measurements chapter 1. units of measurement you are making a measurement when you check you weight...
TRANSCRIPT
MeasurementsChapter 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. . cm
First digit (known)= 2 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. . cm
What is the length of the line?
1) 6.0 cm
2) 6.06 cm
3) 6.60 cm
Zero as a Measured Number
. l3. . . . I . . . . I4 . . . . I . . . . I5. . cm
What is the length of the line?
First digit 4.?? cm
Second digit 4.5? cm
Last (estimated) digit is 4.50 cm
(not to the left or right of .5)
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. counting3. 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
1.8
•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
Significant Figures Summary
Counting Significant Figures
Number of Significant Figures
38.15 cm 4
5.6 ft 2
65.6 lb ___
122.55 m ___
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
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
Learning Check SF3
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 2) 9.2 3) 9.198
B. 4.311 ÷ 0.07 = 1) 61.58 2) 62 3) 60
C. 2.54 X 0.0028 =
0.0105 X 0.060
1) 11.3 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
mega- M 1 000 000
kilo- k 1 000
Prefixes that Decrease A Unit
Prefix Symbol Value
deci- d 0.1centi- c 0.01milli- m 0.001micro- (mu) 0.000 001nano n 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
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 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 EqualitiesLength 1 km = 1000 m 1m = 100 cm1m = 100 cm 1m = 1000 mm
Mass 1 kg = 1000 g1 kg = 1000 g 1 g =
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
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
Learning Check
Some American Equalities
1 ft = inches
1 lb = 16 oz
1 quart = pints
1 quart = 4 cups
Why are the quantities in each pair equal?
Some Metric-American Equalities
1 in. = 2.54 cm
1 qt = 946 mL
1 L = 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 – how close a measurement is to the true value
Precision – how close a set of measurements are to each other
accurate&
precise
precisebut
not accurate
not accurate&
not precise
Accuracy vs. Precision
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 1 L = 1000 mL
1 L and 1000 mL
1000 mL 1 L
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 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 Final unit = _______
inches
ounces
How many minutes are in 2.5 hours?
Initial unit
2.5 hr
Conversion Final
factor unit
2.5 hr x 60 min = 150 min
1 hr
cancel 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 = 244 cm
1 m
Learning Check
How many seconds are in 1.4 days?
Unit plan: days hr min seconds
1.4 days x 24 hr x ??
1 day
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 x 60 min x 60 sec
24 hr 1 hr 1 min
Unit Check
1.4 day x 1 day x 60 min x 60 sec
24 hr 1 hr 1 min
Units = day2-sec/hr2 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 qt gallon
Equalities: 1 quart = 946 mL
1 gallon = 4 quarts
Your Setup:
Solution
Unit plan: mL qt gallon
Setup:
4650 mL x 1 qt x 1 gal = 1.23 gal
946 mL 4 qt
3 SF equality exact 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 x 2.54 cm x 10 mm =
1 ft 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?
Initial
8450 ft x 12 in. x 2.54 cm x 1 m
1 ft 1 in. 100 cm
x 1 min x 60 sec = 2400 sec
65 m 1 minfinal (2 SF)
Solution
Measurements
Density
Density
Density compares the mass of an object to its volume
D = mass = g or g
volume mL cm3
Note: 1 mL = 1 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 mLDensity 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) 3)
K
K
W
W
W
V
V
V
K
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 and 1 mL
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 and 1 kg = 1000 g Setup:
875 mL x 0.702 g x 1 kg = 0.614 kg
1 mL 1000 gdensity metric
factor factor
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 mL L
575 g x 1 mL x 1 L = 0.548 L
1.05 g 1000 mL
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 L = 1.0 L
1 cm3 1000 mL
Learning Check
You have 3 metal samples. Which one will displace the greatest volume of water?
1 2 3
Discuss your choice with another student.
25 g Al2.70 g/mL
45 g of gold19.3 g/mL
75 g of Lead11.3 g/mL
Solution
1) 25 g Al x 1 mL = 9.2 mL 2.70 g
25 g Al2.70 g/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 Kelvin
Water boils 212°F 100°C 373 K
180° 100°C 100K
Water freezes 32°F 0°C 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 = 9°F = 1.8°F 100°C 5°C 1°C
Zero point: 0°C = 32°F
°F = 9/5 (T°C) + 32
or
°F = 1.8 (T°C) + 32
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 1.8
°F - 32 = T°C
1.8
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 exact
= 52.4 + 32
= 84.4°F tenth’s
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
0 K = - 273°C
K °C
K = °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
solidliquid
gas
Physical or Chemical?
A physical change does not alter the composition or identity of a substance.
A chemical change alters the composition or identity of the substance(s) involved.
ice meltingsugar dissolving
in water
hydrogen burns in air to form water
Phase Change
An extensive property of a material depends upon how much matter is is being considered.
An intensive property of a material does not depend upon how much matter is being considered.
• mass
• length
• volume
• density
• temperature
• color
Extensive and Intensive Properties
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
on earth, c = 1.0
on moon, c ~ 0.1
A 1 kg bar will weigh
1 kg on earth
0.1 kg on moon