Post on 07-Apr-2018
transcript
8/6/2019 Chap02 Scientific Measurement
1/66
CHEMISTRYWorld of
8/6/2019 Chap02 Scientific Measurement
2/66
Chapter 2
MeasurementMeasurement
s ands and
CalculationsCalculations
8/6/2019 Chap02 Scientific Measurement
3/66
Scientific Notation
Scientific notation works by expressing very small
or very large numbers as the product of two
numbers that are individually much easier to deal
with.
The first numberis called the base.
The second numberis a power of ten.
The base is usually written with only one digit in
front of the decimal point. ex. 2,500 would be written 2.5 103
The small numeral 3 in 103 is called the
exponent.
8/6/2019 Chap02 Scientific Measurement
4/66
Accuracy and Precision
accuracy is the quality ofbeing exact and free from error.
how close a measurement is to the true value.
precision
is the degree ofmutual agreement among aseries ofindividual measurements, values, or
results.
8/6/2019 Chap02 Scientific Measurement
5/66
Wh
y Is th
ere Uncertainty? Measurements are performed with
instruments, and no instrument can read to an
infinite number of decimal places
8/6/2019 Chap02 Scientific Measurement
6/66
Significant Figures
Which measurement is the best?
What is the
measured
value?
What is the
measured
value?
What is the
measured
value?
8/6/2019 Chap02 Scientific Measurement
7/66
Significant Figures in
Measurements
Significant figures in a
measurement include all ofthe digits that are known,
plus one more digit that is
estimated. Measurements must be
reported to the correct
n m r f i nifi n
8/6/2019 Chap02 Scientific Measurement
8/66
Rules for Counting Significant
Figures
NonNonzeroszeros always count asalways count as
significant figures:significant figures:
34563456 hashas44 significant figuressignificant figures
8/6/2019 Chap02 Scientific Measurement
9/66
Rules for Counting Significant
Figures
Zeros
Leading zeroes do notcount as significant
figures:
0.0486 has
3 significant figures
8/6/2019 Chap02 Scientific Measurement
10/66
Rules for Counting Significant
FiguresZeros
Captive zeroes always
count as significant
figures:
16.07 has
4 significant figures
8/6/2019 Chap02 Scientific Measurement
11/66
Rules for Counting Significant
FiguresZeros
Trailing zeros are
significant only if the
number contains a
written decimal point:
9.300 has
4 si nificant fi ures
8/6/2019 Chap02 Scientific Measurement
12/66
Rules for Counting Significant
Figures
Two special situations have an
unlimited number ofsignificant figures:
1. Counted items
a) 23 people, or 425 thumbtacks2. Exactly defined quantities
b) 60 minutes = 1 hour
8/6/2019 Chap02 Scientific Measurement
13/66
Sig Fig Practice #1How many significant figures in the following?
1.0070 m 5 sig figs
17.10 kg 4 sig figs
100,890 L 5 sig figs
3.29 x 103 s 3 sig figs
0.0054 cm 2 sig figs3,200,000 mL 2 sig figs
5 dogs unlimited
These all come
from some
measurements
This is a
counted value
8/6/2019 Chap02 Scientific Measurement
14/66
Significant Figures inCalculations
In general a calculated answer
cannot be more precise than
the least precise measurement
from which it was calculated.
Sometimes, calculated values
need to be rounded off.
8/6/2019 Chap02 Scientific Measurement
15/66
Rounding Calculated
Answers Rounding Decide how many significant
figures are needed (more on thisvery soon)
Round to that many digits,
counting from the left
Is the next digit less than 5?
Drop it.
8/6/2019 Chap02 Scientific Measurement
16/66
Rounding Calculated
Answers Addition and Subtraction
The answer should berounded to the same
number of decimal places
as the least number ofdecimal places in the
problem.
8/6/2019 Chap02 Scientific Measurement
17/66
Rounding Calculated
Answers
Multiplication and Division
Round the answer to thesame number of
significant figures as theleast number of
significant figures in the
roblem.
8/6/2019 Chap02 Scientific Measurement
18/66
Rules for Significant Figures inRules for Significant Figures in
Mathematical OperationsMathematical Operations
Multiplication andMultiplication and
DivisionDivision: # sig figs in the: # sig figs in the
result equals the number inresult equals the number in
thethe least preciseleast precise
measurement used in themeasurement used in thecalculation.calculation.
6.38 x 2.0 =6.38 x 2.0 =
12.7612.76 1313 2 si fi s2 si fi s
8/6/2019 Chap02 Scientific Measurement
19/66
Sig Fig Practice #2
3.24 m x 7.0 mCalculation Calculator says: Answer
22.68 m2 23 m2
100.0 g 23.7 cm3 4.219409283 g/cm3 4.22 g/cm3
0.02 cm x 2.371 cm 0.04742 cm2 0.05 cm2
710 m 3.0 s 236.6666667 m/s 240 m/s
1818.2 lb x 3.23 ft 5872.786 lbft 5870 lbft
1.030 g x 2.87 mL 2.9561 g/mL 2.96 g/mL
8/6/2019 Chap02 Scientific Measurement
20/66
Rules for Significant Figures inRules for Significant Figures in
Mathematical OperationsMathematical Operations
Addition and SubtractionAddition and Subtraction::
The number of decimalThe number of decimal
places in the result equalsplaces in the result equalsthe number of decimalthe number of decimal
places in theplaces in the least preciseleast precise
measurement.measurement.
6.8 + 11.934 = 18.7346.8 + 11.934 = 18.734 18.718.7(3 sig figs)(3 sig figs)
8/6/2019 Chap02 Scientific Measurement
21/66
Sig Fig Practice #3
3.24 m + 7.0 mCalculation Calculator says: Answer
10.24 m 10.2 m
100.0 g - 23.73 g 76.27 g 76.3 g
0.02 cm + 2.371 cm 2.391 cm 2.39 cm
713.1 L - 3.872 L 709.228 L 709.2 L
1818.2 lb + 3.37 lb 1821.57 lb 1821.6 lb
2.030 mL - 1.870 mL 0.16 mL 0.160 mL
*Note the zero that has been added.
8/6/2019 Chap02 Scientific Measurement
22/66
Two Systems of Units
Science problem solving requires both:
Metric system
English system
8/6/2019 Chap02 Scientific Measurement
23/66
International System of
Units
Measurements depend upon
units that serve asreference standards
The standards ofmeasurement used in
science are those of the
Metric S stem
8/6/2019 Chap02 Scientific Measurement
24/66
International System of
UnitsMetric system is now revised andnamed as the International
System of Units (SI), as of 1960
It has simplicity, and is based on10 or multiples of 10
7 base units, but only fivecommonly used in chemistry: meter,kilogram, kelvin, second, and mole.
8/6/2019 Chap02 Scientific Measurement
25/66
8/6/2019 Chap02 Scientific Measurement
26/66
Measurements
Part 1Part 1
numbernumber Part 2Part 2 scale (unit)scale (unit)
Examples:Examples:20 grams20 grams
6.636.63 x 10x 103434 JouleJoule
Measurement quantitativeobservationconsisting of 2 parts:
8/6/2019 Chap02 Scientific Measurement
27/66
International System ofUnitsSometimes, non-SI units are used
Liter, Celsius, calorieSome are derived units
They are made by joining other
units Speed = miles/hour
(distance/time)
Densit = rams/mL
8/6/2019 Chap02 Scientific Measurement
28/66
Distance and Length
Key Question:
How do we accurately communicate length and
distance?
8/6/2019 Chap02 Scientific Measurement
29/66
Distance and Length
measurement -
a quantity and a unit
distance - is a length
the amount of space
between two points
8/6/2019 Chap02 Scientific Measurement
30/66
LengthIn SI, the basic unit of length is
the meter(m) Length is the distance
between two objects
measured with rulerWe make use of prefixes for
units larger or smaller
8/6/2019 Chap02 Scientific Measurement
31/66
8/6/2019 Chap02 Scientific Measurement
32/66
Units of Length
The common units ofmeasurement in the
English system are inches, feet, yards, and
miles.These four length units are related to the meter.
8/6/2019 Chap02 Scientific Measurement
33/66
Convert length
Afootball field is 100 yards long.
What is this distance expressed in meters?
8/6/2019 Chap02 Scientific Measurement
34/66
Knot (unit)knot is a unit ofspeed equal to one nautical
mile (which is defined as 1.852 km) per hour,
approximately 1.151 mph
kn is preferred by the International Hydrographic
Organization (IHO), which includes every major sea-
faring nation; however, the abbreviations kt (singular)
and kts (plural) are also widely used
is a non-SI unit accepted for use with
the International System ofUnits
8/6/2019 Chap02 Scientific Measurement
35/66
1 international Knot =1 international Knot =
1 nautical mile per hour
1.852 kilometres per
hour (exactly),
0.514 metres per second,1.151 miles per hour
(approximately).
8/6/2019 Chap02 Scientific Measurement
36/66
KNOTS
The U.S. adopted theinternational definition in
1954, having previously used
the U.S. nautical mile(1,853.248 m).
The U.K. adopted the
international nautical miledefinition in 1970, having
previously used the U.K.
Admiralt nautical mile
8/6/2019 Chap02 Scientific Measurement
37/66
Conversions between common units of speed
m/s km/h mph knot ft/s
1 m/s = 1 3.6 2.236936 1.943844 3.280840
1 km/h = 0.277778 1 0.621371 0.539957 0.911344
1 mph = 0.44704 1.609344 1 0.868976 1.466667
1 knot = 0.514444 1.852 1.150779 1 1.687810
1 ft/s = 0.3048 1.09728 0.681818 0.592484 1
8/6/2019 Chap02 Scientific Measurement
38/66
8/6/2019 Chap02 Scientific Measurement
39/66
Volume
The space occupied by any sampleof matter.
Calculated for a solid by
multiplying the length x width xheight; thus derived from units of
length.
SI unit = cubic meter (m3)Everyday unit = Liter (L), which is
nonSI. (Note: 1mL = 1cm3)
8/6/2019 Chap02 Scientific Measurement
40/66
Time
Key Question:
How do we measure and describe time?
8/6/2019 Chap02 Scientific Measurement
41/66
Time
T i ime:W ime i i
. . e Time il
, ,H m ime e
: mi : e .
i ime i e
lle ime i e l.
8/6/2019 Chap02 Scientific Measurement
42/66
Time Units
8/6/2019 Chap02 Scientific Measurement
43/66
Measuring Mass
kilogram -
is the mass of1 liter
ofwater or 1,000
cubiccentimeters of
water.
8/6/2019 Chap02 Scientific Measurement
44/66
Units of Mass
Mass is a measure of thequantity of matter present
eight is a force thatmeasures the pull by
gravity it changes with
location
Mass is constant, regardless of
location
8/6/2019 Chap02 Scientific Measurement
45/66
Working with MassThe SI unit of mass is the
kilogram (kg), even though amore convenient everyday
unit is the gram
Measuring instrument is the
balance scale
8/6/2019 Chap02 Scientific Measurement
46/66
Units of Temperature
Temperature is a measure of how
hot or cold an object is.
eat moves from the object at thehigher temperature to the object
at the lower temperature.
We use two units of temperature:Celsius named after Anders Celsius
Kelvin named after Lord Kelvin
(Measured with
a
thermometer.)
8/6/2019 Chap02 Scientific Measurement
47/66
Units of Temperature
Celsius scale defined by tworeadily determinedtemperatures:
Freezing point of water = 0 oCBoiling point of water = 100 oC
Kelvin scale does not use thedegree sign, but is justrepresented by K
absolute zero = 0 K(thus no
ne a ive value
8/6/2019 Chap02 Scientific Measurement
48/66
8/6/2019 Chap02 Scientific Measurement
49/66
Units of Energy
Energy is the capacity to dowork, or to produce heat.
Energy can also be measured,and two common units are:
1) Joule (J) = the SI unit of
energy, named after JamesPrescott Joule
2) calorie (cal) = the heat needed
to raise 1 gram of water by 1 oC
8/6/2019 Chap02 Scientific Measurement
50/66
Units of EnergyConversions between
joules and calories can becarried out by using the
following relationship:
1 cal = 4.18 J(sometimes you will see 1 cal = 4.184 J)
8/6/2019 Chap02 Scientific Measurement
51/66
Conversion factors
A unique way of writing thenumber 1
In the same system they are
defined quantities so they have an
unlimited number of significant
figures
Equivalence statements always
have this relationship:
big # small unit = small # big unit
8/6/2019 Chap02 Scientific Measurement
52/66
Conversion factorsC
onversion factors
100 cm1 m =100 cm 100 cm
8/6/2019 Chap02 Scientific Measurement
53/66
Conversion factorsConversion factors
11 m =
100 cm
8/6/2019 Chap02 Scientific Measurement
54/66
Conversion factorsConversion factors
11 m =100 cm
100 cm=1 m
1 m 1 m
8/6/2019 Chap02 Scientific Measurement
55/66
Conversion factorsConversion factors
11 m =100 cm
100 cm=
1 m1
8/6/2019 Chap02 Scientific Measurement
56/66
Conversion factorsCalle conversion factors
eca se t e allo s toconvert nits.
reall j st lti l inone, in a creative
a .
Di i l
8/6/2019 Chap02 Scientific Measurement
57/66
Dimensional
AnalysisA way to analyze and solveproblems, by using units (or
dimensions) of the
measurement
Dimension = a unit (such as g,
L, mL)Analyze = to solveUsing the units to solve the
problems.
Di i l A l i
8/6/2019 Chap02 Scientific Measurement
58/66
Dimensional AnalysisDimensional Analysis provides analternative approach to problemsolving, instead of with anequation or algebra.
A ruler is 12.0 inches long. owlong is it in cm? ( 1 inch = 2.54 cm)
ow long is this in meters?
A race is 10.0 km long. ow far isthis in miles, if:
1 mile = 1760 yards
1 meter = 1.094 yards
8/6/2019 Chap02 Scientific Measurement
59/66
Density
Which is heavier a pound of leador a pound of feathers?
Most people will answer lead, butthe weight is exactly the same
They are normally thinking about
equal volumes of the twoThe relationship here betweenmass and volume is called Density
8/6/2019 Chap02 Scientific Measurement
60/66
DensityThe formula for density is:
mass
volumeCommon units are: g/mL, or
possibly g/cm3
, (or g/L forgas)
Density is a physical property,
and does not de end u on
Density
=
8/6/2019 Chap02 Scientific Measurement
61/66
- Page 90Note temperature and density units
8/6/2019 Chap02 Scientific Measurement
62/66
Density and Temperature
What happens to the density as
the temperature of an object
increases?
Mass remains the same
Most substances increase in
volume as temperatureincreases
Thus, density generally
decreases as the
8/6/2019 Chap02 Scientific Measurement
63/66
Density and Water
Water is an importantexception to the previousstatement.
Over certain temperatures,the volume of water increasesas the temperature decreases(Do you want your water pipesto freeze in the winter?)
Does ice float in liquid water?
8/6/2019 Chap02 Scientific Measurement
64/66
Ice floats in liquid water
because hydrogen bonds
more ordered, making
ice less dense
8/6/2019 Chap02 Scientific Measurement
65/66
Ice vs. Liquid Water
8/6/2019 Chap02 Scientific Measurement
66/66