power of 10
mega- M 1,000,000 106
kilo- k 1,000 103
hecto- h 100 102
deca- da 10 101
Base 1 100
deci- d 0.1 10-1
centi- c 0.01 10-2
milli- m 0.001 10-3
micro- ? 0.000001 10-6
nano- n 0.000000001 10-9
20
Converting among prefixes

• When converting from one prefix to another,
  remember this saying
• King Henry Died By Drinking Chocolate Milk.
• When set up as such
• k h da _ d c m
• Now converting among prefixes is just a matter of
  pushing the decimal

21
 Problem Solving

• Dimensional Analysis- technique of converting
  between units.  Unit equalities show how
  different units are related (1g100cm). 
  Conversion factors are written from the unit
  equalities.  The conversion factor is set up so
  that the bottom number cancels the given unit and
  a new unit is created. 
• Example  Convert 10 cm to inches. Conversion
  factors (1m 100 cm)   (1m 39.37inches)
• Start with the given unit, then use your
  conversion factors to cancel units to arrive at
  the unit you want to convert to.

22
Density

• The ratio of mass to volume
• Mass Volume
• The SI unit for density is kg/m3.
• Ex. A sample of metal has a mass of 12.3g and a
  volume of 2.5 cm3. What is the density of this
  metal?

23
2.3 Using Scientific Measurements

• Making Measurements
• When recording a measurement you will record all
  the certain/known/exact digits and one uncertain
  (usually a rounded digit)
• Ex. The measurement should be read to the 1000
  ths place exactly, but you read 21.32584 g on
  your scale you should record 21.3258 g. The 8 is
  the uncertain digit.
• REMEMBER- Always record the units you are
  referring to in the measurement!!!!!!!!!!

24

• How many ml are in this graduated cylinder?
• Hint look at the meniscus.

25
2 reasons for uncertainty in measurement

• 1. Instruments used for measuring are not
  perfect/ without flaws
• 2. Measuring always involves some estimation.
• The type of estimation required depends on the
  instrument you are using.
• Digital display The last digit on the display is
  the estimated digit. The estimation is done for
  you! If the digit flickers record the digit that
  seems to be preferred.
• Using a scale The only certain numbers are
  those marked on the scaleall other values in
  between the markings are the uncertain digits.

26

• Reliability in Measurement
• Measurements can be checked for precision and
  accuracy to determine their reliability.
• Precision- continuing to get the exact reading
  every time.
• Accuracy- getting the accepted value (the exact
  measurement)
• ?? Is it possible to be precise and not accurate?
  Accurate and not precise? Neither accurate nor
  precise? Both accurate and precise?

27
(No Transcript)
28

• Significant Digits
• 1. Leading zeros are never significant.
• 2. Imbedded zeros are always significant.
• 3. Trailing zeros are significant only if the
  decimal point is specified.
• Hint Change the number to scientific notation.
  It is easier to see.

29
EXAMPLES
Example Number ofSignificant Figures Scientific Notation
0.00682 3 6.82 x 10-3 Leading zeros are not significant.
1.072 4 1.072 (x 100) Imbedded zeros are always significant.
300 1 3 x 102 Trailing zeros are significant only if the decimal point is specified.
300. 3 3.00 x 102
30
Addition Subtraction

• The last digit retained is set by the first
  doubtful digit.

31
Addition Even though your calculator gives you the answer 8.0372, you must round off to 8.04. Your answer must only contain 1 doubtful number. Note that the doubtful digits are underlined.
Subtraction Subtraction is interesting when concerned with significant figures. Even though both numbers involved in the subtraction have 5 significant figures, the answer only has 3 significant figures when rounded correctly. Remember, the answer must only have 1 doubtful digit.
32
Multiplication or Division

• The answer contains no more significant figures
  than the least accurately known number.

33
Multiplication The answer must be rounded off to 2 significant figures, since 1.6 only has 2 significant figures.
Division The answer must be rounded off to 3 significant figures, since 45.2 has only 3 significant figures.
34
Notes on Rounding

• When rounding off numbers to a certain number of
  significant figures, do so to the nearest value.
  Round like normal.
• ex Round to 3 significant figures 2.3467 x 104
  (Answer 2.35 x 104)
• ex Round to 2 significant figures 1.612 x 103
  (Answer 1.6 x 103)
• EXCEPT..

35

• What happens if there is a 5 with a 0 after it?
  There is a rule
• If the number before the 5 is odd, round up.
• If the number before the 5 is even, let it be.
  The justification for this is that in the course
  of a series of many calculations, any rounding
  errors will be averaged out.
• ex Round to 2 sig figs 2.350 x 102 (Answer 2.4
  x 102)
• ex Round to 2 sig figs 2.450 x 102 (Answer 2.4
  x 102)
• Of course, if we round to 2 significant figures
• 2.452 x 102, the answer is definitely 2.5 x 102
  since
• 2.452 x 102 is closer to 2.5 x 102 than 2.4 x
  102.

36
Scientific Notation

• Chemists often work with numbers that are
  extremely large or extremely small.
• For example, there are 10,300,000,000,000,000,000,
  000 carbon atoms in a 1-carat diamond each of
  which has a mass of 0.000,000,000,000,000,000,000,
  020 grams. It is impossible to multiply these
  numbers with most calculators because they can't
  accept either number as it is written here.
• To do a calculation like this, it is necessary to
  express these numbers in scientific notation, as
  a number between 1 and 10 multiplied by 10 raised
  to some exponent.

37
Exponent Review

• Some of the basics of exponential mathematics are
  given below.
• Any number raised to the zero power is equal to
  1. 10 1 100 1
• Any number raised to the first power is equal to
  itself. 11 1 101 10
• Any number raised to the nth power is equal to
  the product of that number times itself n-1
  times.
• 22 2 x 2 4 105 10 x 10 x 10 x 10 x
  10 100,000
• Dividing by a number raised to an exponent is the
  same as multiplying by that number raised to an
  exponent of the opposite sign.

38
Converting to Scientific Notation

• The following rule can be used to convert numbers
  into scientific notation The exponent in
  scientific notation is equal to the number of
  times the decimal point must be moved to produce
  a number between 1 and 10.
• Ex In 1990 the population of Chicago was
  6,070,000. To convert this number to scientific
  notation we move the decimal point to the left
  six times.
• 6,070,000 6.070 x 106

39

• To convert 10,300,000,000,000,000,000,000 carbon
  atoms into scientific notation, we move the
  decimal point to the left 22 times.
• 10,300,000,000,000,000,000,000 1.03 x 1022

40

• To convert numbers smaller than 1 into scientific
  notation, we have to move the decimal point to
  the right. The decimal point in 0.000985, for
  example, must be moved to the right four times.
• 0.000985 9.85 x 10-4

41

• The primary reason for converting numbers into
  scientific notation is to make calculations with
  unusually large or small numbers less cumbersome.
  Because zeros are no longer used to set the
  decimal point, all of the digits in a number in
  scientific notation are significant, as shown by
  the following examples.

2.4 x 1022 2 sig. figs
9.80 x 10-4 3 sig. figs
1.055 x 10-22 4 sig. figs
42
Percents and Percent Error

• You can change fractions to percent by dividing
  the top number by the bottom number and
  multiplying by 100
• Ex. There are 29 students in Mrs. Gs first hour,
  17 of the students are girls.  What percent are
  girls?
• 1729 .59 x 100 59

43

• Percent Error calculates how much error you have
  between your answer and a commonly accepted
  value. The formula is
• Error measured value - accepted value X 100
• Accepted value
• What if we calculated the density of water, in
  class, and many students reported values other
  than the accepted value of 1g/ml or 1g/cm3.
  Lets say you calculated the density of water to
  be .9g/ml
• Error 0.9 - 1   x 100  10
  error            1

44
Ratios

• Units found by dividing one unit by another. 
  (The speedometer in your car registers the ratio
  of miles/hour.) The most common ratio in
  chemistry is density (g/ml or g/dm3). Density is
  calculated by this formula density
  mass/volume
• Lets say you had an object thats mass was 20g
  and its volume was 10cm3.  How would you
  calculate the density?
• Density mass/volume 20g/10cm3 2g/cm3
• If you are given the mass and the density can you
  calculate volume?
• Yes!  Density mass/volume ? volume
  mass/density.

45
Graphing

• PRESENTING SCIENTIFIC DATA
• An important part of your lab write-up is the
  presentation of your data. You will commonly
  present data in tables and easy to read graphs.
• Line Graphs- best for continuous changes
• Generally compare 2 variables- one, Independent,
  the other, dependant.
• Graphs made with an x-axis (the independent
  variable) and a y-axis (the dependant variable)

46
Bar Graphs- to compare items/events

• Helps to make clearer how large or small the
  differences in individual values maybe.

47
Pie Charts- show parts of a whole

• Helps to show percentages () of a whole.