Transcript Chapter 2
Chapter 2
Section 2
Section 2 Objectives
• Be able to define: quantity, measurement, standard, length, mass, weight, derived unit, volume, density, conversion factor.
• Be able to state the units of mass, length, temperature, and time in the SI system • Be able to explain the difference between mass and weight.
Section 2 Objectives
• Be able to state the meaning of common prefixes used in the SI system (Deka-, Hecto-, Kilo-, Mega-, Giga-, deci-, centi-, milli-, micro-, nano-.
• Be able to convert units within the SI system.
Section 2: Units of Measure
• Measurements are quantitative information. • Measurements _______________ quantities. • A quantity is something that has __________________, __________, or ________________. • A quantity is not the same as a measurement. • Example: A teaspoon is a unit of measurement for volume (a quantity) • Nearly every measurement is a number plus a ___________.
Section 2: Units of Measure
• Measurements are quantitative information. • Measurements
represent
quantities. • A quantity is something that has __________________, __________, or ________________. • A quantity is not the same as a measurement. • Example: A teaspoon is a unit of measurement for volume (a quantity) • Nearly every measurement is a number plus a ___________.
Section 2: Units of Measure
• Measurements are quantitative information. • Measurements
represent
quantities. • A quantity is something that has
magnitude
,
size
, or
amount
. • A quantity is NOT the same as a measurement. • Example: A teaspoon is a unit of measurement for volume (a quantity) • Nearly every measurement is a number plus a ___________.
Section 2: Units of Measure
• Measurements are quantitative information. • Measurements
represent
quantities. • A quantity is something that has
magnitude
,
size
, or
amount
. • A quantity is NOT the same as a measurement. • Example: A teaspoon is a unit of measurement for volume (a quantity) • Nearly every measurement is a number plus a
unit
.
Section 2: Units of Measure
• Scientists all over the world have agreed on a single measurement system, ____________. • These units are defined in terms of standards of ______________________________.
• International organizations monitor the defining process, such as the ____________________ ________________ ___ __________ ____ ____________________ in the United States.
Section 2: Units of Measure
• Scientists all over the world have agreed on a single measurement system,
SI
. • These units are defined in terms of standards of ______________________________.
• International organizations monitor the defining process, such as the ____________________ ________________ ___ __________ ____ ____________________ in the United States.
Section 2: Units of Measure
• Scientists all over the world have agreed on a single measurement system,
SI
. • These units are defined in terms of standards of
measurement
.
• International organizations monitor the defining process, such as the ____________________ ________________ ___ __________ ____ ____________________ in the United States.
Section 2: Units of Measure
• Scientists all over the world have agreed on a single measurement system,
SI
. • These units are defined in terms of standards of
measurement
.
• International organizations monitor the defining process, such as the
National Institute of Standards and Technology (NIST)
in the United States.
Section 2: Units of Measure
For example, the number seventy five thousand is written ___________________ instead of ____________________________ because the comma is used in other countries to represent a decimal point
Section 2: Units of Measure
For example, the number seventy five thousand is written
75 000
instead of
75,000
because the comma is used in other countries to represent a decimal point
SI System
• The SI system defines 7
base units
for 1. length, 2. mass, 3. time, 4. temperature, 5. amount of a substance
SI Base Units
Quantity Quantity Symbol
1. Length
l
Unit name Unit abbreviation
Meter m 2 . Mass 3. Time 4. Temperature 5. Amt of Subst.
m t
T
n
Kilogram Second Kelvin Mole kg s K mol
SI Base Units: Mass
• Mass is the measure of the ______________ ____ ________________. • The ___________, g, is 1/1000 of a kilogram and is more useful for measuring masses of small objects such as flasks and beakers. • For even smaller objects, such as tiny quantities of chemicals (think: medicines or vitamins!), the _____________ or ____ is used.
SI Base Units: Mass
• Mass is the measure of the
quantity of matter
. • The
gram
, g, is 1/1000 of a kilogram and is more useful for measuring masses of small objects such as flasks and beakers. • For even smaller objects, such as tiny quantities of chemicals (think: medicines or vitamins!), the
milligram
or
mg
is used.
• 1 milligram = 1/1000 of a gram
SI Base Units: Mass
• The measure of the gravitational pull on matter (gravity) is _______________. • Mass does not depend on ____________. • As the force of Earths’ gravity on an object increases, the object’s weight _____________________.
• The weight of an object on the moon is about ___________ of its weight on Earth.
SI Base Units: Mass
• The measure of the gravitational pull on matter (gravity) is
weight
. • Mass does not depend on
gravity
. • As the force of Earths’ gravity on an object increases, the object’s weight _____________________.
• The weight of an object on the moon is about ___________ of its weight on Earth.
SI Base Units: Mass
• The measure of the gravitational pull on matter (gravity) is
weight
. • Mass does not depend on
gravity
. • As the force of Earths’ gravity on an object increases, the object’s weight
increases
.
• The weight of an object on the moon is about
one-sixth
(
1/6)
of its weight on Earth.
SI Base Units: Length
• The SI standard unit for length is the ______________. • To express longer distances, the __________________, ___ is used. •
To express short distances, the _____________, _____ is used. (add to notes)
• One _____________ is 1000 meters.
SI Base Units: Length
• The SI standard unit for length is the
meter
. • To express longer distances, the
kilometer
,
km
is used. •
To express short distances, the _____________, _____ is used. (add to notes)
• One _____________ is 1000 meters.
SI Base Units: Length
• The SI standard unit for length is the
meter
. • To express longer distances, the
kilometer
,
km
is used. •
To express short distances, the centimeter, cm is used. (add to notes)
• One
kilometer
is 1000 meters.
Derived SI Units
• Combination of SI base units form ________ ______.
• For example, area, is ________ x ________.
m
m
2 m
Derived SI Units
• Combination of SI base units form
derived units.
• For example, area, is ________ x ________.
m
m
2 m
Derived SI Units
• Combination of SI base units form
derived units.
• For example, area, is
length x width
.
m Area = L x W Area = m x m
m
2 Area = m 2 m
Derived SI Units
Quantity Symbol Unit name Unit abbrev. Derivation 1. Area 2. Volume 3. Density A V D Square Meter Cubic Meter m 2 m 3 Kilograms per cubic meter kg/ m 3 4. Molar Mass M Kilograms per mole kg/mol 5. Molar Volume V m 6. Energy E cubic meters per mole m 3 /mol Joule J
length
x width
l
x
w
x
height
mass/volume m/amt. of sub.
volume/n force x length
Derived SI Units - Volume
• The amount of space occupied by an object is ____________, and the derived SI unit is ___________ _________. • This amount is equal to the volumne of a cube whose edges are each ____ ___ long.
• But in a chemistry laboratory, we need a smaller unit, so we often use _________________ ______________, ______.
Derived SI Units - Volume
• The amount of space occupied by an object is
volume
, and the derived SI unit is
cubic meters, m 3
.
• This amount is equal to the volume of a cube whose edges are each ____ ___ long.
• But in a chemistry laboratory, we need a smaller unit, so we often use _________________ ______________, ______.
Derived SI Units - Volume
• The amount of space occupied by an object is
volume
, and the derived SI unit is
cubic meters, m 3
.
• This amount is equal to the volume of a cube whose edges are each
1 m
long.
• But in a chemistry laboratory, we need a smaller unit, so we often use
cubic centimeter, cm 3 .
Derived SI Units - Volume
(1 m 3 ) x (100 cm/1m) x (100 cm/1 m) x (100 cm/1 m) = 1 000 000 cm 3
Derived SI Units - Volume
• When chemists measure the volumes of liquid and gases, they often use a non-SI unit called the ________.
• **Another non-SI unit, the ________________, or ___, is used for smaller volumes. There are _____________ mL in 1 L. • Because there are also __________ cm 3 units, ____________ and __________ _______________ are interchangeable.
in a liter, the 2 • View this in a equation: 1 L = 1 dm 3 cm 3 = _________ mL = ___________
Derived SI Units - Volume
• When chemists measure the volumes of liquid and gases, they often use a non-SI unit called the
liter, L
. • **Another non-SI unit, the ________________, or ___, is used for smaller volumes. There are _____________ mL in 1 L. • Because there are also __________ cm 3 units, ____________ and __________ _______________ are interchangeable.
in a liter, the 2 • View this in a equation: 1 L = 1 dm 3 cm 3 = _________ mL = ___________
Derived SI Units - Volume
• When chemists measure the volumes of liquid and gases, they often use a non-SI unit called the
liter, L
. • **Another non-SI unit, the
milliliter, or mL
is used for smaller volumes. There are
1000
mL in 1 L. • Because there are also __________ cm 3 units, ____________ and __________ _______________ are interchangeable.
in a liter, the 2 • View this in a equation: 1 L = 1 dm 3 cm 3 = _________ mL = ___________
Derived SI Units - Volume
• When chemists measure the volumes of liquid and gases, they often use a non-SI unit called the
liter, L
. • **Another non-SI unit, the
milliliter, or mL
is used for smaller volumes. There are
1000
mL in 1 L. • Because there are also
1000 milliliter
and cm
cubic centimeter
3 in a liter, the 2 units, are interchangeable.
• View this in a equation: 1 L = 1 dm 3 cm 3 = _________ mL = ___________
Derived SI Units - Volume
• When chemists measure the volumes of liquid and gases, they often use a non-SI unit called the
liter, L
. • **Another non-SI unit, the
milliliter, or mL
is used for smaller volumes. There are
1000
mL in 1 L. • Because there are also
1000 milliliter
and cm
cubic centimeter
3 in a liter, the 2 units, are interchangeable.
• View this in a equation: 1 L = 1 dm 3
1000
mL =
1000
cm 3 =
Derived SI Units - Density
• Ever heard the riddle: Which is heavier, a pound of feathers or a pound of lead?
• Answer: Neither is heavier, a pound is a pound no matter what the object….but when you want to answer “lead” you are thinking about the object’s density. • For another example, an object made of cork feels lighter than a lead object of the same size. • What you are comparing in such cases is how massive objects are compared with their size.
Derived SI Units - Density
• This property is called __________________, which is the ratio of __________ to ______________, or ____________ divided by _______________________. • Mathematically, the relationship for density can be written: Density = mass/volume or D = MV • By the SI base units of measurement, density is expressed as kg/m 3 . Again, for a chemistry laboratory, we make the units smaller, ___/____ or _______/ ________.
Derived SI Units - Density
• This property is called
Density
, which is the ratio of
mass
to
volume
, or
mass
divided by
volume
. • Mathematically, the relationship for density can be written: Density = mass/volume or D = M/V • By the SI base units of measurement, density is expressed as kg/m 3 . Again, for a chemistry laboratory, we make the units smaller, ___/____ or _______/ ________.
Derived SI Units - Density
• This property is called
Density
, which is the ratio of
mass
to
volume
, or
mass
divided by
volume
. • Mathematically, the relationship for density can be written: Density = mass/volume or D = MV • By the SI base units of measurement, density is expressed as kg/m 3 . Again, for a chemistry laboratory, we make the units smaller,
g/cm 3
or
g/mL
.
Derived SI Units - Density
•
Densities of some familiar materials (Table 4):
•
Solids Density at 20 o C (g/cm 3 ) Liquids Density at 20 0 C (g/mL)
• • • Sucrose (table sugar) 1.59
• • Cork Ice Diamond Lead .24
.92
3.26
11.35
Milk Water Sea Water Gasoline Mercury 1.031 .998
1.025
.67
13.6
Derived SI Units - Density
•
Sample Problem A:
•
A sample of aluminum metal has a mass of 8.4g. The volume of the sample is 3.1 cm 3 . Calculate the density of aluminum.
-Given: mass (m) = 8.4g & volume (v) = 3.1 cm 3 - Unknown: Density (D) Density = mass/volume = 8.4 g/3.1 cm3 = 2.7 g/cm3
Conversion Factors
• A ratio derived from the equality between two different units that can be used to convert from one unit to the other is a _______________________ ___________________. • For example, suppose you want to know how many quarters there are in a certain number of dollars. • To figure out this answer, you need to know how _______________ and _________________ are related.
• There are ____________ quarters in __________ dollar.
Conversion Factors
• A ratio derived from the equality between two different units that can be used to convert from one unit to the other is a
conversion factor
. • For example, suppose you want to know how many quarters there are in a certain number of dollars. • To figure out this answer, you need to know how _______________ and _________________ are related.
• There are ____________ quarters in __________ dollar.
Conversion Factors
• A ratio derived from the equality between two different units that can be used to convert from one unit to the other is a
conversion factor
. • For example, suppose you want to know how many quarters there are in a certain number of dollars. • To figure out this answer, you need to know how
quarters
and
dollars
are related. • There are
4
quarters in
1
dollar.
Conversion Factors
• There are 4 ways to express this:
1.
2.
3.
4.
4 quarters/1 dollar = 1 1 dollar/4 quarters = 1 0.25 dollar/1 quarter = 1 1 quarter/0.25 dollar = 1 • Notice that each conversion factor equals _________. • That is because the top and bottom quantities divided in any conversion factor and ____________ to each other. In this case 4 quarters = 1 dollar.
Conversion Factors
• There are 4 ways to express this:
1.
2.
3.
4.
4 quarters/1 dollar = 1 1 dollar/4 quarters = 1 0.25 dollar/1 quarter = 1 1 quarter/0.25 dollar = 1 • Notice that each conversion factor equals
ONE
. • That is because the top and bottom quantities divided in any conversion factor and ____________ to each other. In this case 4 quarters = 1 dollar.
Conversion Factors
• There are 4 ways to express this:
1.
2.
3.
4.
4 quarters/1 dollar = 1 1 dollar/4 quarters = 1 0.25 dollar/1 quarter = 1 1 quarter/0.25 dollar = 1 • Notice that each conversion factor equals
ONE
. • That is because the top and bottom quantities divided in any conversion factor and
equivalent
to each other. In this case 4 quarters = 1 dollar.
Conversion Factors
• You can use conversion factors to solve problems through __________________ ____________________; which is a mathematical technique that allows you to use __________ to solve problems involving ________________.
• For example, to determine the number of quarters in 12 dollars, you would use a unit conversion that allows you to change from dollars to quarters: • Number of quarters = 12 dollars x conversion factor
Conversion Factors
• You can use conversion factors to solve problems through
dimensional analysis
; which is a mathematical technique that allows you to use
units
to solve problems involving
measurements
.
• For example, to determine the number of quarters in 12 dollars, you would use a unit conversion that allows you to change from dollars to quarters: • Number of quarters = 12 dollars x conversion factor
Conversion Factors
• Then you have to decide which conversion factor gives you an answer in the desired unit. • In this case, you have _____________ and you want __________________, to eliminate dollars, you must divide the quantity by ____________________. • That factor would be __________________ / ___________________
Conversion Factors
• Then you have to decide which conversion factor gives you an answer in the desired unit. • In this case, you have
dollars
and you want quarters, so to eliminate dollars, you must divide the quantity by
dollars
.
• That factor would be __________________ / ___________________
Conversion Factors
• Then you have to decide which conversion factor gives you an answer in the desired unit. • In this case, you have
dollars
and you want quarters, so to eliminate dollars, you must divide the quantity by
dollars
.
• That factor would be:
4 quarters/1 dollar
Conversion Factors
• And the calculation would be set up as follows: ? quarters = 12 dollars x conversion factor 12 dollars x 4 quarters/1 dollar = 48
quarters
• Notice that the
dollars
divided out, leaving the answer in the desired unit, have
quarters
.
Conversion Factors
**For review of this section, it is imperative to be familiar with the SI Prefixes Table on page 35.**
10 100 1000 Million Billion
GREEK
Deka Hecto Kilo Mega Giga 10 x 100 x 100 x Million x Billion x
LATIN
deci centi milli micro nano 1/10 1/100 1/1000 millionth billionth
Deriving Conversion Factors
• You can derive conversion factors if you know the relationship between the unit you HAVE and the unit you WANT. • For example, from the fact that deci- means “1/10”, you know that there is a 1/10 of a meter per decimeter and that each meter must have 10 decimeters. (1m = 10dm).
• You can write the following conversion factor relating meters and decimeters: (1 meter/10 decimeter) and (.1 meter/1 decimeter) and
(10 decimeter/1 meter)
Deriving Conversion Factors
•
Sample Problem B: Express a mass of 5.712 grams in milligrams and in kilograms.
• Given: 5.712 grams • Unknown: mass in mg and kg • 1 g = 1000 mg • Possible conversion factors: • 1000 mg/1 g and 1 g/1000 mg • To derive an answer in mg, you’ll need to multiply 5.712 g by 1000mg/g: • 5.712 g × 1000 mg/1 g =5712 mg • Answer in kg: •
5.712 g × 1 kg/1000 g= .005712 kg