Transcript Chapter 2 - SchoolRack

Chapter 2
Measurements and
Calculations
2-1 The Scientific Method

A logical approach to
solving problems by
observing and
collecting data,
formulating
hypotheses, testing
hypotheses and
formulating theories
that are supported by
data
2-1 Observing and Collecting Data

Qualitative data – descriptive, what is it like?
The ice water was clear and colorless.

Quantitative data – numerical, how much?
The ice water was 4˚C.
The volume of the ice water was 125 mL.
2-1 System

A specific portion of matter in a given
region of space that has been selected for
study during an experiment or observation.
The scientist determines the system.
 Anything outside of the system is called
the surroundings.

2-1 Hypotheses, Models and
Theories


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
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Scientists form hypotheses – a hypothesis is a testable
statement, if-then
Scientists test hypotheses – a hypothesis is tested
through experimentation.
If a hypothesis is not supported by data it must be
rejected.
If a hypothesis is supported by experimental data, a
model is constructed – a model is an explanation of how
data and events are related.
If a model successfully explains a phenomenon, it may
become part of a theory – a theory is a broad
generalization that explains a body of facts.
2-2 Units of Measurement
Measurements represent QUANTITIES.
 A quantity is anything that has magnitude,
size or amount.
 Length, width, temperature, mass, area,
volume and time are examples of
quantities.

2-2 SI Measurement

SI is the
International
System – a
version of the
metric system
used by all
scientists
Quantity
SI Base Unit
length
meter (m)
mass
kilogram (kg)
time
second (s)
temperature
kelvin (K)
amount of
mole (mol)
substance
electric current ampere (A)
luminous
intensity
candela (cd)
2-2 Mass

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
Mass – amount of
matter, SI unit is
kilogram
Based on
International
Prototype Kilogram –
a cylinder of platinumiridium alloy kept near
Paris
Scientists also use
grams, milligrams
2-2 Weight


Weight – measure of
gravitational pull on
matter, can vary with
location because
gravity is not the
same everywhere,
directly proportional to
mass
Weight can vary.
Mass can NOT vary
2-2 Other Base Quantities
Length – distance between 2 points, SI base unit is
meter, scientists also use decimeter, centimeter,
millimeter
Temperature – hotness or coldness, average
kinetic energy, SI base unit is degree kelvin,
scientists also use degree Celsius
Time – interval between events, base unit is
second
2-2 SI Prefixes
2-2 Derived Units

Derived units are formed by combining SI base
units
Quantity
symbol
unit
unit
abbreviation
derivation
area
A
V
D
square meter
m2
length x width
cubic meter
m3
LxWxH
kilograms per
cubic meter
kg/m3
mass/volume
Molar mass
M
kilograms per
mole
kg/mol
mass/amount
concentration
c
Vm
moles per liter
mol/L
amount/volume
cubic meters
per mole
m3/mol
volume/amount
E
joule
J
force x length
volume
density
Molar volume
energy
2-2 Volume

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
Amount of space
occupied by an object
SI derived unit is cubic
meters
Scientists often use liters
(L) or milliliters (mL) for
liquid volume.
1 L = 1 dm3
1 mL = 1 cm3
2-2 Density
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The ratio of mass to volume
Each pure substance has a characteristic
density
Density can sometimes be used to identify
substances.
What is the mass of a 12.4 cm3 sample of gold? (Gold’s density is 19.31 g/cm3.)
2-2 Conversion Factors

A conversion factor is a ratio derived from
the equality between two different units
that can be used to convert from one unit
to the other
example:
1 m = 10 dm
2-2 Using Conversion Factors

Express 5.712 g in milligrams and
kilograms
2-2 Using Conversion Factors

Express 16.45 m in centimeters and
kilometers.
2-2 Using Conversion Factors

Express 1500 cm3 in cubic meters.
2-2 Using Conversion Factors

Express 15 km/hr in meters per second.
2-2 Using Conversion Factors

Express 1.975 g/cm3 in kilograms per
cubic meter.
2-3 Accuracy and Precision
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Accuracy refers to
closeness of
measurements to
correct or accepted
value.
Precision refers to
closeness of
measured values to
each other.
2-3 Accuracy and Precision

The boiling point of acetone is 56.3˚C.
student 1: 50.6˚C, 61.7˚C, 51.0˚C
student 2: 50.1˚C, 49.9˚C, 50.2˚C
student 3: 56.1˚C, 56.5˚C, 56.9˚C
Which student was accurate and precise?
Which student was only precise but not
accurate?
Which student was neither precise nor accurate?
2-3 Percent Error

Percent error is a measure of accuracy.
P.E. = Valueaccepted – Valueexp x 100
Valueaccepted
 If acepted value is greater than
experimental value, PE is positive.
 If accepted value is less than experimental
value, PE is negative.
2-3 Percent Error

A student measures the mass and volume
of copper and calculates its density to be
8.50g/cm3. The accepted value is
8.92g/cm3. What is the percent error of
this measurement?
2-3 Significant Figures
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Any measurement
contains some
uncertainty.
Scientists use
significant figures
to show how
certain they are of
a measurement.
Example:
Which measurement
represents a greater
degree of certainty?
4000 g
4005.32 g
2-3 Significant Figures
Represent any position for which real
measurement has been made, plus one
final digit which is an estimated position
 The number of significant figures you can
record when measuring with an instrument
depends on the sensitivity of the
instrument

2-3 Significant Figures
Record all digits that you can read off the instrument, plus ONE ESTIMATED digit.
2-3 Significant Figures
All nonzero digits are significant.
 Zeros between nonzero digits are
significant.
 Zeros in front of all nonzero digits are NOT
significant.
 Zeros at the end of a number and to the
right of a decimal point are significant.
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2-3 Significant Digits

Determine the number of significant digits
in the following measurements:
 804.05
g
 0.0144030 km
 1002 m
 400 mL
 30000. cm
 0.000625000 kg
2-3 Significant Figures and
Calculations
Addition/subtraction – go by smallest
number of decimal places
 Multiplication/division – go by smallest
number of significant figures

4.57 g
+
3.2 g
7.77g  7.8 g
3.21 m
X
4.512 m
14.48352 m2  14.5 m2
2-3 Significant Figures and
Conversions
Equalities are definitions, and therefore
have NO uncertainty.
 There are EXACTLY 100 cm in a meter, by
definition.
 When you convert a value, your answer
will have the SAME number of significant
figures as the original value.

4.608 m x 100cm/1m = 460.8 cm
2-3 Scientific Notation

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Numbers are written in the form M x 10n, where
M is a number greater than or equal to one but
less than 10 and n is a whole number.
Express the following in scientific notation:
 67000
 0.00325
 9732000000
 0.0000017
 621.0
2-3 Direct Proportions

Two quantities are directly proportional to
each other if dividing one by the other
gives a constant value
 y/x
=k
k is the proportionality constant
 Ratio between the variables remains constant
 Rearrange to get y = kx (straight line)
 Therefore, a graph of a directly proportional
relationship will be linear. (e.g. density)

2-3 Inverse Proportions

Two quantities are inversely proportional
to each other if their product is a constant
 xy
=k
k is the proportionality constant
 A graph of an inversely proportional relationship
produces a curve called a hyperbola

Gas Volume v. Pressure