Transcript Measurements

Measurements
Chapter 1
Units of Measurement
You are making a measurement when you
 Check you weight
 Read your watch
 Take your temperature
 Weigh a cantaloupe
What kinds of measurements did you make
today?
Standards of Measurement
When we measure, we use a measuring tool
to compare some dimension of an object to
a standard.
Some Tools for Measurement
Learning Check
From the previous slide, state the tool (s) you
would use to measure
A. temperature
____________________
B. volume
____________________
____________________
C. time
____________________
D. weight
____________________
Solution
From the previous slide, state the tool (s) you
would use to measure
A. temperature
thermometer
B. volume
measuring cup,
graduated cylinder
C. time
watch
D. weight
scale
Measurement in Chemistry
In chemistry we
 do experiments
 measure quantities
 use numbers to report measurements
Stating a Measurement
In every measurement there is a
Number
followed by a
 Unit from measuring device
Learning Check
What is the unit of measurement in each of the following
examples?
A. The patient’s temperature is 102°F.
B. The sack holds 5 lbs of potatoes.
C. It is 8 miles from your house to school.
D. The bottle holds 2 L of orange soda.
Metric System (SI)



Is a decimal system based on 10
Used in most of the world
Used by scientists and hospitals
Units in the Metric System

length
meter
m

volume
liter
L

mass
gram
g

temperature
Celsius
°C
Learning Check
Identify the measurement in metric units.
A. John’s height is
1) 1.5 yards
2) 6 feet
3) 2 meters
B. The volume of saline in the IV bottle is
1) 1 liters
2) 1 quart
3) 2 pints
C. The mass of a lemon is
1) 12 ounces
2) 145 grams
3) 0.6 pounds
Measurements
Measured Numbers and
Significant Figures
Measured Numbers
When you use a measuring tool to
determine a quantity such as your
height or weight, the numbers you
obtain are called measured
numbers.
Reading a Meterstick
. l2. . . . I . . . . I3 . . . .I . . . . I4. .
First digit (known)
=2
cm
2.?? cm
Second digit (known) = 0.7
2.7? cm
Third digit (estimated) between 0.05- 0.07
Length reported
=
2.75 cm
or
2.76 cm
or
2.77 cm
Known + Estimated Digits

Known digits 2 and 7 are 100% certain

The third digit 6 is estimated (uncertain)

In the reported length, all three digits
(2.76 cm) are significant including the estimated
one
Learning Check
. l8. . . . I . . . . I9. . . .I . . . . I10. .
cm
What is the length of the line?
1) 9.2 cm
2) 9.22 cm
3) 9.23 cm
How your answer compare with your neighbor’s
answer? Why or why not?
Learning Check
l5. . . . I . . . . I6. . . .I . . . . I7. .
What is the length of the line?
1) 6.0 cm
2) 6.06 cm
3) 6.60 cm
cm
Zero as a Measured Number
. l3. . . . I . . . . I4 . . . . I . . . . I5. .
cm
What is the length of the line?
First digit
Second digit
Last (estimated) digit is
(not to the left or right of .5)
4.?? cm
4.5? cm
4.50 cm
Exact Numbers



Obtained when you count objects
2 soccer balls
1 watch
4 pizzas
Obtained from a defined relationship
1 foot = 12 inches
1 meters = 100 cm
Not obtained with measuring tools
Learning Check
A. Exact numbers are obtained by
1. measuring
2. counting
3. definition
B. Measured numbers are obtained by
1. measuring
2. counting
3. definition
Learning Check
Classify each of the following as an exact (1)
or a measured (2) number.
A.___Gold melts at 1064°C
B.___1 yard = 3 feet
C.___A red blood cell with diameter 6 x 10-4 cm
D.___There were 6 hats on the shelf
E.___A can of soda contains 355 mL of soda
Significant Figures in Measurement
 The numbers reported in a measurement are
limited by the measuring tool
 Significant figures in a measurement include
the known digits plus one estimated digit
Significant Figures Summary
•Any digit that is not zero is significant
1.234 kg
4 significant figures
•Zeros between nonzero digits are significant
606 m
3 significant figures
•Zeros to the left of the first nonzero digit are not significant
0.08 L
1 significant figure
•If a number is greater than 1, then all zeros to the right of the
decimal point are significant
2.0 mg
2 significant figures
•If a number is less than 1, then only the zeros that are at the
end and in the middle of the number are significant
0.00420 g
3 significant figures
1.8
Counting Significant Figures
Number of Significant Figures
38.15 cm
5.6 ft
65.6 lb
122.55 m
4
2
___
___
Complete: All non-zero digits in a measured number
are (significant or not significant).
Leading Zeros
Number of Significant Figures
0.008 mm
1
0.0156 oz
3
0.0042 lb
____
0.000262 mL
____
Complete: Leading zeros in decimal numbers are
(significant or not significant).
Sandwiched Zeros
Number of Significant Figures
50.8 mm
3
2001 min
4
0.702 lb
____
0.00405 m
____
Complete: Zeros between nonzero numbers are
(significant or not significant).
Trailing Zeros
Number of Significant Figures
25,000 in.
2
200 yr
1
48,600 gal
3
25,005,000 g
____
Complete: Trailing zeros in numbers without
decimals are (significant or not significant) if
they are serving as place holders.
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
Learning Check
In which set(s) do both measured 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
Learning Check SF3
State the number of significant figures in each of the
following measured/calculated numbers:
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
Significant Numbers in Calculations



A calculated answer cannot be more precise than
the measuring tool.
A calculated answer must match the least precise
measurement.
Significant figures are needed for final answers
from
1) adding or subtracting
2) multiplying or dividing
Adding and Subtracting
The answer has the same number of decimal
places as the measurement with the fewest
decimal places.
25.2
one decimal place
+ 1.34 two decimal places
26.54
answer 26.5 one decimal place
E.g., 25 + 6.022 = 31
Learning Check
In each calculation, round the answer to the
correct number of significant figures.
A. 235.05 + 19.6 + 2.1 =
1) 256.75
2) 256.8
3) 257
B.
58.925 - 18.2 =
1) 40.725
2) 40.73
3) 40.7
Multiplying and Dividing
Round (or add zeros) to the calculated answer
until you have the same number of significant
figures as the measurement with the fewest
significant figures.
Learning Check
A. 2.19 X 4.2
1) 9
B.
C.
=
4.311 ÷ 0.07 =
1) 61.58
2.54 X 0.0028
0.0105 X 0.060
1) 11.3
2) 9.2
2) 62
3) 9.198
3) 60
=
2) 11
3) 11.041
Measurements
Prefixes and
Equalities
Metric Prefixes

Increase or decrease basic unit by 10

Form new units larger or smaller than the basic
units

Indicate a numerical value
prefix
=
value
1 kilometer
=
1000 meters
1 kilogram
=
1000 grams
Prefixes that Increase A Unit
Prefix
Symbol
Value
giga-
G
1 000 000 000
megakilo-
M
k
1 000 000
1 000
Prefixes that Decrease A Unit
Prefix
Symbol
Value
decicentimillimicronano
d
c
m
 (mu)
n
0.1
0.01
0.001
0.000 001
0.000 000 0001
Learning Check
Match 1) length 2) mass
3) volume
____ A.
A bag of tomatoes is 4.6 kg.
____ B.
A person is 2.0 m tall.
____ C.
A medication contains 0.50 g Aspirin.
____ D.
A bottle contains 1.5 L of water.
Learning Check
Select the unit you would use to measure
A. Your height
1) millimeters
2) meters
3) kilometers
2) grams
3) kilograms
B. Your mass
1) milligrams
C. The distance between two cities
1) millimeters
2) meters
3) kilometers
D. The width of an artery
1) millimeters
2) meters
3) kilometers
Learning Check
Indicate the prefix to use for
1. A mass that is 1000 times greater than 1 gram
1) kilo
2) milli
3) mega
2. A length that is 1/100 of 1 meter?
1) deci
2) centi
3) milli
3. A unit of time that is 1/1000 of a second.
1) nanosecond 2) microsecond 3)millisecond
Equalities
State the same measurement in two different units
length
10.0 in.
25.4 cm
Fundamental & Derived SI units and Metric Equalities
Length
Mass
1 km = 1000 m
1 kg = 1000 g
1m = 100 cm
1g=
1m = 1000 mm
Volume
1 kL = 1000 L
1L = 100 cL
1L = 1000 mL
Matter is anything that takes up space and has mass
Fundamental SI Units (Derived SI units are derived from these base units):
Volume – SI derived unit for volume is cubic meter (m3)
1 cm3 = (1 x 10-2 m)3 = 1 x 10-6 m3
1 dm3 = (1 x 10-1 m)3 = 1 x 10-3 m3
1 L = 1000 mL = 1000 cm3 = 1 dm3
1 mL = 1 cm3
Learning Check
A. 1000 m = 1
___
1) mm
2) km
3) dm
B.
0.001 g = 1
___
1) mg
2) kg
3) dg
C.
0.1 L = 1
___
1) mL 2) cL 3) dL
D.
0.01 m = 1
___
1) mm
2) cm
3) dm
Learning Check
Give the value of the following units:
A. 1 kg
= ____ g
1) 10 g
2) 100 g
3) 1000 g
B. 1 mm
= ____ m
1) 0.001 m
2) 0.01 m
3) 0.1 m
Some American Equalities
1 ft
=
1 lb
=
1 quart
=
1 quart
=
inches
16 oz
pints
4 cups
Why are the quantities in each pair equal?
Some Metric-American Equalities
1 in.
=
2.54 cm
1 qt
=
946 mL
1L
=
1.06 qt
1 lb
=
454 g
1 kg
=
2.20 lb
Remember these for exams.
Equalities given in a Problem
Example 1
At the store, the price of one pound of red peppers is
$2.39.
Equality: 1 lb red peppers =
$2.39
Example 2
At the gas station, one gallon of gas is $1.34.
Equality: 1 gallon of gas
=
$1.34
Accuracy vs. Precision
Accuracy – how close a measurement is to the true value
Precision – how close a set of measurements are to each other
accurate
&
precise
precise
but
not accurate
not accurate
&
not precise
Conversion Factors
Fractions in which the numerator and
denominator are quantities expressed in an
equality between those units
Example:
1 in. = 2.54 cm
Factors: 1 in.
and
2.54 cm
2.54 cm
1 in.
Learning Check
Write conversion factors that relate each of the
following pairs of units:
A. Liters and mL
B. Hours and minutes
D. Meters and kilometers
Solution
A. quarts and mL
1L
and
1000 mL
1 L = 1000 mL
1000 mL
1L
B. hours and minutes 1 hr = 60 min
1 hr
and 60 min
60 min
1 hr
C. meters and kilometers 1 km = 1000 m
1 km and 1000 m
1000 m
1 km
Measurements
Problem Solving Using
Conversion Factors
Initial and Final Units
1. A person has a height of 2.0 meters. What is
that height in inches?
Initial unit = m
inches
Final unit = _______
2) Blood has a density of 1.05 g/mL. If a person
lost 0.30 pints of blood at 18°C, how many ounces
of blood would that be?
Initial = pints
ounces
Final unit = _______
How many minutes are in 2.5 hours?
Initial unit
2.5 hr
Conversion
factor
2.5 hr x 60 min
1 hr
cancel
Final
unit
= 150 min
Answer (2 SF)
Learning Check
A rattlesnake is 2.44 m long. How long is the
snake in cm?
1) 2440 cm
2) 244 cm
3) 24.4 cm
Solution
A rattlesnake is 2.44 m long. How
long is the snake in cm?
2) 244 cm
2.44 m x 100 cm
1m
= 244 cm
Learning Check
How many seconds are in 1.4 days?
Unit plan: days
hr
1.4 days x 24 hr x
1 day
min
??
seconds
Solution CF2
Unit plan: days
hr
min
seconds
2 SF
Exact
1.4 day x 24 hr x 60 min x 60 sec
1 day
1 hr
1 min
= 1.2 x 105 sec
Unit Check
What is wrong with the following setup?
1.4 day
x 1 day
24 hr
x
60 min
1 hr
x 60 sec
1 min
Unit Check
1.4 day
x 1 day
24 hr
Units = day2-sec/hr2
x
60 min
1 hr
x 60 sec
1 min
Not the final unit needed
Learning Check
An adult human has 4650 mL of blood. How many
gallons of blood is that?
Unit plan:
mL
Equalities:
1 quart = 946 mL
1 gallon = 4 quarts
Your Setup:
qt
gallon
Solution
Unit plan:
Setup:
4650 mL x
3 SF
mL
1 qt
946 mL
equality
qt
x 1 gal
4 qt
exact
gallon
= 1.23 gal
3 SF
Steps to Problem Solving








Read problem
Identify data
Write down a unit plan from the initial unit
to the desired unit
Select conversion factors
Change initial unit to desired unit
Cancel units and check
Do math on calculator
Give an answer using correct significant figures
Learning Check
If the ski pole is 3.0 feet in length, how long is
the ski pole in mm?
Solution
3.0 ft x 12 in
1 ft
x 2.54 cm x 10 mm =
1 in.
1 cm
Learning Check
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?
Solution
Initial
8450 ft
x 12 in.
1 ft
x 1 min
65 m
x 2.54 cm
1 in.
x 60 sec
1 min
x 1m
100 cm
= 2400 sec
final (2 SF)
Measurements
Density
Density
Density compares the mass of an object to its
volume
D =
mass
= g
volume
mL
Note: 1 mL = 1 cm3
or
g
cm3
Learning Check D1
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
Solution
2) Placing the mass and volume of the osmium metal
into the density setup, we obtain
D = mass = 50.00 g =
volume
2.22 cm3
= 22.522522 g/cm3 = 22.5 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/m3
3) 252 g/cm3
33 mL
25 mL
Solution
2) 6 g/cm3
Volume (mL) of water displaced
= 33 mL - 25 mL
= 8 mL
Volume of metal (cm3)
= 8 mL x 1 cm3 = 8 cm3
1 mL
Density of metal =
mass = 48 g
= 6 g/cm3
volume 8 cm3
Learning Check3
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)
1)
2)
V
W
K
3)
K
W
K
V
V
W
Density as Conversion Factors
A substance has a density of 3.8 g/mL.
Density
= 3.8 g/mL
Equality
3.8 g = 1 mL
Conversion factors.
3.8 g
1 mL
and
1 mL
3.8 g
Density Connections
Mass
Volume
kg
L
g
mL (cm3)
mg
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
Solution
1) 0.614 kg
Unit plan: mL  g  kg
Equalities: 1 mL = 0.702 g
Setup:
875 mL x 0.702 g
1 mL
density
factor
x
and 1 kg = 1000 g
1 kg
1000 g
metric
factor
= 0.614 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
Solution
1)
Unit Plan: g
575 g x
mL
L
1 mL x 1 L
=
1.05 g
1000 mL
0.548 L
Learning Check
A group of students collected 125 empty aluminum
cans to take to the recycling center. If 21 cans
make 1.0 pound of aluminum, how many liters of
aluminum (D=2.70 g/cm3) are obtained from the
cans?
1) 1.0 L
2) 2.0 L
3) 4.0 L
Solution
1) 1.0 L
125 cans x 1.0 lb x 454 g x 1 cm3
21 cans
1 lb
2.70 g
x 1 mL x
1 cm3
1L
1000 mL
= 1.0 L
Learning Check
You have 3 metal samples. Which one will displace the
greatest volume of water?
1
2
3
25 g Al
2.70 g/mL
45 g of gold
19.3 g/mL
75 g of Lead
11.3 g/mL
Discuss your choice with another student.
Solution
1)
25 g Al x
25 g Al
2.70 g/mL
1 mL =
2.70 g
9.2 mL
Chapter 1
Measuring Temperature
Temperature

Particles are always moving.

When you heat water, the water molecules move faster.

When molecules move faster, the substance gets hotter.

When a substance gets hotter, its temperature goes up.
Learning Check
Suppose you place water in a freezer.
A. The water particles move
1) faster
2) slower
3) the same
B. The water will get
1) hotter
2) colder
3) stay the same
C. The temperature of the water will be
1) higher
2) lower
3) the same
Temperature

Measures the hotness or coldness of an object

Determined by using a thermometer that contains a
liquid that expands with heat and contracts with
cooling.
Temperature Scales
Units of Temperature between Boiling
and Freezing
Fahrenheit Celsius
Water boils
212°F
180°
Water freezes 32°F
100°C
100°C
0°C
Kelvin
373 K
100K
273 K
Learning Check
A. Temperature of freezing water
1) 0°F
2) 0°C
3) 0 K
B. Temperature of boiling water
1) 100°F
2) 32°F
3) 373K
C. Number of Celsius units between the
boiling and freezing points of water
1) 100
2) 180
3) 273
Fahrenheit Formula
180°F
100°C
=
9°F
5°C
=
1.8°F
1°C
Zero point: 0°C = 32°F
°F
= 9/5 (T°C) + 32
°F
= 1.8 (T°C) + 32
or
Celsius Formula
Rearrange to find T°C
°F
= 1.8 T°C + 32
°F - 32
= 1.8 T°C ( +32 - 32)
°F - 32
= 1.8 T°C
1.8
°F - 32
1.8
1.8
=
T°C
Temperature Conversions
A person with hypothermia has a body temperature of
29.1°C. What is the body temperature in °F?
°F
=
1.8 (29.1°C) + 32
exact
tenth's
=
52.4 + 32
=
84.4°F
tenth’s
exact
Learning Check
The normal temperature of a chickadee is 105.8°F.
What is that temperature in °C?
1) 73.8 °C
2) 58.8 °C
3) 41.0 °C
Solution
3) 41.0 °C
Solution:
°C
=
=
=
(°F - 32)
1.8
(105.8 - 32)
1.8
73.8°F
1.8°
=
41.0°C
Learning Check
Pizza is baked at 455°F. What is that in °C?
1) 437 °C
2) 235°C
3) 221°C
Learning Check
On a cold winter day, the temperature falls to 15°C. What is that temperature in °F?
1) 19 °F
2) 59°F
3) 5°F
Kelvin Scale
On the Kelvin Scale
1K
=
1°C
0 K is the lowest temperature
0K
K
K =
= - 273°C
°C
°C + 273
Learning Check
What is normal body temperature of 37°C in
kelvins?
1) 236 K
2) 310 K
3) 342 K
Three States of Matter
gas
liquid
solid
Physical or Chemical?
A physical change does not alter the composition
or identity of a substance.
sugar dissolving
ice melting Phase Change
in water
A chemical change alters the composition or
identity of the substance(s) involved.
hydrogen burns in
air to form water
Extensive and Intensive Properties
An extensive property of a material depends upon
how much matter is is being considered.
• mass
• length
• volume
An intensive property of a material does not
depend upon how much matter is being
considered.
• density
• temperature
• color
Matter - anything that occupies space and has mass.
mass – measure of the quantity of matter
SI unit of mass is the kilogram (kg)
1 kg = 1000 g = 1 x 103 g
weight – force that gravity exerts on an object
weight = c x mass
A 1 kg bar will weigh
on earth, c = 1.0
1 kg on earth
on moon, c ~ 0.1
0.1 kg on moon