Transcript Chapter 2 lecture

Video 2-1



Scientific Method
Units of Measurement
Metric Conversions
Chapter 2
MEASUREMENT AND
CALCULATIONS
I. Scientific Method

logical approach to problem solving
I. Scientific Method
Basic Steps:
1. State problem (based on observations)
2. Observe and collect data (senses and
instruments)

Data—recorded observations


qualitative (descriptive)
quantitative (numerical)
I. Scientific Method
Basic Steps:
3. Form hypothesis (testable statement)
4. Testing
a.
b.
c.
d.
Experimental setup (contains variable being
tested)
Control (identical to experimental setup
EXCEPT for the variable)
Ideally, only one variable
Done multiple times (for consistency)
I. Scientific Method
Basic Steps:
5. Theorizing (conclusion)
a. hypotheses  model  theory
NOTE: Theories CANNOT turn into Laws
WHY?
I. Scientific Method
Basic Steps:
Theory– attempts to explain WHY a set
of conditions produce a certain result
Law– states that a certain set of
conditions will always produce a
certain result but DOES NOT
EXPLAIN WHY.
I. Scientific Method
Basic Steps:
Ex. Theory of Plate Tectonics
Ex. Law of Universal Gravitation
I. Scientific Method
Basic Steps:
A scientific theory makes falsifiable
predictions about things not yet observed.

A “theory” that makes no predictions that
will ever be observed is not a theory.

Predictions which are not sufficiently
specific to be falsified are meaningless and
likewise not a scientific theory.
II. Units of Measurements

Temperature Scales:
180
Water
100
100
oF
oC
(Fahrenheit)
K
(Kelvin)
373.15
Boiling pt.
212
(Celsius)
100
Freezing
pt.
Absolute
Zero
32
0
273.15
-459.67
-273.15
0
II. Units of Measurements



Temperature Scales:
180 oF = 100 oC = 100 K
1.8 oF = 1 oC = 1 K
II. Units of Measurements



Converting between Temperature Scales:
K = oC + 273.15
oF = (oC x 9/5) + 32
NOTE: You solve for the variable on the LEFT
SIDE (your given quantity goes on the right
side. Rearrange equations using algebra if
necessary.
II. Units of Measurements
Converting between Temperature Scales:
Ex. Normal body temperature of humans is
often described as around 98.6 oF.
Determine what this is on the Celsius and
Kelvin scales.

II. Units of Measurements


Density:
mass per unit volume
D=m/V
m=DxV
II. Units of Measurements





Density:
Units:
kg / m3 (gives VERY large numbers for
dense substances; good for gases)
g / cm3
g / mL
II. Units of Measurements

Density:
NOTE: 1 cm3 = 1 mL
1 cm3 is the volume occupied by a cube that
measures 1 cm on each side.
Denser objects will sink in less dense fluids.
II. Units of Measurements
Density:
Ex. An object is placed into a graduated
cylinder with 35.3 mL of water. After the
object sinks, the volume of the water rises
to 46.8 mL. If the object’s density is 2.47
g/cm3, what is the mass of the object?

II. Units of Measurements
Density:
Ex. Why will a 10.0 gram ball of clay sink if
placed into a tray of water, but float if the
clay is flattened out into the shape of a
boat? NOTE: The density of water is 1.00
g/mL.

IV. Metric Conversion
Kids Have Dropped over dead converting metrics
I
L
O
E
C
T
A
e
c
i
E
K
A
2.45 hg =
e
n
t
i
245.
KHDodcm
END
START
i
l
l
i
g
IV. Metric Conversion
Kids Have Dropped over dead converting metrics
0 0 0 8.3 mm =
.00083
KHDodcm
END
START
dam
IV. Metric Conversion
Kids Have Dropped over dead converting metrics



mega (M) = 106
giga (G) = 109
tera (T) = 1012
micro (m) = 10-6
nano (n) = 10-9
pico (p) = 10-12
T__G__M__ KHDodcm__m__n__p
Video 2-2




Scientific Notation
Significant Figures
Math and Sigfigs
Percent Error
VII. Scientific Notation

value is expressed in the form:
a.bbb x 10y
where a.bbb must be between 1 and 10
VII. Scientific Notation

Ex. Write the following in scientific notation:
5203.04
= 5.20304 x 103
 0.000254
= 2.54 x 10-4
 102.56 x 102
= 1.0256 x 104
 2.5498
= 2.5498 x 100

VII. Scientific Notation


Use your calculator to convert standard
notation into scientific notation
Look for the “sci” mode (varies with
calculators)
VIII. Significant Figures


Significant figures: all the numbers in a
measurement that can be known precisely
plus a last digit that must be estimated.
All the numbers you are sure of plus one
more decimal place (estimated).
VIII. Significant Figures
Rules for determining HOW MANY
SIGFIGS in a measurement:
1) Count all nonzero digits (no matter is before
or after decimal).
Ex. 584.39 g
2) Count all zeros between nonzero numbers.
Ex. 4300.002308 mL

VIII. Significant Figures
Rules for determining HOW MANY
SIGFIGS in a measurement:
3) Do NOT count zeros in front of nonzero
digits (place holders).
Ex. 0.000546902 kg

VIII. Significant Figures
Rules for determining HOW MANY
SIGFIGS in a measurement:
4) Count zeros at the END of a number ONLY
if the number contains a decimal point. If
there is no decimal point, the zeros are
UNCERTAIN.
Ex.
4950.87000 mm
678900 L

VIII. Significant Figures

Ex. Determine how many sigfigs are in each
of the following measurements:

354.2 g
4
6
32.0305 mL
0.00254 km 3
5
0.34050 mm
235000 hL
?




VIII. Significant Figures

When rounding off a number to a specific
number of sigfigs:


Find the LAST sigfig in the number and look at
the number AFTER it. If it is 5 or greater, round
the last sigfig up (ignore book rules). If it is less
than five, drop all digits after the last sigfig.
NOTE: When converting a measurement to
scientific notation, the number of sigfigs
MUST be the same as in the original
measurement.
VIII. Significant Figures

Ex. Round off the following numbers to the
indicated number of sigfigs and rewrite the
answer in scientific notation.
measurement
No. of sigfigs
Answer
Scientific Notation
5247.23 g
5
5247.2 g
5.2472 x 103 g
96742.35 m
3
96700 m
9.67 x 104 m
0.045038 L
1
0.05 L
5 x 10-2 L
24.85 x 106 g
2
25 x 106 g
2.5 x 107 g
IX. Mathematical Operations
with Sigfigs

Addition or Subtraction:

The answer must have the same number of
DECIMAL PLACES as the measurement with
the LEAST number of decimal places.
IX. Mathematical Operations
with Sigfigs
Ex. Answer the following with the correct
number of sigfigs:
575.047 = 575.05
563.02 + 12.027 =
1002.5 + 0.254831 = 1002.754831 = 1002.8
500 – 6.842 + 24.51 = 517.668 = 518
IX. Mathematical Operations
with Sigfigs

Multiplication or Division:

The answer cannot have more sigfigs than the
measurement with the LEAST total number of
sigfigs.
IX. Mathematical Operations
with Sigfigs
Ex. Answer the following with the correct
number of sigfigs:
46.8402662 = 46.84
563.02 ÷ 12.02 =
10.05 x 0.254 = 2.5527 = 2.55
508 ÷ 6.842 x 24.51 = 1819.801228 = 1.82 x 103
IX. Mathematical Operations
with Sigfigs

For all operations, perform ALL similar
operations (+ and – are similar; x and  are
similar) FIRST, then round off to the proper
number of sigfigs.

Do NOT round off after each calculation
IX. Mathematical Operations
with Sigfigs
Ex. Answer the following with the correct
number of sigfigs:
563.02 x 12.02 / 21.3 = 317.7230235
10.05 + 0.254 – 6.2 = 4.104 = 4.1
= 318
IX. Mathematical Operations
with Sigfigs

If there is a mixture of operations, round off
before going to a “dissimilar” operation.

Use the rules for the last operation you just did.
IX. Mathematical Operations
with Sigfigs
Ex. Answer the following with the correct
number of sigfigs:
(563.02 ÷ 12.02) + 3.2 = 46.8402662 + 3.2
= 46.84 + 3.2
= 50.04 = 50.0
IX. Mathematical Operations
with Sigfigs
Ex. Answer the following with the correct
number of sigfigs:
(563.02 + 12.8) x 3.2 / 5.408 =
575.82 x 3.2 / 5.408 = 575.8 x 3.2 / 5.408
= 340.7100592
= 340 = 3.4 x 102
X. Calculating Percent Error

Percent error
% error =


Valueaccepted - Valueexperimental
Valueaccepted
can have a positive or negative value
Less than 5% error (for small values)
X 100%
Video 2-3

Graphing Data and Numerical
Relationships
XI. Graphing Data and
Numerical Relationships




Directly proportional quantities:
y/x = a constant
y = kx
where k is the slope
 straight line
XI. Graphing Data and
Numerical Relationships
.
.
.
.
Y
.
.
.
X
.
XI. Graphing Data and
Numerical Relationships




Inversely proportional quantities:
xy = a constant
y = k/x
 hyperbola
XI. Graphing Data and
Numerical Relationships
.
Y
.
.
.
.
X
.
.
XI. Graphing Data and
Numerical Relationships


GRAPHING DATA:
Often, you will have to graph data that you
measured. In experimental sciences, there
are two types of variables:
XI. Graphing Data and
Numerical Relationships
1.
2.
Independent variables—a variable that
YOU can determine, manipulate, vary,
control, etc.
Dependent variable—a variable that
CHANGES (or is determined) by your
actions or input.
XI. Graphing Data and
Numerical Relationships



X-axis: independent axis (variable)
Y-axis: dependent axis (variable)
Graphing is ALWAYS the dependent vs.
independent variable (y vs. x)
XI. Graphing Data and
Numerical Relationships
Temperature vs. Time
Temperature
(oC)
Time (seconds)
Video 2-4



Dimensional Analysis
Derived Units
Problem Solving Strategies
XII. Dimensional Analysis

When CONVERTING a measurement
between one system of units to another,
simply do this:
Given Quantity (units) X
number new units
number units getting rid of
XII. Dimensional Analysis

When CONVERTING a measurement
between one system of units to another,
simply do this:
number new units
Given Quantity (units) X
number units getting rid of
CONVERSION FACTOR
XII. Dimensional Analysis



Conversion factor is simply (and ALWAYS)
a fraction that is equal to 1
Numerator is equivalent to the denominator
Use EQUALITIES
XII. Dimensional Analysis

Examples:
1 ft = 12 inches
1 hr = 3600 sec
2.205 lbs = 1 kg
1000 m = 1 km
NOTE: the 1 ft, 1 kg, 1 km, 1 hr in these
equalities are EXACT (defining) quantities
and have an INFINITE number of sigfigs
(values are 1.000000000000000 . . .)
XII. Dimensional Analysis

Examples:
How many pounds are in 9.8 kg?
9.8 kg
x
2.205
1
= 21.609 lbs
lbs
kg
= 22 lbs
XII. Dimensional Analysis

Examples:
If 1 inch is equivalent to 2.54 cm, how many
inches are in 2.50 m? 1 inch = 2.54 cm
100 cm
2.50 m
x
1
= 98.42519685 in
m
x
= 98.4 in
1 in
2.54 cm
III. Derived Units

units that are obtained by multiplying or
dividing standard units:



Ex. volume = length (m) x width (m) x height (m)
V = m x m x m = m3
Finding equivalent units:
III. Derived Units

Finding equivalent units:
1 m3 = ? cm3
1 m = 100 cm
(1 m)3 = (100 cm)3
1 m3 = 1,000,000 cm3 = 1 x 106 cm3
III. Derived Units

Finding equivalent units:
Ex. How many square feet are equivalent to a
square meter? 1 meter = 3.28 feet
XIII. Problem Solving
Strategies
The problems facing you in this class will fall
into one of the following categories:
1. Conversion (changing a measurement to a
different unit)
2. Formula (changing one type of
measurement to a different TYPE of
measurement)
XIII. Problem Solving
Strategies
Often, you will need to do both things. So,
 first, determine which formula you need to
use (rearrange the formula for the
unknown)
 second, convert any given quantities into
the proper units if necessary
 third, plug the values in and calculate
XIII. Problem Solving
Strategies
What are some terms that mean:
 Equals
 Add
 Subtract
 Multiply
 Divide
Video 2-5


Measuring Techniques
Accuracy and Precision
V. MEASURING TECHNIQUES


A measurement is a comparison against a
STANDARD UNIT.
3 Standard types of measurements:



Mass (the amount of matter present in
something)
Volume (the amount of space something takes
up)
Length (the distance from one part of the object
to another part)
V. MEASURING TECHNIQUES

Standard units (Metric System)



Length: Meter (millimeter, centimeter,
kilometer)
Volume: Liter (milliliter, cubic centimeter)
Mass: Kilogram (gram, milligram)
V. MEASURING TECHNIQUES
MAKING MEASUREMENTS:

1) Determine the value of the
SMALLEST unit (line) that the
instrument will measure.
V. MEASURING TECHNIQUES

Meter stick (ruler):

1 line = 1 millimeter = 0.1 centimeters
V. MEASURING TECHNIQUES

Electronic Balance (mass):

No lines (digital display)
V. MEASURING TECHNIQUES

Graduated cylinder (volume): varies with
capacity of the cylinder
V. MEASURING TECHNIQUES
2) Use proper techniques for measuring:
 Rulers: Do NOT start measuring from the
beginning of the ruler. Start from the 1
centimeter (10 millimeter) mark.
SUBTRACT 1 cm (or 10 mm) from your
measurement.
V. MEASURING TECHNIQUES
V. MEASURING TECHNIQUES
2) Use proper techniques for measuring:
 Balance: Record reading after it has
stabilized (check and include units)
V. MEASURING TECHNIQUES
2) Use proper techniques for measuring:
 Graduated cylinder: Make sure the
meniscus (curve of fluid) is at eye level.
Read the BOTTOM of the meniscus.
V. MEASURING TECHNIQUES
3) Estimating decimal places.
 Make sure you ESTIMATE one more
decimal place to the right. If the instrument
reads to the 0.1, estimate to the 0.01 place.
V. MEASURING TECHNIQUES
3) Estimating decimal places.
V. MEASURING TECHNIQUES
3) Estimating decimal places.
V. MEASURING TECHNIQUES
4) Filling a cylinder to a specific volume.

Use a beaker and dropper to fill a
GRADUATED CYLINDER.
V. MEASURING TECHNIQUES
5) Electronic Balance:


Tare (or Zero) button will set reading
to 0.00 g (ignores any mass on
balance)
Do NOT estimate an extra decimal
place (last digit is already an
estimate).
V. MEASURING TECHNIQUES
5) Electronic Balance:
V. MEASURING TECHNIQUES
6) Choosing the correct piece of lab
equipment:
When should you use a
 Beaker?
V. MEASURING TECHNIQUES
6) Choosing the correct piece of lab
equipment:
When should you use a
 Beaker?
 Holding liquid (easy to pour)
 Mixing liquid with stirring rod
 Heating liquid
 NOT for measuring volume
V. MEASURING TECHNIQUES
6) Choosing the correct piece of lab
equipment:
When should you use a
 Erlenmeyer flask?
V. MEASURING TECHNIQUES
6) Choosing the correct piece of lab
equipment:
When should you use a
 Erlenmeyer flask?
 Mixing (swirling) liquid
 Heating liquid
 NOT for pouring
 NOT for measuring volume
V. MEASURING TECHNIQUES
6) Choosing the correct piece of lab
equipment:
When should you use a
 Graduated cylinder?
V. MEASURING TECHNIQUES
6) Choosing the correct piece of lab
equipment:
When should you use a
 Graduated cylinder?
 Measuring volumes accurately
 NOT for heating
 NOT for storing large quantities
V. MEASURING TECHNIQUES
6) Choosing the correct piece of lab
equipment:
When should you use a
 Pipet?
V. MEASURING TECHNIQUES
6) Choosing the correct piece of lab
equipment:
When should you use a
 Pipet?
 TRANSFERRING a precise amount of
liquid
V. MEASURING TECHNIQUES
6) Choosing the correct piece of lab
equipment:
When should you use a
 Buret?
V. MEASURING TECHNIQUES
6) Choosing the correct piece of lab
equipment:
When should you use a
 Buret?
 When you DON’T know how much of a
liquid you will need
 Transferring precise amounts of liquid.
V. MEASURING TECHNIQUES
6) Choosing the correct piece of
lab equipment:
 What size should you use?

Smallest size possible that
will “get the job done”
(measure quantities without
being refilled).
VI. Accuracy and Precision



Accuracy: the closeness of measurements
to the correct or accepted value of the
measured quantity.
Precision: the reproducibility of a set of
measurements made in the same way.
Significant figures (sigfigs) reflect the
precision of a measurement.
VI. Accuracy and Precision

Neither accurate nor precise
VI. Accuracy and Precision

Precise
VI. Accuracy and Precision

Both accurate and precise
VI. Accuracy and Precision
Examples:
 One students measures the length of an
object to be 10.2 cm. The actual length is
10.8 cm. Is his measurement accurate?
Precise?
VI. Accuracy and Precision
Examples:
 One students measures the length of an
object to be 10.2 cm. The actual length is
10.8 cm. Is his measurement accurate?
Precise?
 % error = (10.8 – 10.2) / 10.8 x 100
= 5.56 %
VI. Accuracy and Precision
Examples:
 One students measures the length of an
object to be 10.2 cm. The actual length is
10.8 cm. Is his measurement accurate?
Precise?
 To determine if it is precise, more
measurements are needed.
VI. Accuracy and Precision
Examples:
 One students measures the length of an
object to be 10.2 cm. The actual length is
10.8 cm. Is his measurement accurate?
Precise?
 He measures it 3 more times. Values are
10.7 cm, 11.4 cm, and 10.9 cm.
VI. Accuracy and Precision
Examples:
 One students measures the length of an
object to be 10.2 cm. The actual length is
10.8 cm. Is his measurement accurate?
Precise?
 NOT precise. But, the average of his 4
measurements is 10.8 cm.
 Improved ACCURACY
VI. Accuracy and Precision
Why is his precision poor?
 What do the markings on his ruler look like?
 Remember the rules for measuring


One more decimal place than the ruler can read
to.
Ruler’s smallest marking are 1 cm
VI. Accuracy and Precision
Why is his precision poor?
 If the marking are worth 0.1 cm he can
better estimate the measurement (sure of
the 0.1 cm, estimate the 0.01 cm place).
 Measurements should be REPRODUCIBLE
to the 0.1 cm
 Does NOT mean they will be accurate