Transcript Scientific Measurement

Chemistry 1 – McGill
Chapter 3
Scientific Measurement
3.1
Qualitative measurements
– measurements that give results in a descriptive,
non-numerical form.
Examples:
He is tall
Electrons are tiny
Quantitative measurements
–measurement that gives results in a
definite form, usually as numbers
and units.
Examples:
He is 2.2 m tall
Electrons are 1/1840
times the mass of a
proton
What is Scientific Notation?
• Scientific notation is a way of
expressing really big numbers or
really small numbers.
• It is most often used in “scientific”
calculations where the analysis
must be very precise.
• For very large and very small
numbers, scientific notation is
more concise.
Scientific notation consists of
two parts:
• A number between 1 and 10
• A power of 10
Nx
x
10
To change standard form to
scientific notation…
• Place the decimal point so that there is one nonzero digit to the left of the decimal point.
• Count the number of decimal places the decimal
point has “moved” from the original number.
This will be the exponent on the 10.
• If the original number was less than 1, then the
exponent is negative. If the original number
was greater than 1, then the exponent is
positive.
Scientific Notation
–a number is written as the product
of two numbers: a coefficient and
10 raised to a power.
Examples:
567000 = 5.67 X 105
0.00231 = 2.31 X 10-3
Examples:
Convert to or from Scientific
Notation:
241
6015
.0162
.512
6.62 x 102
3.4 x 10-3
=
=
=
=
=
=
2.41 x 102
6.015 x 103
1.62 x 10-2
5.12 x 10-1
662
.0034
Learning Check
• Express these numbers in
Scientific Notation:
1)
2)
3)
4)
5)
405789
0.003872
3000000000
2
0.478260
4.05789 X 105
3.872 X 10-3
3 X 109
2 X 100
4.78260 X 10-1
Scientific Notation Cont.
(This is important to master!!!)
FYI: “EE” button on calc= typing “X10^”
6.25 x 103 - 2.01 x 102 = 6.05 x 103
(2.15 x
103)(6.1
3.25 x 108
3.6 x 107
x
105)(5.0
= 9.03
x
10-6)
3
6.6
x
10
=
Accuracy Vs. Precision
What do you
think the
differences are?
Ideas anyone???
3.2
Accuracy
–the measure of how close a
measurement comes to the actual or
true value of whatever is measured.
–how close a measured value is to the
accepted value.
Precision
–the measure of how close a series of
measurements are to one another.
Can you hit the bull's-eye?
Three targets
with three
arrows each to
shoot.
How do
they
compare?
Both
accurate
and precise
Precise
but not
accurate
Neither
accurate
nor precise
Can you define accuracy and precision?
Let’s use a golf analogy
Accurate? No
Precise? Yes
10
Accurate? Yes
Precise? Yes
12
Precise?
No
Accurate? Maybe?
13
Accurate? Yes
Precise? We cant say!
18
In terms of measurement
• Three students measure the
room to be 10.2 m, 10.3 m
and 10.4 m across.
• Were they precise?
• Were they accurate?
Percent Error Formula:
% Error =
accepted value- experimental value
accepted value
x 100
*always a positive number- indicated by the
absolute value sign*
You will use this formula when checking
the accuracy of your experiment.
Significant Figures – includes all
of the digits that are known plus a
last digit that is estimated.
FYI: These rules are not fun, but they will
save you many points in the future if you learn
them NOW!
Rules for determining
Significant Figures
1. All non-zero digits are significant.
1, 2, 3, 4, 5, 6, 7, 8, 9
2. Zeros between non-zero digits are
significant. (AKA captive zeros)
102
7002
3. Leading zeros (zeros at the
beginning of a measurement) are
NEVER significant.
0.0152
00542
4. Trailing zeros (zeros after last
integer) are significant only if the
number contains a decimal point.
210.0
0.860
210
5. All digits are significant in
scientific notation.
2.1 x 10-5
6.02 x 1023
Exact numbers have unlimited
Significant Figures
Do not use
these when
you are
figuring out
sig figs…
Examples:
1 dozen = exactly 12
29 people in this room
Examples:
How many significant digits do each of
the following numbers contain:
a) 1.2
b) 2.0
c) 3.002
2
2
4
d) 4600
2
e) 23.450
5
f) 6.02 x 1023
3
Learning Check
A. Which answers contain 3 significant figures?
1) 0.4760
2) 0.00476 3) 4760
B. All the zeros are significant in
1) 0.00307
2) 25.300
3) 2.050 x 103
C. 534,675 rounded to 3 significant figures is
1) 535
2) 535,000
3) 5.35 x 105
Solution
A. Which answers contain 3 significant figures?
1) 0.4760
2) 0.00476
3) 4760
B. All the zeros are significant in
1) 0.00307
2) 25.300
3) 2.050 x 103
C. 534,675 rounded to 3 significant figures is
1) 535
2) 535,000
3) 5.35 x 105
Learning Check
In which set(s) do both
numbers contain the same
number of significant figures?
1) 22.0 and 22.00
2) 400.0 and 40
3) 0.000015 and 150,000
Solution
In which set(s) do both
numbers contain the same
number of significant figures?
3) 0.000015 and
150,000
Learning Check
State the number of significant figures in each
of the following:
A. 0.030 m
1
2
3
B. 4.050 L
2
3
4
C. 0.0008 g
1
2
4
D. 3.00 m
1
2
3
E. 2,080,000 bees
3
5
7
Learning Check
State the number of significant figures in
each of the following:
A. 0.030 m
1
2
3
B. 4.050 L
2
3
4
C. 0.0008 g
1
2
4
D. 3.00 m
1
2
3
E. 2,080,000 bees
3
5
7
Rounding Rules:
 5 round up
< 5 round down (don’t change)
Examples:
Round 42.63 to 1 significant digit = 40
Round 61.57 to 3 sig. digs. =
61.6
Round 0.01621 to 2 = 0.016
Round 65,002 to 2 sig. digs. = 65,000
Addition and
Subtraction
The measurement with the
fewest significant figures to
the right of the decimal point
determines the number of
significant figures in the
answer.
Examples:
Solve using correct significant figures
45.756 m
+
75.263 m
+
62.1 m
=
1123.93 m
107.9
= 1199.19
Multiplying and Dividing
Measurements
The measurement with the
fewest significant figures
determines the number of
significant figures in the
answer.
Examples:
Solve using correct significant figures:
3.43 m
45.756 m
X
22.0 m2
6.4253 m =
X
1.2 m =
45.01 m / 2.2 m =
***Why did the “m” unit go away on
the last example?***
55 m2
20.
Notice the
decimal!
Uncertainty
In lab, you record all numbers you
know for sure plus the first uncertain
digit. The last digit is estimated and
is said to be uncertain but still
considered significant.
Graduated cylinders have markings to the
nearest mL (milliliter) and you will
determine volume to the nearest 0.1 mL…
because that is ONE DIGIT OF
UNCERTAINTY.
International System of Units
• revised version of the metric system
• abbreviated SI
All units, their meanings and values can
be found on pgs. 63,64,65.
Meter (m) – SI unit for length
Liter (L) – SI unit for volume
Gram (g) –
SI unit for mass
Some Tools for
Measurement
Which tool(s)
would you use
to measure:
A. temperature
B. volume
C. time
D. weight
Solution
A. temperature thermometer
B. volume
measuring cup,
graduated cylinder
C. time
watch
D. weight
scale
Learning Check
Match
L) length
M) mass
V) volume
M A.
____
A bag of tomatoes is 4.6 kg.
L B.
____
A person is 2.0 m tall.
M C.
____
A medication contains 0.50 g Aspirin.
V D.
____
A bottle contains 1.5 L of water.
Learning Check
What are some U.S. units that
are used to measure each of
the following?
A. length
B. volume
C. weight
Solution
Some possible answers are
A. length
inch, foot, yard, mile
B. volume cup, teaspoon, gallon, pint, quart
C. weight ounce, pound (lb), ton
D. temperature F
Metric
Prefixes
• Kilo- means 1000 of that unit
– 1 kilometer (km) = 1000 meters (m)
• Centi- means 1/100 of that unit
– 1 meter (m) = 100 centimeters (cm)
– 1 dollar = 100 cents
• Milli- means 1/1000 of that unit
– 1 Liter (L) = 1000 milliliters (mL)
Metric Prefixes
Metric Prefixes
Learning Check
Select the unit you would use to measure
1. Your height
a) millimeters
2. Your mass
b) meters
a) milligrams b) grams
c) kilometers
c) kilograms
3. The distance between two cities
a) millimeters
b) meters
c) kilometers
4. The width of an artery
a) millimeters
b) meters
c) kilometers
Solution
1. Your height
b) meters
2. Your mass
c) kilograms
3. The distance between two cities
c) kilometers
4. The width of an artery
a) millimeters
Equalities
State the same measurement in two
different units
length
10.0 in.
25.4 cm
Learning Check
1. 1000 m = 1
___
a) mm b) km c) dm
2.
0.001 g = 1
___
a) mg
b) kg c) dg
3.
0.1 L = 1
___
a) mL
b) cL c) dL
4.
0.01 m = 1
___
a) mm b) cm c) dm
Learning Check
1. 1000 m = 1 ___
2.
a) mm b) km c) dm
0.001 g = 1 ___
a) mg
b) kg c)
dg
3.
0.1 L = 1 ___
a) mL
b) cL c) dL
4.
0.01 m = 1 ___
a) mm b) cm c) dm
Instruments for Measuring Volume
Graduated
cylinder
Syringe
Buret
Pipet
Volumetric
flask
Units of Measuring Volume
1 L = 1000 mL
1 qt = 946 mL
Timberlake, Chemistry 7th Edition, page 3
Reading a Meniscus
Units for Measuring Mass
1 kg = 2.20 lb
Timberlake, Chemistry 7th Edition, page 3
1024 g
1021 g
Quantities of
Mass
1018 g
1015 g
1012 g
Giga-
109 g
Mega-
106 g
Kilo-
103
base
100 g
milli-
10-3 g
micro-
10-6 g
nano-
10-9 g
pico-
10-12 g
femto-
10-15 g
atomo-
10-18 g
g
Ocean liner
Indian elephant
Average human
1.0 liter of water
Grain of table salt
10-21 g
10-24 g
Kelter, Carr, Scott, Chemistry A Wolrd of Choices 1999, page 25
Earth’s atmosphere
to 2500 km
Typical protein
Uranium atom
Water molecule
LAB TIME!!
• Metric Lab
Dimensional Analysis
(Conversion Factors)
Fractions in which the numerator and
denominator are EQUAL quantities
expressed in different units
Example:
1 in. = 2.54 cm
Factors: 1 in.
2.54 cm
and
2.54 cm
1 in.
How many minutes are in 2.5
hours?
Conversion factor
2.5 hr x
60 min
= 150 min
1 hr
cancel
By using dimensional analysis / factor-label method,
the UNITS ensure that you have the conversion right
side up, and the UNITS are calculated as well as the
numbers!
Sample Problem
• You have $7.25 in your pocket
in quarters. How many quarters
do you have?
7.25 dollars X 4 quarters = 29 quarters
1 dollar
Learning Check
Write conversion factors that
relate each of the following
pairs of units:
1. Liters and mL
2. Hours and minutes
3. Meters and kilometers
Learning Check
A rattlesnake is 2.44 m long. How
long is the snake in cm?
a) 2440 cm
b) 244 cm
c) 24.4 cm
Learning Check
How many seconds are in 1.4 days?
Unit plan: days
hr
min
seconds
1.4 days x 24 hr
1 day
x
??
Wait a minute!
What is wrong with the following
setup?
1.4 day x 1 day
24 hr
x
60 min
1 hr
x 60sec
1 min
Learning Check
An adult human has 4.65 L of
blood. How many gallons of blood
is that?
Unit plan: L
qt
Equalities: 1 quart = 0.946 L
1 gallon = 4 quarts
Your Setup:
gallon
Solution
Unit plan:
gallon
L
qt
Setup:
4.65 L x
1 qt
x 1 gal
0.946 L
4 qt
= 1.23 gal
Dealing with Two Units – PreAP Only
If your pace on a treadmill is 65
meters per minute, how many
seconds will it take for you to walk
a distance of 8450 feet?
8450 ft
1
1m
3.28 ft
1 min
65m
60 sec
1 min
The Mole
• A counting unit
• Similar to a dozen, except instead
•
•
of 12, it’s 602 billion trillion
602,000,000,000,000,000,000,000
6.02 X 1023 (in scientific notation)
This number is named in honor of
Amedeo Avogadro (1776 – 1856),
who studied quantities of gases
and discovered that no matter what
the gas was, there were the same
number of molecules present
Just How Big is a Mole?
• Enough soft drink cans to cover the
surface of the earth to a depth of
over 200 miles.
• If you had Avogadro's number of
unpopped popcorn kernels, and
spread them across the United
States of America, the country would
be covered in popcorn to a depth of
over 9 miles.
• If we were able to count atoms at the
rate of 10 million per second, it
would take about 2 billion years to
count the atoms in one mole.
The Mole
• 1 dozen cookies = 12 cookies
• 1 mole of cookies = 6.02 X 1023 cookies
• 1 dozen cars = 12 cars
• 1 mole of cars = 6.02 X 1023 cars
• 1 dozen Al atoms = 12 Al atoms
• 1 mole of Al atoms = 6.02 X 1023 atoms
Note that the NUMBER is always the same,
but the MASS is very different!
Mole is abbreviated mol (gee, that’s a lot
quicker to write, huh?)
Avogadro’s Number as
Conversion Factor
6.02 x 1023 particles
1 mole
or
1 mole
6.02 x 1023 particles
Note that a particle could be an atom OR a molecule!
Learning Check
1. Number of atoms in 0.500 mole of Al
a) 500 Al atoms
b) 6.02 x 1023 Al atoms
c) 3.01 x 1023 Al atoms
2.Number of moles of S in 1.8 x 1024 S atoms
a) 1.0 mole S atoms
b) 3.0 mole S atoms
c) 1.1 x 1048 mole S atoms`
DENSITY - an important
and useful physical property
Density 
Mercury
mass (g)
volume (cm3)
Platinum
Aluminum
13.6 g/cm3
21.5 g/cm3
2.7 g/cm3
-Mass – (g) amount of matter in an
object
-Volume – (mL) amount of space
occupied by an object
-Density – (g/mL) a ratio of mass to
volume
Formula:
m
D=
v
Rewrite this formula to solve for m & v!
What is the unit for Density????
Remember: A material has the
same density no matter how
big or small it is!
Example:
• A piece of metal has a volume of 4.70
mL and a mass of 57.3 g. What is
the density?
M = 57.3 g
D=M/V
V = 4.70 mL
D = 57.3 g / 4.70 mL
D = 12.19148936 g/mL
D = 12.2 g/mL
Problem A piece of copper has a
mass of 57.54 g. It is 9.36 cm
long, 7.23 cm wide, and 0.95
mm thick. Calculate density
(g/cm3).
M
D
V
mass
(g)
Density 
volume (cm3)
Strategy
1. Get dimensions in common units.
2.
Calculate volume in cubic
centimeters.
3.
Calculate the density.
Learning Check
Osmium is a very dense metal. What is
its
density in g/cm3 if 50.00 g of the metal
occupies
a volume of 2.22cm3?
1) 2.25 g/cm3
2) 22.5 g/cm3
3) 111 g/cm3
Volume Displacement
A solid displaces a matching volume
of water when the solid is placed in
water.
33 mL
25 mL
Learning Check
What is the density (g/cm3) of 48 g of a metal if the metal
raises the level of water in a graduated cylinder from 25 mL
to 33 mL?
1) 0.2 g/ cm3
2) 6 g/mL3
3) 252 g/cm3
33 mL
25 mL
Learning Check
Which diagram represents the liquid
layers in the cylinder?
(K) Karo syrup (1.4 g/mL), (V)
vegetable oil (0.91 g/mL,) (W) water
(1.0 g/mL)
K 3)
1) V
W 2)
W
K
K
V
V
W
Solution
(K) Karo syrup (1.4 g/mL), (V)
vegetable oil (0.91 g/mL,) (W)
water (1.0 g/mL)
1)
V
W
K
Learning Check
The density of octane, a component
of gasoline, is 0.702 g/mL. What is
the mass, in kg, of 875 mL of octane?
1) 0.614 kg
2) 614 kg
3) 1.25 kg
Learning Check
If blood has a density of 1.05 g/mL,
how many liters of blood are donated
if 575 g of blood are given?
1) 0.548 L
2) 1.25 L
3) 1.83 L
• Graphs of density and volume can be
used to find the density of a
substance. The slope of the line
formed when mass and volume are
plotted is the density. Remember
“rise over run”.