Download Chemistry: Matter and Change

Measurement and Dimensional Analysis
Vocabulary:
Qualitative
Quantitative
Accuracy
Precision
Metric Units
Meters
Grams
Liters
Significant Figures
Conversion Factors
Objectives:
1. Compare accuracy and precision.
2. Define base units for time, length and mass.
3. Explain how adding a prefix changes a unit.
4. Compare the derived units for volume and
density.
5. Apply rules for significant figures.
6. Express numbers in scientific notation
7. Convert between units using dimensional
analysis.
Qualitative vs. Quantitative
Qualitative measurements give results in a descriptive
nonnumeric form. (The result of a measurement is
an adjective describing the object.)
Examples: short , heavy , long, cold, etc…
Quantitative measurements give results in numeric
form. (The results of a measurement contain a
number.)
Examples: 4’6”, 600 lbs, 22 meters, 5 ᵒC, etc…
Accuracy and Precision
• Accuracy refers to how close a measured
value is to an accepted value.
• Precision refers to how close a series of
measurements are to one another.
Practice Problem: Describe the shots for the targets.
Accuracy and Precision (cont.)
• Error is defined as the difference between
an experimental value and an accepted
value.
Accuracy and Precision (cont.)
• The error equation is
error = experimental value – accepted value.
• Percent error expresses error as a
percentage of the accepted value.
Significant Figures
• Often, precision is limited by the tools
available.
• Significant figures include all known digits
plus one estimated digit.
Significant Figures in class
In Lab:
Whenever a value is measured, (such as the length of
an object with a ruler), it must have correct sig figs
this means all numbers that are known
Record one last digit for the measurement that is
estimated. (This means that you will reading in-between the
marks of the device and make a thoughtful approximation of what
the next number is.)
Significant Figures (cont.)
• Rules for significant figures
– Rule 1: Nonzero numbers are always significant.
– Rule 2: Zeros between nonzero numbers are
always significant.
– Rule 3: All final zeros to the right of the decimal
are significant.
– Rule 4: Placeholder zeros are not significant. To
remove placeholder zeros, rewrite the number in
scientific notation.
– Rule 5: Counting numbers and defined constants
have an infinite number of significant figures.
Rounding Numbers
• Calculators are not aware of significant
figures.
• Answers should include the number of
significant figures from the data with the
smallest number of significant figures.
Rounding Numbers (cont.)
• Rules for rounding
– Rule 1: If the digit to the right of the last significant
figure is less than 5, do not change the last
significant figure.
– Rule 2: If the digit to the right of the last significant
figure is greater than 5, round up to the last
significant figure.
– Rule 3: If the digits to the right of the last significant
figure are a 5 followed by a nonzero digit, round up
to the last significant figure.
Rounding Numbers (cont.)
• Rules for rounding (cont.)
– Rule 4: If the digits to the right of the last significant
figure are a 5 followed by a 0 or no other number at
all, look at the last significant figure. If it is odd,
round it up; if it is even, do not round up.
Rounding Numbers (cont.)
• Addition and subtraction
– Round numbers so all numbers have the same
number of digits to the right of the decimal.
• Multiplication and division
– Round the answer to the same number of significant
figures as the original measurement with the fewest
significant figures.
Significant Figures
Practice Problems: What is the length recorded to
the correct number of significant figures?
length =
________cm
(cm) 10
20
30
40
length = ________cm
50
60
70
80
90
100
The SI System
(Système Internationale d'Unités )
The system of measurements
used throughout the scientific
community is called “The SI
system”
Scientists use this system
internationally which allows
for consistency between
research communities.
Metric Conversions
The metric system prefixes are based on mass.
Here is a list of the common prefixes used in chemistry:
Units (cont.)
• The SI base unit of temperature
is the kelvin (K).
• Zero kelvin is the point where
there is virtually no particle
motion or kinetic energy, also
known as absolute zero.
• Two other temperature scales
are Celsius and Fahrenheit.
• K = °C + 273
Derived Units
• Not all quantities can be measured with SI
base units.
• A unit that is defined by a combination of
base units is called a derived unit.
Derived Units (cont.)
• Volume is measured in cubic meters (m3), but
this is very large. A more convenient measure
is the liter, or one cubic decimeter (dm3).
Derived Units (cont.)
• Density is a derived unit, g/cm3, the
amount of mass per unit volume.
• The density equation is
density = mass/volume.
Section 2.1 Assessment
Which of the following is a derived unit?
A. yard
B. second
C. liter
D
C
A
0%
B
D. kilogram
A. A
B. B
C. C
0%
0%
0%
D. D
Section 2.1 Assessment
What is the relationship between mass
and volume called?
A. density
B. space
D
A
0%
C
D. weight
A. A
B. B
C. C
0%
0%
0%
D. D
B
C. matter
Scientific Notation
Scientific notation can be used to express any number
as a number between 1 and 10 (the coefficient)
multiplied by 10 raised to a power (the exponent).
Scientific notation is a shorthand to express a very large
or small number.
Examples:
5,203,000,000,000 miles = 5.203 x 1012 miles
0.000 000 042 mm = 4.2 x 10−8 mm
Steps for Writing Numbers in Scientific Notation
1. Write down all of the sig. figs.
2. Put the decimal point between the first and second
digit.
3. Write “x 10”
4. Count how many places the decimal point has
moved from its original location. This will be the
exponent...either + or −.
5. If the original # was >1, the exponent is (+), and if
the original # was <1, the exponent is (-)
....(In other words, large numbers have (+)
exponents, and small numbers have (-) exponents.
Scientific Notation
Practice Problems: Write the following measurements
in scientific notation or back to their expanded form.
477,000,000 miles =
0.000 910 m =
6.30 x 109 miles =
3.88 x 10−6 kg =
Notes Check:
What is the difference between accuracy and precision?
What are significant figures and why do we use them?
What are SI Units?
Why do we use scientific notation?
Dimensional Analysis
• Dimensional analysis is a systematic approach to
problem solving that uses conversion factors to move,
or convert, from one unit to another.
• A conversion factor is a ratio of equivalent values
having different units.
Examples:1 min/ 60 sec
(or 60 sec/ 1 min)
7 days/ 1 week (or 1 week/ 7 days)
1000 m/ 1 km
(or 1 km/ 1000 m)
Dimensional Analysis
(cont.)
• Using conversion factors
– A conversion factor must cancel one unit
and introduce a new one.
Dimensional Analysis
How to Solve Conversion Problems
Step 1: Find what you know! Draw a long line and place
what you know at the beginning. At the end of the line
put an equals sign.
Step 2: Identify what you are trying to get. Put the units
after the equals sign.
Step 3: Identify the conversion factors needed to get to
the final units.
Step 4: Let’s do a practice problem to figure out the
answer. (Make sure your units cancel out)
Step 5: Multiply everything on top and divide by
everything on the bottom.
Practice Problems:
1. How many hours are there in 3.25 days?
2. How many yards are there in 504 inches?
3. How many days are there in 26,748 seconds?
Converting “Complex” Units
Complex Units are any unit with something in the
numerator and denominator (top and bottom of a
fraction)
example:
When doing a problem with complex units:
-follow the same steps as before
-put the denominator unit beneath the line.
-pick one unit to change at a time.
Practice Problems: (1) The speed of sound is about 330
meters/sec. What is the speed of sound in units of
miles/hour?
(2) The density of water is 1.0 g/mL. What is the density of
water in units of lbs/gallon? (2.2 lbs = 1 kg) (3.78 L = 1 gal)
(3) Convert 33,500 in2 to m2 (5280 ft = 1609 m) (12 inches =
1 foot)
Section 2.2 Assessment
What is a systematic approach to problem
solving that converts from one unit to
another?
A. conversion ratio
A
0%
D
D. dimensional analysis
C
C. scientific notation
A. A
B. B
C. C
0%
0%
0%
D. D
B
B. conversion factor
Section 2.2 Assessment
Which of the following expresses
9,640,000 in the correct scientific
notation?
A. 9.64  104
A
0%
D
D. 9.64  610
C
C. 9.64 × 106
A. A
B. B
C. C
0%
0%
0%
D. D
B
B. 9.64  105
Section 2.3 Assessment
Determine the number of significant
figures in the following:
8,200, 723.0, and 0.01.
A. 4, 4, and 3
A
0%
D
D. 2, 4, and 1
C
C. 2, 3, and 1
A. A
B. B
C. C
0%
0%
0%
D. D
B
B. 4, 3, and 3
Section 2.3 Assessment
A substance has an accepted density of
2.00 g/L. You measured the density as
1.80 g/L. What is the percent error?
A. 0.20 g/L
A
0%
D
D. 0.90 g/L
C
C. 0.10 g/L
A. A
B. B
C. C
0%
0%
0%
D. D
B
B. –0.20 g/L
Which of the following is the SI derived
unit of volume?
A. gallon
B. quart
D
A
0%
C
D. kilogram
A. A
B. B
C. C
0%
0%
0%
D. D
B
C. m3
Which prefix means 1/10th?
A. deciB. hemi-
C. kilo-
D
C
A
0%
B
D. centi-
A. A
B. B
C. C
0%
0%
0%
D. D
Divide 6.0  109 by 1.5  103.
A. 4.0  106
B. 4.5  103
C. 4.0  103
D
C
A. A
B. B
C. C
0%
0%
0%
D. D
B
0%
A
D. 4.5 
106
Round the following to 3 significant
figures 2.3450.
A. 2.35
B. 2.345
D
A
0%
C
D. 2.40
A. A
B. B
C. C
0%
0%
0%
D. D
B
C. 2.34
The rise divided by the run on a line graph
is the ____.
A. x-axis
B. slope
D
A
0%
C
D. y-intercept
A. A
B. B
C. C
0%
0%
0%
D. D
B
C. y-axis
Which is NOT an SI base unit?
A. meter
B. second
C. liter
D
C
A
0%
B
D. kelvin
A. A
B. B
C. C
0%
0%
0%
D. D
Which value is NOT equivalent to the
others?
A. 800 m
B. 0.8 km
D
A
0%
C
D. 8.0 x 105 cm
A. A
B. B
C. C
0%
0%
0%
D. D
B
C. 80 dm
Find the solution with the correct number
of significant figures:
25  0.25
A. 6.25
A
0%
D
D. 6.250
C
C. 6.3
A. A
B. B
C. C
0%
0%
0%
D. D
B
B. 6.2
How many significant figures are there in
0.0000245010 meters?
A. 4
B. 5
D
A
0%
C
D. 11
A. A
B. B
C. C
0%
0%
0%
D. D
B
C. 6
Which is NOT a quantitative measurement
of a liquid?
A. color
B. volume
D
A
0%
C
D. density
A. A
B. B
C. C
0%
0%
0%
D. D
B
C. mass
Section 2.1 Units and Measurements
Key Concepts
• SI measurement units allow scientists to report data
to other scientists.
• Adding prefixes to SI units extends the range of
possible measurements.
• To convert to Kelvin temperature, add 273 to the
Celsius temperature. K = °C + 273
• Volume and density have derived units. Density, which
is a ratio of mass to volume, can be used to identify an
unknown sample of matter.
Section 2.2 Scientific Notation and
Dimensional Analysis
Key Concepts
• A number expressed in scientific notation is written as a
coefficient between 1 and 10 multiplied by 10 raised to a
power.
• To add or subtract numbers in scientific notation, the
numbers must have the same exponent.
• To multiply or divide numbers in scientific notation,
multiply or divide the coefficients and then add or
subtract the exponents, respectively.
• Dimensional analysis uses conversion factors to solve
problems.
Section 2.3 Uncertainty in Data
Key Concepts
• An accurate measurement is close to the accepted
value. A set of precise measurements shows little
variation.
• The measurement device determines the degree of
precision possible.
• Error is the difference between the measured value and
the accepted value. Percent error gives the percent
deviation from the accepted value.
error = experimental value – accepted value
Section 2.3 Uncertainty in Data (cont.)
Key Concepts
• The number of significant figures reflects the
precision of reported data.
• Calculations should be rounded to the correct number
of significant figures.
Section 2.4 Representing Data
Key Concepts
• Circle graphs show parts of a whole. Bar graphs
show how a factor varies with time, location, or
temperature.
• Independent (x-axis) variables and dependent (y-axis)
variables can be related in a linear or a nonlinear
manner. The slope of a straight line is defined as
rise/run, or ∆y/∆x.
• Because line graph data are considered continuous,
you can interpolate between data points or
extrapolate beyond them.