Honors: Chapter 3
Data Analysis
3.2 Temperature
What contains more heat?
a glass of boiling water or an iceberg
What does your body sense?
3.2 Temperature
Heat – type of energy transferred because of
a difference in temperature.
Can’t be measured directly
Temperature – measure of the average
kinetic energy of the particles in a sample of
matter.
Determines the direction of heat transfer
Heat moves from object of high temperature to
object at lower temperature
3.2 Temperature Scales
Fahrenheit (
F) – zero based on equal mix of
snow and ammonium chloride.
32
F = freezing point of water
212
F = boiling point of water
•
Celsius (
C) – based on water
0
C = freezing point of water
100
C = boiling point of water
3.2 Temperature Scales
Kelvin (K) - only temperature scale that is
proportional to the speed of the particles.
0 K = all particle motion stops
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The figure below compares the Celsius and Kelvin
scales.
The zero point on the Kelvin scale, 0 K, or absolute
zero, is equal to –273.15°C.
3.2 Temperature Scales
3.2 Temperature Conversion
t(K) = t(
C) + 273.15
•
t(
C) = t(K) – 273.15
What is 25.0
C (room temp.) in Kelvin?
3.1 Scientific Notation
Scientific notation
–provides a
convenient way to write very large and
small numbers
Written as a number (A), multiplied by 10
raised to an exponent (x)
(A) must be greater than 1 and less than 10
3.1 Scientific Notation
Understanding scientific notation
Exponent is always a whole number
When exponent is positive, decimal moves to the right
3.1 Scientific Notation
Convert the following into scientific notation:
0.00000025
9500
62.3
0.0425671
Convert the following into regular notation:
5.4 x 10
3
8.00006 x 10
-4
9.21 x 10
-2
6.54 x 10
92.5 x 10-7
9.5 x 103
6.23 x 101
4.25671 x 10-2
5400
0.000800006 0.0921
Scientific Notation and Calculators
Calculations using scientific notation should be entered in to your calculator using special keys. For example: To enter 1.82 x 103,
enter the data as follows:
1.82
PRESS DISPLAY
1.82
EE
3 1.82 03
1.82 00
Scientific Notation and Calculators
To enter numbers with a negative exponent such as 1.73 x 10-6 ,
enter the data as follows:
1.73
PRESS DISPLAY
1.73
EE
6 1.73 06
1.73 00
1.73 -06 + /
3.2 Units of Measurement
Which is bigger?
5 or 120
It depends upon the units!!!
5 quarters and 120 pennies
3.2 Units of Measurement –
English
1.
English – Developed from common use.
Lacks uniformity
Lacks coherency
Not easy to use
2.
Metric – Developed in France in 1795.
Simple base units
Interchangeable prefixes
Decimal (base 10) system
Metric Prefixes
Prefix
Symbol
Meaning
kilo- k hecto- h deca- da deci- d centi- c milli- m 1000
1 km = 1000 m 100
1 hm = 100 m 10
1 dam = 10 m .1
10 dm = 1 m .01
100 cm = 1 m .001
Making Metric You
Own
When you see
Think of
Liter (L) half a 2L pop
meter (m) inches longer than a yard stick
decimeter (dm) length of an audiocassette
centimeter (cm) thickness of an audiocassette
millimeter (mm) thickness of CD
kilometer (km) more than 1/2 a mile (about .6)
gram (g) mass of a paper clip
Using SI Units
These figures give you some idea
of the relative sizes of a liter and a
milliliter.
Units of Volume
1 mL
3.2 Units of Measurement –
History
3.
SI (International System of Units) –
Developed by scientists in 1960.
Only 7 fundamental units
Derived units based on fundamental units
3.2 Units of Measurement –
SI Base Units
Quantity
Unit
Symbol
Length meter m
Mass kilogram kg
Time second s
Temperature kelvin K
Amount of Substance mole mol
Electrical current ampere A
Quantity
Unit
Symbol
DerivationUnits
Area square meter m2 length
width m m
Volume cubic meter m3 length width
height m m m
Density kilogram per cubic meter kg/m3 mass
volume
kg
m3
Velocity meter per second m/s length/time ms
Force newton N (mass (time length) time) kg s2 m
Pressure pascal Pa forcearea mN = kg 2 m s2
Energy joule J force length N m =kg m
2 s2
3.2 Units of Measurement –
SI Derived Units
kilo- hecto deca- base unit deci- centi- (k) (h) (da) (d) (c) (m)
Meter (m) Liter (L)
Gram (g) Second (s)
1000 100 10 1/10 1/100 1/1000
kilo- hecto deca- base unit deci- centi- (k) (h) (da) (d) (c) (m)
Meter (m) Liter (L)
Gram (g) Second (s)
How many centigrams (cg) are in 5g?
1 2
=
5 g cg
g cg 1
100
500
There is 10
2or 100 cg in a g
.
kilo- hecto deca- base unit deci- centi- (k) (h) (da) (d) (c) (m)
Meter (m) Liter (L)
Gram (g) Second (s)
How many kilometers (km) are in 12 meters m?
1 2
3
=
12 m km
m km 1000 1
.012
Conversion Practice
•
Convert the following with the dimensional
analysis method:
–
0.015 m = ______ mm
–
9345 daL = _____ kL
–
52 mL = ________hL
–
0.34 cg = _______ g
–
0.87 dg = _______ mg
3.1 Measurements
Precision tells us how close the individual measurements
are to each other.
Precise measurements are very close to each other
Accuracy describes how close the measurement is to the
accepted value.
Accurate measurements are close to the accepted value
Measurements can be described as
Precise and accurate
Precise but not accurate
Neither precise nor accurate
Every measurement
requires us to estimate.
1 2 3
cm
Each division on this ruler is 1/10 cm = 1mm
.5
.5
The estimation depends on the
number of divisions on the device
We can only be certain about this measurement to the
If we were to measure the rod below we would be certain that it is at least 1.7 cm
1 2 3
cm
.5
.5
We can see that the rod is slightly longer
The measurement lies between 1.7 and 1.8
1 2 3
cm
.5
.5
Mentally divide this space into 10 equal
partitions
We are uncertain about the fraction between 1.7 and 1.8
so we must guess
1 2 3 cm
.5
.5
We can say that this measurement is 1.75 cm
1 2 3 cm
.5
.5
Note that another person could say
1 2 3 cm
.5
.5
Another might say 1.74 cm
1 2 3 cm
.5
.5
The uncertainty in this measurement is represented by
1.75 ±0.01 cm
By convention, the uncertainty in any measurement is represented
1 2 3 cm
.5
.5
There are three digits obtained from this measuring device: 1, 7 & 5. We say that there are “three significant digits” in this
measurement: 1.75 cm.
Significant digits (or significant figures): all numbers from
a measurement including one guessed digit.
1 2 3 cm
.5
.5
What are the lengths of the objects pictured below?
1 2 3 cm
.5
.5
What are the lengths of the objects pictured below?
0.73 cm has 2 significant figures
Remember, the ‘3’ is a guessed digit. This measurement may have been read as 0.72 or 0.75 cm. It is still more correct to add the guessed digit than to leave
it off.
This bar is slightly larger than 0.7 cm. It lies about 1/3 between 0.7 and 0.8 cm. We could say the length of the bar is 0.73 cm
1 2 3 cm
.5
.5
What are the lengths of the objects pictured below?
This bar is slightly larger than 2.9 cm. It lies about halfway between 2.9 and 3.0 cm. We could say the length of the bar is 2.95 cm
2.95 cm has 3 significant figures
Remember, the ‘5’ is a guessed digit. This measurement may have been read as 2.93 or 2.96 cm. It is still more correct to add the guessed digit than to leave
1 meter
What are the lengths of the objects pictured below?
Making Measurements
0.3 m
3
.9 m
1 2 3 cm
What are the lengths of the objects pictured below?
0.8 cm
Compare the two measurements below. Which is more precise?
1 2 3
cm
.5
.5
1 2 3
cm
2.95
cm
2.9
cm
Compare the two measurements below. Which is more precise?
The measurement 2.95 cm
has
three significant digits
The measurement 2.9 cm
has
two significant digits
2.95 cm
is more precise!
o Graduated cylinders are used for measuring liquids
o Water forms a “meniscus” or dip. Measurements are made at the bottom of the “dip”
o The measurement at the left
indicates at least 21.1mL but not quite 21.2mL.
o One must estimate (guess) how far from 21.1mL
o This measurement might be taken as 21.15mL
o Another person may have a
slightly different number 21.16 or
21.14mL! 20
22
21
Each line is an increment of 0.1 mL
21.15mL ± 0.01mL
Meniscus forms due to surface tension of water
20 22
21 mL
20 22
20.63mL ± .01
21.80mL ± .01
20 22
21 mL
20 22
21 mL
Using A Ruler
= 1.94 cm
= 3.00 cm
1 2 3
1 =
2 =
3 =
5.73 mL
3.0 mL
.35 mL
2.3 Measurement –
Significant Figures
Significant Figures
All of the known digits plus the estimated digit are
significant – they are not placeholders.
When we measured the volume of cylinder 1 on
the last slide we got:
5.73 mL
known estimated
100 200 300
100 200 300
Significant Figures
Number of
Quantity Certain Uncertain Significant Digits Digits Figures
14.379 g 1 4 3 7 9 (thousandths) 5 6.02 mL 6 0 2 (hundredths) 3
120.580 m 1 2 0 5 8 0 (thousandths) 6 7.5 g 7 5 (tenths) 2
0.037 g 3 7 (thousandths) 2 0.0370 g 3 7 0 (ten-thousandths) 3
*The position of the decimal point has nothing to do with the number of significant figures.
3.1 Measurement –
Significant Figures
Significant Figure Rules
1.
Every nonzero is significant.
123.2 g
2.
Zeros between nonzero digits are significant.
1004 m
3.
Zeros to left of nonzero are NOT significant.
0.01 g
4 sig figs
4 sig figs
1 sig figs
3.1 Measurement –
Significant Figures
4. Zeros to the right of nonzero digits are significant
ONLY when the decimal is shown.
12.00 m
1200. m
1200 m
1.20 ×103 m
5. Counting numbers and defined quantities have
unlimited significant digits.
3 gold atoms unlimited
1 hour = 60 minutes 1 and 60 unlimited
•
Is the decimal point
– Present (P in Pacific):
– Absent (A in Atlantic)
Atlantic
Ocean
Pacific
Ocean
Start on the right and count the first nonzero and every digit to
the left
Start on the left and count the first nonzero and every digit to the
right
0.0340 has 3 significant figures
340000 has 2 significant figures
3.1 Significant Figures in
Calculations
An answer can’t have more significance than
the measurements upon which it is based.
YOUR ANSWER IS ONLY AS GOOD AS
3.1 Significant Figures
How many sig figs are in the following
numbers?
3.0005
3.000
3000
3000.
2.30 x 10
-3
2.0000 x 10
-33.1 Significant Figures
Round the following to 3 sig figs.
3.0005
9.058
30005
2903682
2.309 x 10
-3
5.99 x 10
-33.1 Significant Figures in
Calculations
Addition Subtraction
Round your answer to the same number of
decimal places as your least significant number.
Think of it as the leftmost uncertainty. LINE UP
THE DECIMALS.
124.0 m + .12 m 420 m
544.12 m 540 m
3.1 Significant Figures in
Calculations
Multiplication and Division
Round answer to the same number of significant
digits as the measurement with the least number
of significant digits.
238.63 m × 12.0 m
2863.56 m2
5 3
3.1 Significant Figures in
Calculations
Addition and Subtraction Practice
5.8887 + 4.24
900.3 + 0.774
82.56-4.7372
Multiplication and Division
5.99 x 34
6 x 6.0
3.4543 x 10
3/ 6.02 x 10
233.2 Density
mass
volume
=
Density
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This figure compares the density of four
substances: lithium, water, aluminum, and lead.
3.2 Density
Increasing density (mass per unit volume)
10 g
0.53 g/cm3
19 cm3
10 g 10 cm3
10 g 3.7 cm3
10 g 0.88 cm3
3.2 Density - Problem
A piece of aluminum (density 2.7 g/mL) is added to a graduated cylinder with 12.4 mL of water in it. The volume of the water
rises to 19.5 mL, what is the mass of the aluminum?
(volume) (volume)
mass = (2.7 g/mL) × (19.5 mL – 12.4 mL)
mass = (2.7 g/mL)(7.1 mL)
mass = 19 g
volume mass Density
volume
density
3.1 How reliable are
Measurements?
Error (measuring experimental accuracy)
Error = experimental value – accepted value
Percent Error = error
accepted value
× 100
3.1 How reliable are
Measurements?
Experimentally, the boiling point of a substance is
found to be 99.12 °C. The actual value of the
substance is 100.0 °C. Find the error and percent
error of the measured value.
Error = experimental - accepted
=99.12 °C – 100.0 °C
= -.88 °C
% error = error
×
100
accepted
= -.9 °C
× 100
100.0 °C
= -.9%
99.12 °C
100.0 °C
- .88 °C
--.9 °C
Graphing
•
A
graph
is a visual display of data.
•
Using data to create a graph can help to
reveal a pattern if one exists.
Circle Graph
• A circle graph is
sometimes called a pie chart because it is divided into wedges like a pie or pizza.
• A circle graph is useful for showing parts of a fixed whole.
• The parts are usually
labeled as percents with the circle as a whole
Bar Graph
• A bar graph often is used to
show how a quantity varies with factors such as time, location, or temperature.
• In those cases, the quantity
being measured appears on the vertical axis (y-axis).
• The independent variable
appears on the horizontal axis (x-axis).
• The relative heights of the bars
show how the quantity varies.
Line Graph
• In chemistry, most graphs that you create and interpret will be line graphs.
• The points on a line graph represent the intersection of data for two variables.
• The dependent variable is plotted on the y-axis and the independent variable on the
x-axis.
• Remember that the
independent variable is the variable that a scientist
deliberately changes during
Line Graph
•
Sometimes points are
scattered, the line cannot
pass through all the data
points.
•
The line must be drawn so
that about as many points
fall above the line as fall
below it.
•
This line is called a best fit
line.
Line Graph
• If the best fit line is straight, there is a linear relationship
between the variables and the variables are directly related.
• This relationship can be further described by the steepness,
or slope, of the line.
• If the line rises to the right, the slope is positive.
• A positive slope indicates that the
Line Graph
•
If the line sinks to the right, the slope is
negative
.
•
A negative slope
indicates that the
dependent variable
decreases as the
independent
variable increases.
Line Graph
•
Either way, the slope of the graph is constant.
You can use the data points to calculate the
slope of the line.
•
The slope is the change in
y
divided by the
Interpreting Graphs
•
An organized approach can help you
understand the information on a graph.
• First, identify the independent and dependent variables.
• Look at the ranges of the data and consider
what measurements were taken.
• Decide if the relationship between the
variables is linear or nonlinear.
• If the relationship is linear, is the slope
positive or negative?
• If a graph has multiple lines or regions, study
one area at a time.
