Download Chapter 3 Scientific Measurement

Chapter 3
“Scientific
Measurement”
Olympic High School
Chemistry - Mr Daniel
Credits: Stephen L. Cotton
Charles Page High School
Section 3.1
Measurements and Their
Uncertainty
OBJECTIVES:
 Convert measurements to scientific
notation.
Section 3.1
Measurements and Their
Uncertainty
OBJECTIVES:
 Distinguish among accuracy, precision,
and error of a measurement.
Section 3.1
Measurements and Their
Uncertainty
OBJECTIVES:
 Determine the number of significant figures
in a measurement and in a calculated
answer.
Measurements

Qualitative measurements are descriptive
words, such as “heavy” or “warm”
 Quantitative measurements involve
numbers (quantities), and depend on:
1) The reliability of the measuring instrument
2) the care with which it is read – this is
determined by YOU!
Accuracy, Precision, and Error
It is necessary to make good, reliable
measurements in the lab
 Accuracy – how close a measurement is to the
true value
 Precision – how close multiple measurements
are to each other (reproducibility)
Precision and Accuracy
Neither
accurate
nor precise
Precise,
but not
accurate
Precise
AND
accurate
Accuracy, Precision, and Error
Error = accepted value – experimental value
Can be positive or negative


Accepted value = the correct value based
on reliable references
Experimental value = the value measured
in the lab
Accuracy, Precision, and Error
Percent error = the absolute value of the
error divided by the accepted value,
then multiplied by 100.
accepted (true) value
% error =
| error |
accepted value
x 100
Chemistry
“Scientific Notation
Review”
Olympic High School
Mr. Daniel
1. Scientific Notation
…Is also called Exponential Notation
Scientists often use very large or very small
numbers
 602 000 000 000 000 000 000 000
Called Avogadro’s Number
 0.000 000 000 114 m
The radius of a bromine atom
1. Scientific Notation
Large numbers are very inconvenient, even difficult
Thus, very large or small numbers should be
written in Scientific Notation

In Scientific Notation, the number is the product
of two different components:
 A coefficient
 Exponent: A power of 10
1. Scientific Notation
2300 is: 2.3 x 103
A coefficient is a number greater than or equal to
one, and less than ten
 The coefficient here is 2.3
The exponent is how many times the coefficient is
multiplied by ten…
The product of 2.3 x 10 x 10 x 10 equals 2300 (2.3
x 103)
1. Scientific Notation
The value of the exponent changes to
indicate the number of places the decimal
has moved left or right.
12 000 000 = 1.2 x 107
0.00356 = 3.56 x 10-3
85 130 = 8.513 x 104
0.000 05 = 5 x 10-5
0.0342 = 3.42 x 10-2
1. Scientific Notation
Multiplication and Division
 Use of a calculator is permitted
 use it correctly
 No
calculator? Multiply the coefficients, and
add the exponents:
(3 x 104) x (2 x 102) = 6 x 106
(3.5 x 106) x (4.0 x 1012) = 1.4 x 1019
1. Scientific Notation
Multiplication and Division
• In division, divide the coefficients, and
subtract the exponent in the denominator
from the numerator
3.0 x 105
6.0 x 102
=
5 x 102
1. Scientific Notation
•Addition and Subtraction
•Before numbers can be added or
subtracted, the exponents must be the
same
•Calculators will take care of this
•Doing it manually, you will have to
make the exponents the same - it does
not matter which one you change.
1. Scientific Notation
•Addition and Subtraction
(6.6 x
10-8)
(3.42 x
+ (4.0 x
-5
10 )
10-9)
– (2.5 x
=
-6
10 )
7.0 x 10-8
= 3.2 x 10-5
(Note that these answers have
been expressed in standard form)
Why Is there Uncertainty?
Measurements are performed with instruments,
and no instrument can read to an infinite number
of decimal places
•Which of the balances shown has the greatest
uncertainty in measurement?
Significant Figures!!
Significant Figures in
Measurements

Significant figures in a measurement
include all of the digits that are known, plus
one more digit that is estimated.
 Measurements must be reported to the
correct number of significant figures.
Figure 3.5 Significant Figures - Page 67
Which measurement is the best?
What is the
measured value?
What is the
measured value?
What is the
measured value?
Rules for Counting
Significant Figures
Non-zeros always count as
significant figures:
3456 km has
4 significant figures
Rules for Counting
Significant Figures
Zeros
Captive zeros always count as
significant figures:
16.07 cm has
4 significant figures
Rules for Counting
Significant Figures
Zeros
Leading zeros never count as
significant figures:
0.0486 mL has
3 significant figures
Rules for Counting
Significant Figures
Zeros
Trailing zeros are significant only if the
number contains a written decimal point:
9.300 g has 4 significant figures
9300 g has 2 significant figures
9300. g has 4 significant figures
Rules for Counting
Significant Figures
Two special situations have an unlimited
number of significant figures:
1. Counted items
a) 23 people, or 425 thumbtacks
2. Exactly defined quantities
b) 60 minutes = 1 hour
Sig Fig Practice #1
How many significant figures in the following?
1.0070 m  5 sig figs
17.10 kg  4 sig figs
100,890 L 
5 sig figs
3.20 x 103 s  3 sig figs
0.0054 cm 
2 sig figs
3,200,000 g 
5 dogs 
2 sig figs
unlimited
These come
from
measurements
This is a
counted value
Significant Figures in
Calculations
 A calculated answer is only as accurate as
the least accurate measurement from which
it is calculated.
Just like a chain which is only as strong as the
weakest link…
…sometimes, calculated values need to be
rounded off.
Rounding Calculated
Answers
 A quick reminder about Rounding




Determine how many significant figures are
needed
Locate that final digit by counting from the left
Is the next digit to the right less than 5?
 No change to the final digit
Is the next digit to the right 5 or greater?
 Increase the final digit by 1
- Page 59
Round off each measurement to the number of
significant figures shown in parentheses:
a) 314.721 meters (four)
314.7 meters
b) 0.001775 meter (two)
0.0018 meter
c) 8792 meters (two)
8800 meters
Rules for Significant Figures in
Mathematical Operations
Multiplication and Division: The number of
significant figures in an answer equals
the number in the least accurate
measurement used in the calculation.
6.38 cm x 2.0 cm = 12.76 cm2
sigfig answer : 13 cm2 (2 sig figs)
Sig Fig Practice #2
Calculation
3.24 m x 7.0 m
Calculator says:
22.68 m2
Answer
23 m2
100.0 g ÷ 23.7 cm3 4.214409283 g/cm3 4.21 g/cm3
0.02 cm x 2.371 cm 0.04742 cm2
710 m ÷ 3.0 s
236.6666667 m/s
0.05 cm2
240 m/s
1818.2 lb x 3.23 ft 5871.786 lb·ft
5870 lb·ft
1.030 g x 2.87 mL 2.9561 g/mL
2.96 g/mL
Rules for Significant Figures in
Mathematical Operations
Addition and Subtraction: The number
of decimal places in the answer equals
the number of decimal places in the
least accurate measurement.
6.8 cm +11.934 cm = 18.734 cm
sigfig answer  18.7 cm (3 sig figs)
Sig Fig Practice #3
Calculation
Calculator says:
Answer
3.24 m + 7.0 m
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.
Section 3.3
The International System of Units
OBJECTIVES:
 List SI units of measurement and common
SI prefixes.
 Distinguish between the mass and weight
of an object.
 Convert between the Celsius and Kelvin
temperature scales.
International System of Units
 Measurements depend upon units that serve
as reference standards
 The Metric system was first introduced by the
French following the French Revolution
 It was revised and renamed the International
System of Units (SI), as of 1960.
 The standards of measurement used in
science are those of the SI.
International System of Units
SI has several advantages:
-Used world-wide
-Simple
-Based on powers of 10
 There are eight base units which are
commonly used in chemistry: meter, cubic
meter, kilogram, kelvin, second, joule,
pascal and mole.
The Fundamental SI Units
(Le Système International, SI)
(Liter)
(gram)
(ºCelsius)
(calorie)
Nature of Measurements
Measurement - quantitative observation
consisting of 2 parts:
1 ) number
2 ) unit
Examples:
20 grams
6.63 x 10-34 joules-seconds
International System of Units
Derived units: These are not measured directly,
but are calculated, showing the relationship
between two other measurements:
 Speed = miles/hour (distance/time)
 Density = grams/mL (mass/volume)
Length
 In SI, the basic unit of length is the meter (m)
The meter is one ten millionth (0.000 000 1 ) the
distance from the equator to the North Pole.
 Or more accurately for the 21st century:
1 meter equals 1,650,763.73 wavelengths of
light given off from an isotope of Krypton…

We make use of prefixes for units larger or smaller…
SI Prefixes Common to Chemistry
Prefix
Unit
Meaning Exponent
Abbreviation
Kilo-
k
thousand
103
Deci-
d
tenth
10-1
hundredth
10-2
Centi-
Learn
These!!!
c
Milli-
m
thousandth
10-3
Micro-

millionth
10-6
Nano-
n
billionth
10-9
Pico-
P
Trillionth
10-12
Converting Measurements in the SI
e.g. 1.2 mm=
µm
1) Mark the value of prefixes of both units
10-6
10-3
1.2 mm=
µm
2) Determine the difference in the number of
place values of the two prefixes by subtracting.
This is how many places the decimal is to be
moved.
-3-(-6) = +3
Converting Measurements in the SI
(continued)
3) If the difference is a positive number, move
the decimal place to the right to make the
numerical value larger
If the difference is a negative number, move
the decimal place to the left to make the
numerical value smaller
The difference is positive (+3) therefore 1.2
becomes 1200
The final answer is 1200 µm
Volume
 The space occupied by any sample of matter.
 Calculated for a solid by multiplying the length x
width x height; thus derived from units of length.
 SI unit = cubic meter (m3)
 Everyday unit = Liter (L), which is non-SI.
Note: 1000mL = 1 L
1mL = 1cm3
Devices for Measuring Liquid
Volume
 Graduated cylinders
 Pipets
 Burets
 Volumetric Flasks
 Syringes
The Volume Changes!
 Volumes of a solid, liquid, or gas will
generally increase with temperature
 Therefore, measuring instruments are
calibrated for a specific temperature, usually
20 oC, which is about room temperature
Units of Mass
 Mass is a measure of the quantity of matter
present

Mass is constant, regardless of location
Weight is a force that measures the pull by
gravity- it changes with location
Working with Mass
 The SI unit of mass is the kilogram (kg),
even though a more convenient everyday unit
is the gram
 It’s measuring instrument is the balance
Units of Temperature
Temperature is a measure of how hot or cold
an object is based upon the kinetic energy
(movement) of the atoms. (Measured with
a thermometer.)
Heat is a form of energy which moves from
objects at higher temperatures to objects at
lower temperatures.
Temperature Units
We use two units of temperature:
 Celsius – named after Anders Celsius
 Kelvin – named after Lord Kelvin
Units of Temperature
Celsius scale is defined by two readily
determined temperatures:
 Freezing point of water = 0 oC
 Boiling point of water = 100 oC
Kelvin scale is based on the concept of
Absolute Zero: the point at which there is no
atom movement
•
absolute zero = 0 K
(thus no negative values)
Temperature Continued…
•
Kelvin does not use the degree sign,
but is just represented by K
•
The formulas to convert between
Kelvin and Celsius:
• K = oC + 273
• oC = K - 273
Units of Energy
Energy is the capacity to do work, or to
produce heat.
Energy can also be measured, and two
common units are:
1) Joule (J) = the SI unit of energy, named
after James Prescott Joule
2) calorie (cal) = the heat needed to raise 1
gram of water by 1 oC
Units of Energy
Conversions between joules and calories can
be carried out by using the following
relationship:
1 cal = 4.184 J
Density
 Which is heavier- a kilogram of lead or a
kilogram of feathers?
 Many people will answer lead, but the
weight is exactly the same
 They are normally thinking about equal
volumes of the two
 The relationship here between mass and
volume is called density
Section 3.4
Density
OBJECTIVES:
 Calculate the density of a material
from experimental data.
 Describe how density varies with
temperature.
Density
 The formula for density is:
Density =
• units used:
Mass
Volume
g/mL (g/cm3)
g/L for gases
• Density is a physical property which does
not depend upon sample size (intensive
property)
- Page 90
Note temperature and density units
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
temperature increases
 Thus, density generally decreases as the
temperature increases
Density and Water
 Water is an important exception to the
previous statement.
 Over certain temperatures, the volume of
water increases as the temperature
decreases (Do you want your water pipes to
freeze in the winter?)
 Does ice float in liquid water?
 Why?
- Page 91
- Page 92