Transcript CH2 Notes

Chapter 2
Scientific Measurement
Chapter 2 Goals – Scientific Measurement
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Calculate values from measurements using the
correct number of significant figures.
List common SI units of measurement and
common prefixes used in the SI system.
Distinguish mass, volume, density, and specific
gravity from one another.
Evaluate the accuracy of measurements using
appropriate methods.
Introduction
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Everyone uses measurements in some form
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Deciding how to dress based on the temperature;
measuring ingredients for a recipes; construction.
Measurement is also fundamental in the sciences
and for understanding scientific concepts
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It is important to be able to take good
measurements and to decide whether a measurement
is good or bad
Introduction
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In this class we will make measurements and
express their values using the International
System of Units or the SI system.
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All measurements have two parts: a number and a
unit.
2.1 The Importance of Measurement
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Qualitative versus Quantitative Measurements
Qualitative measurements give results in a
descriptive, nonnumeric form; can be influenced by
individual perception
 Example: This room feels cold.
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2.1 The Importance of Measurement
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Qualitative versus Quantitative Measurements
Quantitative measurements give results in definite
form usually, using numbers; these types of
measurements eliminate personal bias by using
measuring instruments.
 Example: Using a thermometer, I determined that
this room is 24°C (~75°F)
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Measurements can be no more reliable than
the measuring instrument.
2.1 Concept Practice
1. You measure 1 liter of water by filling an empty 2liter soda bottle half way. How can you improve the
accuracy of this measurement?
2. Classify each measurement as qualitative or
quantitative.
a. The basketball is brown
b. the diameter of the basketball is 31 centimeters
c. The air pressure in the basketball is 12 lbs/in2
d. The surface of the basketball has indented seams
2.2 Accuracy and Precision
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Good measurements in the lab are both correct
(accurate) and reproducible (precise)
accuracy – how close a single measurement comes
to the actual dimension or true value of whatever is
measured
 precision – how close several measurements are to
the same value
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Example: Figure 2.2, page 29 – Dart boards….
2.2 Accuracy and Precision
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All measurements made with instruments are
really approximations that depend on the quality
of the instruments (accuracy) and the skill of the
person doing the measurement (precision)
The precision of the instrument depends on the
how small the scale is on the device.
The finer the scale the more precise the instrument.
 2.2 Demo, page 28
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2.2 Concept Practice
3. Which of these synonyms or characteristics
apply to the concept of accuracy? Which apply
to the concept of precision?
a. multiple measurements
b. correct
c. repeatable
d. reproducible
e. single measurement
f. true value
2.2 Concept Practice
4. Under what circumstances could a series of
measurements of the same quantity be precise
but inaccurate?
2.3 Scientific Notation
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In chemistry, you will often encounter numbers
that are very large or very small
One atom of gold = 0.000000000000000000000327g
 One gram of H = 301,000,000,000,000,000,000,000 H
molecules
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Writing and using numbers this large or small is
calculations can be difficult
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It is easier to work with these numbers by writing them
in exponential or scientific notation
2.3 Scientific Notation
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scientific notation – a number is written as the
product of two numbers: a coefficient and a
power of ten
Example: 36,000 is written in scientific notation
as 3.6 x 104 or 3.6e4
Coefficient = 3.6 → a number greater than or equal
to 1 and less than 10.
 Power of ten / exponent = 4
 3.6 x 104 = 3.6 x 10 x 10 x 10 x 10 = 36,000
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2.3 Scientific Notation
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When writing numbers greater than ten in
scientific notation the exponent is positive
and equal to the number of places that the
exponent has been moved to the left.
2.3 Scientific Notation
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Numbers less than one have a negative
exponent when written in scientific notation.
Example: 0.0081 is written in scientific notation as
8.1 x 10-3
 8.1 x 10-3 = 8.1/(10 x 10 x 10) = 0.0081
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When writing a number less than one in
scientific notation, the value of the exponent
equals the number of places you move the
decimal to the right.
2.3 Scientific Notation
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To multiply numbers written in scientific notation,
multiply the coefficients and add the
exponents.
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(3 x 104) x (2 x 102) = (3 x 2) x 104+2 = 6 x 106
To divide numbers written in scientific notation,
divide the coefficients and subtract the
exponent in the denominator (bottom) from the
exponent in the numerator (top).
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(6 x 103)/(2 x 102) = (6/2) x 103-2 = 3 x 101
2.3 Scientific Notation
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Before numbers written in scientific notation are
added or subtracted, the exponents must be
made the same (as a part of aligning the
decimal points).
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(5.4 x 103)+(6 x 102) = (5.4 x 103)+(0.6 x 103)
= (5.4 + 0.60) x 103 = 6.0 x 103
2.3 Concept Practice
5. Write the two measurements given in the first
paragraph of this section in scientific notation.
a. mass of a gold atom =
0.000000000000000000000327g
b. molecules of hydrogen =
301,000,000,000,000,000,000,000 H molecules
2.3 Concept Practice
6. Write these measurements in scientific notation.
The abbreviation m stands for meter, a unit of
length.
a. The length of a football field, 91.4 m
b. The diameter of a carbon atom, 0.000000000154 m
c. The radius of the Earth, 6,378,000 m
d. The diameter of a human hair, 0.000008 m
e. The average distance between the centers of the
sun and the Earth, 149,600,000,000 m
2.4 Significant Figures in
Measurement
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The significant figures in a measurement
include all the digits that are known precisely
plus one last digit that is estimated.
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Example: With a thermometer that has 1° intervals,
you may determine that the temperature is between
24°C and 25°C and estimate it to be 24.3°C.
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You know the first two digits (2 and 4) with certainty, and
the third digit (3) is a “best guest”
By estimating the last digit, you get additional
information
Rules
1. Every nonzero digit in a recorded measurement is
significant.
- Example: 24.7 m, 0.743 m, and 714 m all have three sig.
figs.
2. Zeros appearing between nonzero digits are significant.
- Example: 7003 m, 40.79 m, and 1.503 m all have 4 sig.
figs.
Rules
3. Zeros appearing in front of all nonzero digits are not
significant; they act as placeholders and cannot
arbitrarily be dropped (you can get rid of them by
writing the number in scientific notation).
- Example: 0.0071 m has two sig. figs. And can be
written as 7.1 x 10-3
4. Zeros at the end of the number and to the right
of a decimal point are always significant.
- Example: 43.00 m, 1.010 m, and 9.000 all have
4 sig. figs.
Rules
5. Zeros at the end of a measurement and to the
left of the decimal point are not significant
unless they are measured values (then they
are significant). Numbers can be written in
scientific notation to remove ambiguity.
- Example: 7000 m has 1 sig. fig.; if those zeros
were measured it could be written as 7.000 x 103
Rules
6. Measurements have an unlimited number of
significant figures when they are counted or
if they are exactly defined quantities.
- Example: 23 people or 60 minutes = 1 hour
* You must recognize exact values to round of
answers correctly in calculations involving
measurements.
Significant Figures – Example 1
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How many significant figures are in each of the
following measurements?
a. 123 m
b. 0.123 cm
c. 40506 mm
d. 9.8000 x 104 m
e. 4.5600 m
f. 22 meter sticks
g. 0.07080 m
h. 98000 m
2.4 Concept Practice
7. Write each measurement in scientific notation
and determine the number of significant figures
in each.
a. 0.05730 m
b. 8765 dm
c. 0.00073 mm
d. 12 basketball players
e. 0.010 km
f. 507 thumbtacks
Significant Figures in Calculations
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The number of significant figures in a
measurement refers to the precision of a
measurement; an answer cannot be more
precise than the least precise measurement
from which it was calculated.
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Example: The area of a room that measures 7.7 m (2
sig. figs.) by 5.4 m (2 sig. figs.) is calculated to be
41.58 m2 (4 sig. figs.) – you must round the answer to
42 m2
Rounding – The Rule of 5
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If the digit to the right of the last sig. fig is less
than 5, all the digits after the last sig. fig. are
dropped.
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Example: 56.212 m rounds to 56.21 m (for 4 sig. figs.)
If the digit to the right is 5 or greater, the value of
the last sig. fig. is increased by 1.
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Example: 56.216 m rounds to 56.22 m (for 4 sig. figs.)
Rounding – Example 2
Addition and Subtraction
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The answer to an addition or subtraction
problem should be rounded to have the
same number of decimal places as the
measurement with the least number of
decimal places.
Multiplication and Division
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In calculations involving multiplication and
division, the answer is rounded off to the
number of significant figures in the least precise
term (least number of sig. figs.) in the
calculations
2.6 SI Units
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The International System of Units, SI, is a
revised version of the metric system
Correct units along with numerical values are
critical when communicating measurements.
The are seven base SI units (Table 2.1) of which
other SI units are derived.
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Sometimes non-SI units are preferred for
convenience or practical reasons
2.6 SI Units – Table 2.2
Quantity
Length
SI Base or Derived Unit
meter (m)
Non-SI Unit
cubic meter (m3)
liter
kilogram (kg)
grams per cubic centimeter
(g/cm3); grams per mililiter
(g/mL)
Temperature kelvin (K)
degree Celcius (°C)
Volume
Mass
Density
Time
Pressure
second (s)
Pascal (Pa)
Energy
joule (J)
atmosphere (atm); milimeter
of mercury (mm Hg)
calorie (cal)
Common SI Prefixes
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Units larger than the base unit
Tera
Giga
Mega
Kilo
Hecto
Deka
Base Unit
T
G
M
k
h
da
e-12 = 0.000000000001 terameter (Tm)
e-9 = 0.000000001
e-6 = 0.000001
e-3 = 0.001
e-2 = 0.01
e-1 = 0.1
e0 = 1
gigameter (Gm)
megameter (Mm)
kilometer (km)
hectometer (hm)
decameter (dam)
meter (m)
Common SI Prefixes
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Units smaller than the base unit
Base Unit
Deci
Centi
Milli
Micro
Nano
Pico
e0 = 1
d e1 = 10
c e2 = 100
m e3 = 1000
μ e6 = 1,000,000
n e9 = 1,000,000,000
p e12 = 1,000,000,000,000
meter (m)
decimeter (dm)
centimeter (cm)
millimeter (mm)
micrometer (μm)
Nanometer (nm)
picometer (pm)
Common SI Prefixes
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A mnemonic device can be used to memorize
these common prefixes in the correct order:
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The Great Monarch King Henry Died By Drinking
Chocolate Mocha Milk Not Pilsner
2.7 Units of Length
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The basic unit of length is the meter
Prefixes can be used with the base unit to more
easily represent small or large measurements
Example: A hyphen (12 point font) measures about
0.001 m or 1 mm.
 Example: A marathon race is approximately
42,000 m or 42 km.
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2.7 Concept Practice
15. Use the tables in the text to order these lengths
from smallest to largest.
a. centimeter
b. micrometer
c. kilometer
d. millimeter
e. meter
f. decimeter
2.8 Units of Volume
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The space occupied by any sample of matter is
called its volume
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The volume of rectangular solids can be calculated
by multiplying the length by width by height
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Units are cubed because you are measuring in 3
dimensions
Volume of liquids can be measured with a
graduated cylinder, a pipet, a buret, or a
volumetric flask
2.8 Units of Volume
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A convenient unit of measurement for volume
in everyday use is the liter (L)
Milliliters (mL) are commonly used for smaller
volume measurements and liters (L) for larger
measurements
1 mL = 1 cm3
 10 cm x 10 cm x 10 cm = 1000 cm3 = 1 L
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2.8 Units of Volume
2.8 Concept Practice
17. From what unit is a measure of volume
derived?
2.8 Practice
18. What is the volume of a paperback book 21
cm tall, 12 cm wide, and 3.5 cm thick?
19. What is the volume of a glass cylinder with an
inside diameter of 6.0 cm and a height of 28
cm?
V=πr2h
2.9 Units of Mass
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A person on the moon would weigh 1/6 of his/her
weight on Earth.
This is because the force of gravity on the moon is
approximately 1/6 of its force of Earth.
 Weight is a force – it is a measure of the pull on a
given mass by gravity; it can change by location.
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Mass is the quantity of matter an object
contains
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Mass remains constant regardless of location.
Mass v. Weight
2.9 Units of Mass
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The kilogram is the basic SI unit of mass
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It is defined as the mass of 1 L of water at 4°C.
A gram, which is a more commonly used unit of
mass, is 1/1000 of a kilogram
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1 gram = the mass of 1 cm3 of water at 4°C.
2.9 Concept Practice
20. As you climbed a mountain and the force of
gravity decreased, would your weight increase,
decrease, or remain constant? How would your
mass change? Explain.
21. How many grams are in each of these quantities?
a. 1 cg b. 1 μg
c. 1 kg
d. 1mg
2.10 Density
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Density is the ratio of the mass of an object to
its volume.
Equation → D = mass/volume
Common units: g/cm3 or g/mL
 Example: 10.0 cm3 of lead has a mass 114 g
Density (of lead) = 114 g / 10.0 cm3 = 11.4 g/cm3
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See Table 2.7, page 46
2.10 Density
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Density determines if an object will float in a
fluid substance.
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Examples: Ice in water; hot air rises
Density can be used to identify substances
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See Table 2.8, page 46
2.10 Concept Practice
22. The density of silver is 10.5 g/cm3 at 20°C.
What happens to the density of a 68-g bar of
silver that is cut in half ?
2.10 Concept Practice
23. A student finds a shiny piece of metal that she
thinks is aluminum. In the lab, she determines
that the metal has a volume of 245 cm3 and a
mass of 612 g. Is the metal aluminum?
24. A plastic ball with a volume of 19.7 cm3 has a
mass of 15.8 g. Would this ball sink or float in a
container of gasoline?
2.10 Specific Gravity (Relative Density)
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Specific gravity is a comparison of the density
of a substance to the density of a reference
substance, usually at the same temperature.
Water at 4°C, which has a density of 1 g/cm3, is
commonly used as a reference substance.
Specific gravity = density of substance (g/cm3)
density of water (g/cm3)
 Because units cancel, a measurement of specific
gravity has no units
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A hydrometer can be used to measure the specific
gravity of a liquid.
2.11 Concept Practice
25. Why doesn’t a measurement of specific gravity
have a unit?
26. Use the values in Table 2.8 to calculate the
specific gravity of the following substances.
a. Aluminum
b. Mercury
c. ice
2.12 Measuring Temperature
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Temperature determines the direction of heat
transfer between two objects in contact with each
other.
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Heat moves from the object at the higher temperature
to the object at a lower temperature.
Temperature is a measure of the degree of
hotness or coldness of an object.
Almost all substances expand with an increase in
temperature and contract with a decrease in
temperature
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An important exception is water
2.12 Measuring Temperature
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There are various temperature scales
On the Celsius temperature scale the freezing
point of water is taken as 0°C and the boiling
point of water at 100°C
2.12 Measuring Temperature
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The Kelvin scale (or absolute scale) is another
temperature scale that is used
On the Kelvin scale the freezing point of water is
273 K and the boiling point is 373 K (degrees are not
used).
 1°C = 1 Kelvin
 The zero point (0 K) on the Kelvin scale is called
absolute zero and is equal to -273°C
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Absolute zero is where all molecular motion stops
2.12 Measuring Temperature
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Converting Temperatures:
K = °C + 273
 °C = K - 273
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2.12 Concept Practice
27. Surgical Instruments may be sterilized by
heating at 170°C for 1.5 hours. Convert 170°C
to kelvins.
28. The boiling point of the element argon is 87
K. What is the boiling point of argon in °C?
2.13 Evaluating Measurements
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Accuracy in measurement depends on the
quality of the measuring instrument and the
skill of the person using the instrument.
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Errors in measurement could have various causes
In order to evaluate the accuracy of a
measurement, you must be able to compare it to
the true or accepted value.
2.13 Evaluating Measurements
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accepted value – the true or correct value
based or reliable references
experimental value – the measured value
determined in the experiment
The difference between the accepted value and
the experimental value is the error.
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error = accepted value – experimental value
2.13 Evaluating Measurements
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The percent error is the error divided by the
accepted value, expressed as a percentage of
the accepted value.
|error|
Percent Error =
x 100
AV
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An error can be positive or negative, but an
absolute value of error is used so that the
percentage is positive
2.13 Concept Practice
32. A student estimated the volume of a liquid in a
beaker as 208 mL. When she poured the liquid
into a graduated cylinder she measured the value
as 200 mL. What is the percent error of the
estimated volume from the beaker, taking the
graduated cylinder measurement as the accepted
value?