Transcript Chapter 1

CHAPTER 2
Metric System
THE METRIC SYSTEM
Measuring
• The numbers are only half of a measurement.
• It is 10 long.
• 10 what?
• Numbers without units are meaningless.
• How many feet in a yard?
• A mile?
• A rod?
The Metric System
• Easier to use because it is a decimal system.
• Every conversion is by some power of 10.
• A metric unit has two parts.
• A prefix and a base unit.
• prefix tells you how many times to divide or multiply by 10.
Length - straight distance
between two points
-Meters (m)
Length
meter
m
Mass
gram
g
Time
Second
s
Temperature
Kelvin
K
Amount of a
substance
Mole
Mol
Volume
Liter
L
Mass - how much matter
in an object
-grams (g)
Volume - amount of space
taken up by an object
Cubic meters (m3) or
-Liters (L)
Base Units
• Length - meter - more than a yard - m
• Mass - grams - about a raisin - g
• Time - second - s
• Temperature - Kelvin or ºCelsius K or ºC
• Energy - Joules- J
• Volume - Liter - half of a two liter bottle- L
• Amount of substance - mole - mol
Metric System
Prefixes convert the base units into units that
are appropriate for the item being measured.
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Prefix
Kilo- Hecta-
Deka- UNITS Deci- Centi- Mili-
k
da
h
d
c
m
Prefixes
• giga• mega -
G
1,000,000,000
109
M
1,000,000
106
1,000 103
• kilo - k
• deci- d
• centi-
10-1
0.1
c
• milli- m
-2
0.01
0.001
10
10-3
10-6
• micro-
m
0.000001
• nano-
n
0.000000001 10
-9
Prefixes
• kilo k 1000 times
• deci d 1/10
• centi c 1/100
• milli m 1/1000
• kilometer - about 0.6 miles
• centimeter - less than half an inch
• millimeter - the width of a paper clip wire
DIMENSIONAL
ANALYSIS
Using the units to solve problems
Chapter 1: Chemistry: Matter and Measurement
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A Problem-Solving Method
Chemistry problems usually require calculations,
and yield quantitative (numerical) answers
The unit-conversion method is useful for
solving most chemistry problems – the
focus here is on “unit equivalents”
For example,
1 inch = 2.54 cm
EOS
4m = ________ cm
.34km = ________ cm
5km = ____________m
5km = ____________m
40mm = __________m
19cm = __________mm
67m = __________ hm
98m = __________km
135cm =
_____________km
135m =
_____________km
0.1km = _________dm
Converting
k h
D
d
c
m
• how far you have to move on this chart, tells you how far,
and which direction to move the decimal place.
• The box is the base unit, meters, Liters, grams, etc.
Conversions
k h
D
d
c
m
• convert 25 mg to grams
• convert 0.45 km to mm
• convert 35 mL to liters
• It works because the math works, we are dividing or
multiplying by 10 the correct number of times.
Chapter 1: Chemistry: Matter and Measurement
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Other Equivalents and Conversion
Factors
A conversion factor
is the fractional
expression of the
equivalents
1inch
2.54 cm
or
2.54 cm
1inch
EOS
Dimensional Analysis
• We use dimensional analysis
to convert one quantity to
another.
• Most commonly dimensional
analysis utilizes conversion
factors (e.g., 1 in. = 2.54 cm)
1 in.
2.54 cm
or
2.54 cm
1 in.
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© 2009, Prentice-Hall, Inc.
Dimensional Analysis
Use the form of the conversion factor that puts the
sought-for unit in the numerator.
Given unit 
Conversion factor
desired unit
given unit
 desired unit
© 2009, Prentice-Hall, Inc.
Dimensional Analysis
• For example, to convert 8.00 m to inches,
• convert m to cm
• convert cm to in.
100 cm
1 in.
8.00 m 

1m
2.54 cm
 315 in.
Dimensional Analysis
• Use conversion factors to change the units
• Conversion factors = 1
• 1 foot = 12 inches (equivalence statement)
• 12 in
= 1 =
1 ft.
1 ft.
12 in
• 2 conversion factors
• multiply by the one that will give you the correct units in your
answer.
Chapter 1: Chemistry: Matter and Measurement
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Two Examples
How many cm are in 26 inches?
2.54 cm
26 in ×
= 66 cm
1 in
EOS
Examples
• 11 yards = 2 rod
• 40 rods = 1 furlong
• 8 furlongs = 1 mile
• The Kentucky Derby race is 1.25 miles. How long is
the race in rods, furlongs, meters, and kilometers?
• A marathon race is 26 miles, 385 yards. What is this
distance in rods and kilometers?
Units to a Power
• How many m
3 is 1500 cm3?
1500 cm3
1500
1m
1m
1m
100 cm 100 cm 100 cm
cm3
1m
100 cm
3
Units to a Power
• How many cm2 is 15 m2?
• 36 cm3 is how many mm3?
Multiple units
• The speed limit is 65 mi/hr. What is this in m/s?
• 1 mile = 1760 yds
• 1 meter = 1.094 yds
65 mi
hr
1760 yd
1m
1 hr 1 min
1 mi
1.094 yd 60 min 60 s
Multiple units
• Lead has a density of 11.4 g/cm3. What is this in pounds
per quart?
• 454 g = 1 lb
• 1 L = 1.094 qt
Scientific Notation
• To write in Scientific Notation you need a number between
1 & 9 in front of the decimal.
• When going from right to left you add the exponent
(positive exponent)
• When going from left to right you subtract the exponent
(negative exponent)
Converting Cont.
•
I.
II.
III.
IV.
Examples
345
.000345
56890
.000000000134
WHICH IS HEAVIER?
it depends
Density
• How heavy something is for its size
• The ratio of mass to volume for a substance
• D = M/V
• Independent of how much of it you have
• Gold- high density
• Air- low density
Floating
• Lower density floats on higher density
• Ice is less dense than water
• Most wood is less dense than water
• Helium is less dense than air.
• A ship is less dense than water
Density of Water
• 1g of water is 1mL of water
• Density of water is 1 g/mL
• At 40C
• Otherwise it is less
Calculating
• The formula tells you how
• Units will be g/ml or g/cm3
• A piece of wood has a mass of 11.2g and a volume of
23mL. What is the density?
• A piece of wood has a density of 0.93 g/mL and a volume
of 23 mL what is the mass?
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UNCERTAINY IN
MEASUREMENT
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Significant Figures
• The term significant figures refers to digits that were
measured.
• When rounding calculated numbers, we pay attention to
significant figures so we do not overstate the accuracy of
our answers.
Chapter 1: Chemistry: Matter and Measurement
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Significant Figures
• All digits in a number that are known with
certainty plus the first uncertain digit
• The more significant digits obtained, the better the
precision of a measurement
• The concept of significant figures applies only to
measurements
• Exact values have an unlimited number of
significant figures
EOS
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Significant Figures
1.
2.
3.
4.
All nonzero digits are significant.
Zeroes between two significant figures are
themselves significant.
Zeroes at the beginning of a number are never
significant.
Zeroes at the end of a number are significant if a
decimal point is written in the number.
Chapter 1: Chemistry: Matter and Measurement
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Rules for Zeros in
Significant Figures
Zeros between two other significant digits ARE
significant
e.g., 10023
A zero preceding a decimal point is not significant
e.g., 0.10023
Zeros between the decimal point and the first nonzero
digit are not significant
e.g., 0.0010023
EOS
Chapter 1: Chemistry: Matter and Measurement
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Rules for Zeros in
Significant Figures
Zeros at the end of a number are significant if they are
to the right of the decimal point
e.g., 0.1002300
1023.00
Zeros at the end of a number may or may not be
significant if the number is written without a decimal
point
e.g., 1000. compared to 1000
EOS
Chapter 1: Chemistry: Matter and Measurement
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Rules for Significant Figures
in Calculations
KEY POINT: A calculated quantity can be no
more precise than the least precise data used in
the calculation
… and the reported result should reflect this fact
Analogy: a chain is only as strong as
its weakest link
EOS
© 2009, Prentice-Hall, Inc.
Significant Figures
• When addition or subtraction is performed, answers
are rounded to the least significant decimal place.
• When multiplication or division is performed, answers
are rounded to the number of digits that corresponds
to the least number of significant figures in any of the
numbers used in the calculation.
Chapter 1: Chemistry: Matter and Measurement
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Significant Figures
in Calculations
Multiplication and Division:
the reported results should
have no more significant
figures than the factor with the
fewest significant figures
1.827 m × 0.762 m = ?
0.762 has 3 sigfigs so the
reported answer is 1.39 m2
EOS
Chapter 1: Chemistry: Matter and Measurement
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Significant Figures
in Calculations
Addition and Subtraction: the reported results
should have the same number of decimal places as the
number with the fewest decimal places
NOTE - Be cautious of
round-off errors in multistep problems. Wait until
calculating the final answer
before rounding.
EOS
Conservation of Mass
• Law of Conservation of Mass- in a physical or chemical
reaction, mass is neither created nor destroyed; it is
conserved.
• All mass can be accounted for.
• Mass of the Reactants = Mass of Products
Weight vs. Mass
Weight
Mass
• Measures the force of
• How much matter is in an
gravity on an object
• Weight can change if the
force of gravity acting on
the object changes
object
• Remains constant (the
same) no matter where it
is
Mass and Weight
• Mass is measure of resistance to change in motion
• Weight is force of gravity.
• Sometimes used interchangeably
• Mass can’t change, weight can
Mass
• Weight is a force. Mass is the amount of matter.
3 of water at 4 ºC.
• 1 gram is defined as the mass of 1 cm
3 of water
• 1000 g = 1000 cm
• 1 kg = 1 L of water
Mass
• 1 kg = 2.5 lbs
• 1 g = 1 paper clip
• 1 mg = 10 grains of salt
Volume
• calculated by multiplying L x W x H
• Liter the volume of a cube 1 dm (10 cm) on a side
• 1L = 1 dm3
• so 1 L = 10 cm x 10 cm x 10 cm
3
• 1 L = 1000 cm
3
• 1/1000 L = 1 cm
• 1 mL = 1 cm
3
Volume
• 1 L about 1/4 of a gallon - a quart
• 1 mL is about 20 drops of water or 1 sugar cube
Measurement
• How do we measure in science?
• What do measurements mean?
• How do we tell?
• Let’s start with Accuracy vs. Precision
How good are the measurements?
• Scientists use two words to describe how good the
measurements are• Accuracy- how close the measurement is to the actual
value
• Precision- how well can the measurement be repeated
Uncertainty
• Basis for significant figures
• All measurements are uncertain to some degree
• Precision- how repeatable
• Accuracy- how correct - closeness to true value.
• Random error - equal chance of being high or low-
addressed by averaging measurements - expected
Accuracy versus Precision
• Accuracy refers to the proximity of
a measurement to the true value of
a quantity.
• Precision refers to the proximity of
several measurements to each
other.
© 2009, Prentice-Hall, Inc.
Uncertainty
• Systematic error- same direction each time
• Want to avoid this
• Bad equipment or bad technique.
• Better precision implies better accuracy
• You can have precision without accuracy
• You can’t have accuracy without precision (unless
you’re really lucky).
Temperature
• A measure of the average kinetic energy
• Different temperature scales, all are talking about the
same height of mercury.
• Derive a equation for converting ºF toºC
Temperature is different
• from heat.
• Temperature is which way heat will flow. (from hot to cold)
• Heat is energy, ability to do work.
• A drop of boiling water hurts,
• kilogram of boiling water kills.
Calculating Temp.
•
•
•
•
•
I.
II.
From Celsius to Fahrenheit
F= (C x 9/5) + 32
From Fahrenheit to Celsius
C= 5/9 (F-32)
Examples:
49 0F to 0C
97 0C to 0F
0ºC
Measuring Temperature
• Celsius scale.
• water freezes at 0ºC
• water boils at 100ºC
• body temperature 37ºC
• room temperature 20 - 25ºC
273 K
Measuring Temperature
• Kelvin starts at absolute zero (-273 º C)
• degrees are the same size
• C = K -273
• K = C + 273
• Kelvin is always bigger.
• Kelvin can never be negative.
Problems
•
1.
2.
3.
4.
How many????
349K to 0C
120C to K
340F to 0C
1010C to 0F
Units of heat are
• calories or Joules
• 1 calorie is the amount of heat needed to raise the
temperature of 1 gram of water by 1ºC.
• A food Calorie is really a kilocalorie.
• How much energy is absorbed to heat 15 grams of water
by 25ºC.
• 1 calorie = 4.18 J
Conservation of Mass
• Law of Conservation of Mass- in a physical or chemical
reaction, mass is neither created nor destroyed; it is
conserved.
• All mass can be accounted for.
• Mass of the Reactants = Mass of Products
Energy
• The ability to do work.
• Work - cause a change or move an object.
• Many types- all can be changed into the other.
Types of energy
• Potential- stored energy
• Kinetic Energy- energy something has because its moving
• Heat- the energy that moves because of a temperature
difference.
• Chemical energy- energy released or absorbed in a
chemical change.
• Electrical energy - energy of moving charges
Types of Energy
• Radiant Energy- energy that can travel through empty
space (light, UV, infrared, radio)
• All types of energy can be converted into others.
• If you trace the source far enough back, you will end up at
nuclear energy.
Conservation of Energy
• Energy can be neither created or destroyed in ordinary
changes (not nuclear), it can only change form.
• Its not just a good idea, its the law.