Introduction:
Matter and Measurement
Stoichiometry
Units of
Measurement
Stoichiometry
SI Units
• Système International d’Unités
• Uses a different base unit for each quantity
Stoichiometry
Metric System
Prefixes convert the base units into units that
are appropriate for the item being measured.
Stoichiometry
THE METRIC SYSTEM
Stoichiometry
WHY DO WE USE THE METRIC SYSTEM?
• Almost all other countries are using the
metric system
• Other countries’ companies are refusing
to buy products from the U.S. if not
labeled in metric units
• Scientists need a universal way to
communicate data (SI Units)
Stoichiometry
APPROXIMATE CONVERSIONS BETWEEN
METRIC & US LENGTH UNITS
• A meter is about the same length as a
yard
• A meter is about three feet long
• A decimeter is about four inches long
• An inch is about 25 millimeters
• A foot contains about 30 centimeters
• A foot contains about 3 decimeters
Stoichiometry
WHAT DOES THE METRIC
SYSTEM MEASURE?
• The gram measures mass or how much
something weighs
• The liter measures volume which is
used when measuring liquids
• The meter measures the length of an
object or the distance from place to
place
Stoichiometry
THE METRIC CONVERSION
CHART (STAIRCASE METHOD)
Kilo
1000 Hecto
units
100 Deka
units
10
To convert to a smaller unit, move
decimal point to the right or
multiply.
Basic
Unit Deci
0.1 Centi
units 0.01 Milli
units 0.001
units
To convert to a larger unit, move
decimal point to the left or divide
units
Stoichiometry
TRY THIS USING THE
STAIRCASE METHOD
1000 mg = ______ g
Step 1: Determine if you are going to go up or down the ladder.
Step 2: Determine how many steps there are from milligrams to
grams.
Step 3: Move the decimal point the amount of places that was
determined in steps 1 & 2.
Stoichiometry
TRY THIS USING THE
STAIRCASE METHOD
1000 mg = ______
1 g
Step 1: Determine if you are going to go up or down the ladder.
Step 2: Determine how many steps there are from milligrams to
grams.
Step 3: Move the decimal point the amount of places that was
determined in steps 1 & 2.
Stoichiometry
TRY THIS USING THE
STAIRCASE METHOD
.15 L = __________ ml
Stoichiometry
TRY THIS USING THE
STAIRCASE METHOD
.15 L = __________
ml
150
Stoichiometry
Volume
• The most commonly
used metric units for
volume are the liter (L)
and the milliliter (mL).
□ A liter is a cube 1 dm
long on each side.
□ A milliliter is a cube 1 cm
long on each side.
Stoichiometry
Uncertainty in Measurements
Different measuring devices have different
uses and different degrees of accuracy.
Stoichiometry
Temperature:
A measure of the
average kinetic
energy of the
particles in a sample.
Stoichiometry
Temperature
• In scientific
measurements, the
Celsius and Kelvin
scales are most often
used.
• The Celsius scale is
based on the
properties of water.
□ 0C is the freezing point
of water.
□ 100C is the boiling
point of water.
Stoichiometry
Temperature
• The Kelvin is the SI
unit of temperature.
• It is based on the
properties of gases.
• There are no
negative Kelvin
temperatures.
• K = C + 273.15
Stoichiometry
Temperature
• The Fahrenheit
scale is not used in
scientific
measurements.
• F = 9/5(C) + 32
• C = 5/9(F − 32)
Stoichiometry
A Standard Measurement System
The Metric System
Stoichiometry
When and why was the metric system
invented?
• The metric system was invented in
1790
• The metric system was invented
because countries were using many
different systems of measurement
causing confusion and lack of
consistency
Stoichiometry
Who invented the metric system?
• The metric system was invented by a
group of French scientists
Stoichiometry
Metric System
• A system of measurement used by
the majority of countries on Earth
based on the number 10
Stoichiometry
A Standard Measurement System
The International System of Units (SI)
Stoichiometry
Scientists all over the world use the
International System of Units to
measure:
•
•
•
•
•
•
Length
Volume
Mass
Density
Temperature
Time
Stoichiometry
Figure 1: Calculating - How
much larger is a kilo- than a
deka-?
• 100 times
Stoichiometry
 Reading Checkpoint (page 45): SI units
are based on multiples of what number?
• SI units are based on multiples of 10
• Add a zero
• Subtract a zero
Stoichiometry
Key Concept: Why do scientists use a
standard measurement system?
• Using SI as the standard system of
measurement allows scientists to
compare data and communicate with
each other about their results
• Using SI measurement also allows
experiments to be repeated and most
importantly achieve a desired resultStoichiometry
Length
Stoichiometry
What is length?
• Length is the distance from one point
to another
Stoichiometry
Length
Units of Length
Stoichiometry
The basic unit of length in the SI system is
the …
• The basic unit of length in the SI
system is the meter
Stoichiometry
The two units that measure the length of
smaller objects are, …
• millimeter
• centimeter
Stoichiometry
Complete the Table Below
Prefix
Meaning
Unit of Length
milli
one-hundredth
meter
one-thousand
Stoichiometry
Complete the Table Below
Prefix
Meaning
milli
One-thousandth
Unit of Length
one-hundredth
meter
one-thousand
Stoichiometry
Complete the Table Below
Prefix
Meaning
Unit of Length
milli
One-thousandth
millimeter
one-hundredth
meter
one-thousand
Stoichiometry
Complete the Table Below
Prefix
Meaning
Unit of Length
milli
One-thousandth
millimeter
centi
one-hundredth
meter
one-thousand
Stoichiometry
Complete the Table Below
Prefix
Meaning
Unit of Length
milli
One-thousandth
millimeter
centi
one-hundredth
centimeter
meter
one-thousand
Stoichiometry
Complete the Table Below
Prefix
Meaning
Unit of Length
milli
One-thousandth
millimeter
centi
one-hundredth
centimeter
none
meter
one-thousand
Stoichiometry
Complete the Table Below
Prefix
Meaning
Unit of Length
milli
One-thousandth
millimeter
centi
one-hundredth
centimeter
none
one
meter
one-thousand
Stoichiometry
Complete the Table Below
Prefix
Meaning
Unit of Length
milli
One-thousandth
millimeter
centi
one-hundredth
centimeter
none
one
meter
kilo
one-thousand
Stoichiometry
Complete the Table Below
Prefix
Meaning
Unit of Length
milli
One-thousandth
millimeter
centi
one-hundredth
centimeter
none
one
meter
kilo
one-thousand
kilometer
Stoichiometry
Length
Measuring Length
Stoichiometry
The longer lines on the metric
ruler are called…
• centimeters
Stoichiometry
The shorter lines on the metric
ruler are called…
• millimeters
Stoichiometry
 Checkpoint
One centimeter is divided into
how many millimeters?
• 10 millimeters
(mm)
Stoichiometry
Figure 2: Calculating: Measure the
turtle in figure 2 from the rear of its
shell to the tip of its nose. Record its
length in both centimeters and
millimeters.
• 10.5 cm
• 105 mm
Stoichiometry
Density
Stoichiometry
Density
• The measure of how much mass is
contained in a given volume
Stoichiometry
The formula of density is:
Density = Mass / Volume
Stoichiometry
Figure 5: Comparing Densities
- Inferring: Which item has
the greater density?
• The bowling ball
• Since the bowling
bowl has a greater
mass, it has a
greater density,
even though both
balls have the same
volume
Stoichiometry
Density
Units of Density
Stoichiometry
Why is density expressed as a
combination of two different
units?
• Because density is actually made up
of two other measurements – mass
and volume – an objects density is
expressed as a combination of two
units
Stoichiometry
Two Common Units For Density
• Grams per cubic centimeter (g/cm³)
• Grams per milliliter (g/mL)
Stoichiometry
Math Practice: What is the density
of a wood block with a volume of 125
cm³ and a mass of 57 g?
Density = mass / volume
Density = 57 g / 125 cm³
Density = 0.46 g/ cm³
Stoichiometry
Math Practice: What is the density
of a liquid with a mass of 45 g and a
volume of 48 mL?
Density = mass / volume
Density = 45 g / 48 mL
Density = 0.94 g/mL
Stoichiometry
Density
Densities of Common
Substances
Stoichiometry
The density of a substance is the
______for all samples of that
substance.
• Same
Stoichiometry
An object will float if it is _____
_____ than a surrounding liquid.
• Less dense
Stoichiometry
Figure 6: Applying Concepts: How could
you use density to determine whether a
bar of metal is pure gold?
• If the bar of gold
has a density that
is greater than or
less than 19.3
g/cm³, then the
sample is not pure
gold.
Densities of Some
Common Substances
Substance
Density
(g/cm³)
Air
0.001
Ice
0.9
Water
1.0
Aluminum
2.7
Stoichiometry
Gold
19.3
 Checkpoint
Will an object with a density of 0.7
g/cm³ float or sink in water?
• An object that has a density of 0.7
g/cm³ will float in water (1 g/cm³)
because it is less dense than water
Stoichiometry
Density:
Physical property of a substance
m
d=
V
Stoichiometry
Time
Stoichiometry
Time
Units of Time
Stoichiometry
What is the SI unit used to
measure time?
• The second(s) is the SI unit to
measure time
Stoichiometry
Common Conversions for Time
1s
=
=
1h
60 s
=
Stoichiometry
Common Conversions for Time
1s
1h
=
1,000 ms
=
60 s
=
Stoichiometry
Common Conversions for Time
1s
=
1,000 ms
1 min
=
60 s
1h
=
Stoichiometry
Common Conversions for Time
1s
=
1,000 ms
1 min
=
60 s
1h
=
60 min
Stoichiometry
Time
Measuring Time
Stoichiometry
Why would a stop watch be used
to measure time in an important
race?
• Because stop watches measure in
units smaller than the second
• These measurements include the
tenth and hundredth of a second
Stoichiometry
 Checkpoint
- How many milliseconds are in one
second?
• 1,000 milliseconds
Stoichiometry
Temperature
Stoichiometry
Temperature
Units of Temperature
Stoichiometry
A common unit to measure
temperature is the ___ ___.
• Celsius scale
Stoichiometry
Water freezes at ______ and
boils at ______.
• 0 °C
• 100 °C
Stoichiometry
The normal human body
temperature is approximately
________.
• 37 °C
Stoichiometry
What is the official SI unit for
temperature?
• The Kelvin Scale (°K)
• 0 °K = -273 °C
Stoichiometry
Figure 8: Measuring
Temperature - Observing: At
what temperature on the Kelvin
scale does water boil?
• 373 °K
Stoichiometry
What is absolute zero?
• Absolute zero is considered by
scientists to be the coldest
temperature possible
• 0 °K or –273 °C
Stoichiometry
Temperature
Measuring Temperature
Stoichiometry
What instrument is used to
measure temperature?
• Thermometer
Stoichiometry
Volume
Stoichiometry
Volume
• The amount of space an object takes
up
Stoichiometry
Volume
Volume of Liquids
Stoichiometry
When measuring the volume of a
liquid, scientists use a unit known as
the…
• Liter (L).
Stoichiometry
To measure the volume of smaller
liquids, the _________ is used.
• Milliliter (mL)
Stoichiometry
The instrument used to
measure the volume of liquids is
called the…
• Graduated cylinder.
Stoichiometry
This instrument has markings
that are in increments of…
• 1 milliliter (mL)
Stoichiometry
Meniscus
• The curve in the top surface of water
in the graduated cylinder
Stoichiometry
Figure 4: Observing - What
is the proper way to read a
meniscus?
• Read the
milliliter marking
at the bottom
of the curve
Stoichiometry
Volume
Volume of Rectangular Solids
Stoichiometry
Common Conversions For Volume
1L
=
=
1 mL
1,000 cm³
=
Stoichiometry
Common Conversions For Volume
1L
1 mL
=
1,000 mL
=
1,000 cm³
=
Stoichiometry
Common Conversions For Volume
1L
=
1,000 mL
1 L
=
1,000 cm³
1 mL
=
Stoichiometry
Common Conversions For Volume
1L
=
1,000 mL
1 L
=
1,000 cm³
1 mL
=
1 cm³
Stoichiometry
How can the volume of a solid object
such as a shoebox be measured?
• To measure a solid objects that are
regular shaped, a formula for volume
can be applied
• To measure a rectangular object such
as a shoebox, multiply the object’s
Stoichiometry
length, width, and height
The SI unit known for measuring
solids with a larger volume is known
as the…
• Cubic meter (m³).
Stoichiometry
The formula for calculating the
volume of a rectangular object is:
Volume = Length x Width x Height
Stoichiometry
Why is the unit cm³ used when
calculating the volume of a
rectangular object?
• When multiplying the object’s length,
width and height, the cm units are
also multiplied
cm x cm x cm = cm³
Stoichiometry
Suppose a cereal box is 10 centimeters long, 4
centimeters wide, and 20 centimeters high.
What would be the volume of the box?
Volume = Length x Width x Height
Volume = 10 cm x 4 cm x 20 cm
Volume = 800 cm³
Stoichiometry
 Checkpoint
What is a cubic meter?
• The SI unit used to measure solids
with a larger volume
• A cubic meter is equal to the volume
of a cube that measures 1 meter on
each side
Stoichiometry
Volume
Volume of Irregular Solids
Stoichiometry
How is the volume of an irregular
solid such as a rock measured?
• To measure the volume of an irregular
solid, immerse the object in water,
and measure how much the water
level rises
• Water displacement method
Stoichiometry
How does the water displacement
method work?
• Record the volume of water in the
graduated cylinder
• Carefully place the irregular solid into the
water. Record the volume of the water
plus the object
• Subtract the volume of the water alone
from the volume of the water plus the
object
Stoichiometry
Uncertainty in
Measurement
Stoichiometry
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.
Stoichiometry
Significant Figures
1. All nonzero digits are significant.
2. Zeroes between two significant figures
are themselves significant.
3. Zeroes at the beginning of a number
are never significant.
4. Zeroes at the end of a number are
significant if a decimal point is written
in the number.
Stoichiometry
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.
Stoichiometry
Relating Significant Figures to the Uncertainty of a
Measurement
What difference exists between the measured values 4.0 g and 4.00 g?
Solution Many people would say there is no difference, but a scientist
would note the difference in the number of significant figures in the two
measurements. The value 4.0 has two significant figures, while 4.00
has three. This difference implies that the first measurement has more
uncertainty. A mass of 4.0 g indicates that the uncertainty is in the first
decimal place of the measurement. Thus, the mass might be anything
between 3.9 and 4.1 g, which we can represent as 4.0 ± 0.1 g. A
measurement of 4.00 g implies that the uncertainty is in the second
decimal place. Thus, the mass might be anything between 3.99 and
4.01 g, which we can represent as 4.00 ± 0.01 g. Without further
information, we cannot be sure whether the difference in uncertainties
of the two measurements reflects the precision or accuracy of the
measurement.
Stoichiometry
PRACTICE EXERCISE
A balance has a precision of ± 0.001 g. A sample
that has a mass of about 25 g is placed on this
balance. How many significant figures should be
reported for this measurement?
Answer: five, as in the measurement
24.995 g
Stoichiometry
SAMPLE EXERCISE 1.6 Determining the Number of Significant Figures in a Measurement
How many significant figures are in each of the following numbers
(assume that each number is a measured quantity):
(a) 4.003,
Four; the zeros are significant figures
(b) 6.023  1023, Four; the exponential term does not add to the
number of significant figures.
(c) 5000?
One. We assume that the zeros are not
significant when there is no decimal point
shown. If the number has more significant
figures, a decimal point should be employed
or the number written in exponential
notation. Thus, 5000. has four significant
Stoichiometry
figures, whereas 5.00  103 has three.
PRACTICE EXERCISE
How many significant figures are in each of
the following measurements:
Answers:
(a) 3.549 g,
(a) four,
(b) two,
(b) 23  104 cm,
(c) three
(c) 0.00134 m3?
Stoichiometry
Determining the Number of Significant Figures in a
Calculated Quantity
The width, length, and height of a small box are 15.5 cm,
27.3 cm, and 5.4 cm, respectively. Calculate the volume of
the box, using the correct number of significant figures in
your answer.
Solution The volume of a box is determined by the product
of its width, length, and height. In reporting the product, we
can show only as many significant figures as given in the
dimension with the fewest significant figures, that for the
height (two significant figures):
When we use a calculator to do this calculation, the display shows 2285.01,
which we must round off to two significant figures. Because the resulting
number is 2300, it is best reported in exponential notation, 2.3  103, to clearly
Stoichiometry
indicate two significant figures.
PRACTICE EXERCISE
It takes 10.5 s for a sprinter to run 100.00 m.
Calculate the average speed of the sprinter
in meters per second, and express the result
to the correct number of significant figures.
Answer: 9.52 m/s (3 significant figures)
Stoichiometry
Determining the Number of Significant Figures in a
Calculated Quantity
A gas at 25°C fills a container whose volume is 1.05  103 cm3. The container plus gas have a mass
of 837.6 g. The container, when emptied of all gas, has a mass of 836.2 g. What is the density of the gas
at 25°C?
Solution
To calculate the density, we must know both the mass and the volume of the gas. The
mass of the gas is just the difference in the masses of the full and empty container:
(837.6 – 836.2) g = 1.4 g
In subtracting numbers, we determine the number of significant figures in our result by counting
decimal places in each quantity. In this case each quantity has one decimal place. Thus, the mass of
the gas, 1.4 g, has one decimal place.
Using the volume given in the question, 1.05  103 cm3, and the definition of density, we have
In dividing numbers, we determine the number of significant figures in our result by counting the
number of significant figures in each quantity. There are two significant figures in our answer,
corresponding to the smaller number of significant figures in the two numbers that form the ratio.
Stoichiometry
To how many significant figures should the mass of the
container be measured (with and without the gas) in
Sample Exercise 1.8 in order for the density to be
calculated to three significant figures?
Answer: five (In order for the difference in the two masses
to have three significant figures, there must be two decimal
places in the masses of the filled and empty containers.)
Stoichiometry
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.
Stoichiometry