Transcript Chapter 2 - Mrs. G Chemistry 2015-2016

MEASUREMENTS
AND CALCULATIONS
SCIENTIFIC METHOD
DISCUSSION
• How can we find the quickest way to
school?
SCIENTIFIC METHOD
• A logical approach to solving problems by
• Observing and collecting data
• Formulating hypotheses
• Testing hypotheses
• Theorizing
OBSERVING AND COLLECTING DATA
• Observations are also called data.
• There are two kinds of data:
• Qualitative data are descriptions that do not have numbers.
It is so hot today, you could fry an egg on a sunny spot on the
sidewalk, is an example of qualitative data.
• Quantitative data are obtained by measuring and have numbers.
Scientists use instruments (tools) to obtain numbers based data.
8/18/08 1300 hours GMT - the thermometer reads 42° Celsius on the
playground.
FORMULATING HYPOTHESES
• Hypotheses are just testable statements.
• They are often written as if-then statements
THEY ARE NOT EDUCATED GUESSES
TESTING HYPOTHESES
• During testing:
• Conditions that remain constant are controls
• Conditions that are manipulated are variables
THEORIZING
• Model—can be a physical object but is often an
explanation of how phenomena occur and how
data or events are related.
• Theory—a broad generalization that explains a
body of facts or phenomena.
CHAPTER 2
MEASUREMENTS
UNITS OF MEASUREMENT
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?
LEARNING CHECK
What are some U.S. units that are used to
measure each of the following?
A. length
B. volume
C. weight
D. temperature
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
UNITS IN THE METRIC SYSTEM

length
meter
m

volume
liter
L (m3, cm3)

mass
gram

temperature
Celsius
g
°C
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.
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
SOLUTION
A. John’s height is
3) 2 meters
B. The volume of saline in the IV bottle is
1) 1 liter
C. The mass of a lemon is
2) 145 grams
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
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PREFIXES THAT INCREASE A UNIT
Prefix
Symbol
Value
deca-
D
10
hectokilo-
h
k
100
1 000
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PREFIXES THAT DECREASE A UNIT
Prefix
Symbol
decicentimilli-
d
c
m
Value
0.1
0.01
0.001
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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.
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SOLUTION
Match 1) length
2) mass 3) volume
_2 A.
A bag of tomatoes is 4.6 kg.
_1_ B.
A person is 2.0 m tall.
_2_ C.
A medication contains 0.50 g Aspirin.
_3_ D.
A bottle contains 1.5 L of water.
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LEARNING CHECK
Select the unit you would use to measure
A. Your height
1) millimeters
2) meters
3) kilometers
B. Your mass
1) milligrams
2) grams
3) kilograms
C. The distance between two cities
1) millimeters
2) meters
3) kilometers
D. The width of an artery
1) millimeters
2) meters
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3) kilometers
23
SOLUTION
A. Your height
2) meters
B. Your mass
3) kilograms
C. The distance between two cities
3) kilometers
D. The width of an artery
1) millimeters
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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
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SOLUTION
1. 1) kilo
2. 2) centi
3. 3) millisecond
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SOME METRIC EQUALITIES
Length
1m
=
100 cm
Mass
1 kg
=
1000 g
Volume
1L
=
1000 mL
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LEARNING CHECK
A. 1000 m = 1 ___
B.
0.001 g = 1
1) mm
___ 1) mg
2) km
3) dm
2) kg
3) hg
3) dL
C.
0.1 L = 1 ___
1) mL
2) cL
D.
0.01 m = 1 ___ 1) mm
2) cm
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3) dm
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SOLUTION
A. 1000 m = 1 ___
2) km
B.
1) mg
0.001 g = 1 ___
C.
0.1 L = 1 ___ 3) dL
D.
0.01 m = 1 ___ 2) cm
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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
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SOLUTION
A. 1 kg
= ____ g
3) 1000 g
B. 1 mm = ____ m
1) 0.001 m
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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
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SOLUTION
A. Liters 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
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GIVEN AND DESIRED UNITS
1. A person has a height of 2.0 meters.
What is that height in centimeters?
Given unit = m
Desired unit = _______
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HOW MANY MINUTES ARE IN 2.5
HOURS?
Given unit
2.5 hr
2.5 hr x
Conversion
factor
60 min
1 hr
Desired
unit
= 150 min
cancel
Answer (2 SF)
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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
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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
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LEARNING CHECK
How many seconds are in 1.4 days?
Unit plan: days
hr
1.4 days x 24 hr
1 day
x
min
seconds
??
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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
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UNIT CHECK
What is wrong with the following setup?
1.4 day
x 1 day
24 hr
x
60 min
1 hr
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x 60 sec
1 min
40
UNIT CHECK
1.4 day
x 1 day
24 hr
Units = day2/hr2
x
60 min
1 hr
x 60 sec
1 min
Not the final unit needed
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STEPS TO PROBLEM SOLVING








Read problem
Identify data
Write down a unit plan from the given 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 significant figures
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CHAPTER 2
MEASUREMENTS
Significant Figures in
Calculations
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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
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COUNTING SIGNIFICANT
FIGURES
Number of Significant Figures
38.15 cm
5.6 ft
65.6 lb
122.55 m
4
2
___
___
RULE 1: All non-zero digits are significant
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LEADING ZEROS
Number of Significant Figures
0.008 mm
1
0.0156 oz
3
0.0042 lb
____
0.000262 mL
____
RULE 2: Leading zeros are NEVER significant
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CAPTIVE ZEROS
Number of Significant Figures
50.8 mm
3
2001 min
4
0.702 lb
____
0.00405 m
____
RULE 3: Captive zeros are ALWAYS
significant.
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TRAILING ZEROS
Number of Significant Figures
25,000 in.
2
200 yr
1
48,600 gal
3
25,005,000 g
____
RULE 4: Trailing zeros are significant IF
there is a decimal present
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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
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3) 5.35 x 105
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SOLUTION
A. Which answers contain 3 significant
figures?
2) 0.00476
3) 4760
B. All the zeros are significant in
2) 25.300
3) 2.050 x 103
C. 534,675 rounded to 3 significant figures is
2) 535,000
3) 5.35 x 105
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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
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SOLUTION
In which set(s) do both numbers contain
the same number of significant figures?
3) 0.000015 and 150,000
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LEARNING CHECK SF3
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
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SOLUTION
A. 0.030 m
2
B. 4.050 L
4
C. 0.00008 g
1
D. 3.00 m
3
E. 2,080,000 bees
3
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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
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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
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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
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3) 40.7
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SOLUTION
A. 235.05 + 19.6 + 2.1 =
2) 256.8
B.
58.925 - 18.2
3) 40.7
=
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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.
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LEARNING CHECK
A. 2.19 X 4.2 =
1) 9
2) 9.2
B. 4.311 ÷ 0.07 =
1) 61.58
2) 62
C.
2.54 X 0.0028 =
0.0105 X 0.060
1) 11.3
2) 11
Timberlake lecture plus
3) 9.198
3) 60
3) 0.041
60
SOLUTION
A.
2.19 X 4.2
=
2) 9.2
B.
4.311 ÷ 0.07 =
3) 60
C.
2.54 X 0.0028 =
0.0105 X 0.060
2) 11
Continuous calculator operation =
2.54 x 0.0028  0.0105  0.060
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CHAPTER 1
MEASUREMENTS
Density
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DENSITY
Density compares the mass of an object to its
volume
D =
mass
= g
volume
mL
or
g
cm3
Note: 1 mL = 1 cm3
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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
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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
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VOLUME DISPLACEMENT
A solid displaces a matching volume of
water when the solid is placed in water.
33 mL
25 mL
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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
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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
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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
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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
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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
lecturePLUS Timberlake
1 mL
3.8 g
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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
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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
= 0.614 kg
1000 g
metric
factor
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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
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SOLUTION
1)
Unit Plan: g
575 g x
mL
1 mL x
1.05 g
L
1L
=
1000 mL
lecturePLUS Timberlake
0.548 L
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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.
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SOLUTION
1)
25 g Al x
1 mL =
2.70 g
9.2 mL
25 g Al
2.70 g/mL
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CHAPTER 2
SECTION 3
USING SCIENTIFIC MEASUREMENTS
ACCURACY AND PRECISION
Accuracy—refers to the closeness of measurements to the correct
or accepted value of the quantity measured
Precision—refers to the closeness of a set of measurements of the
same quantity made in the same way.
PERCENTAGE ERROR
Percentage error is calculated by subtracting the
accepted value from the experimental (measured) value,
dividing the difference by the accepted (known) value,
and then multiplying by 100.
SAMPLE PROBLEM
A student measures the mass and volume of a
substance and calculates its density as 1.40 g/mL.
The correct, or accepted, value of the density is
1.30 g/mL. What is the percentage error of the
student’s measurement?
Percentage error =
value experimental – value accepted
value accepted
• Percentage error = 1.40 g/mL – 1.30 g/mL
× 100
1.30 g/mL
Percentage error = 7.7%
PRACTICE PROBLEMS
• 1. What is the percentage error for a mass
measurement of 17.7 g, given that the correct
value is 21.2g?
PRACTICE PROBLEMS
• A volume is measured experimentally as 4.26 mL,
What is the percentage error, given that the correct
value is 4.15 mL?