Keys to the Study of Chemistry

• Ashton T. Griffin
• Wayne Community College
• Chapter 1.1-1.6 in Silberberg 5th and 6th ...
Goals & Objectives

• The student will be able to identify the name
and symbol of the first 36 elements on the
periodic ta...
Goals & Objectives

• The student will understand the meaning of
uncertainty in measurements and the use of
significant fi...
Master these Skills

• The student will be able to:
• Use conversion factors in calculations (1.4; SP
1.3-1.5)
• Find the ...
Master these Skills

• The student will be able to:
• Determine the number of significant figures
(SP 1.8) and rounding to...
Chemistry

Chemistry is the study of matter,
its properties,
the changes that matter undergoes,

and
the energy associated...
Definitions
Matter

anything that has both mass and volume
- the “stuff” of the universe: books, planets,
trees, professor...
Physical Properties
properties a substance shows by itself without
interacting with another substance
- color, melting poi...
Figure 1.1 The distinction between physical and chemical change.
Table 1.1 Some Characteristic Properties of Copper
Elements

• The simplest forms of matter
• Cannot be separated by chemical means into
simpler stable substances
• Represen...
The States of Matter
A solid has a fixed shape and volume. Solids may be hard
or soft, rigid or flexible.
A liquid has a v...
Figure 1.2

The physical states of matter.
Temperature and Change of State
• A change of state is a physical change.
– Physical form changes, composition does not.

...
Sample Problem 1.2

Distinguishing Between Physical
and Chemical Change

PROBLEM: Decide whether each of the following pro...
Sample Problem 1.2
SOLUTION:
(a) Frost forms as the temperature drops on a humid winter night.

physical change
(b) A corn...
Energy in Chemistry
Energy is the ability to do work.
Potential Energy
is energy due to the position of an object.

Kineti...
Energy Changes
Lower energy states are more stable and are favored
over higher energy states.
Energy is neither created no...
Figure 1.6

The scientific approach to understanding nature.
Observations

Natural phenomena and measured
events; can be s...
Chemical Problem Solving

• All measured quantities consist of
– a number and a unit.
• Units are manipulated like numbers...
Conversion Factors
A conversion factor is a ratio of equivalent quantities
used to express a quantity in different units.
...
A conversion factor is chosen and set up so that all
units cancel except those required for the answer.

PROBLEM: The heig...
Systematic Approach to Solving Chemistry Problems
• State Problem

Clarify the known and unknown.
• Plan

Suggest steps fr...
Sample Problem 1.3

Converting Units of Length

PROBLEM: To wire your stereo equipment, you need 325 centimeters
(cm) of s...
Sample Problem 1.3
SOLUTION:
Length (in) = length (cm) x conversion factor
1 in
= 325 cm x
= 128 in
2.54 cm
Length (ft) = ...
Table 1. 2

SI Base Units

Physical Quantity
(Dimension)

Unit Name

Unit Abbreviation

Mass

kilogram

kg

Length

meter
...
Units -- Metric System


Mass

kilogram(kg), gram(g)



Length meter(m), centimeter(cm)



Volume cubic meter(m3),
cubi...
Additional SI Units

• Current – Ampere
• Amount of Substance – Mole
• Luminous Intensity – Candela
• Four of these units ...
The Second

• Initially the second was tied to the Earth’s
rotation. 1/86,400th of the mean solar day.
• In 1967, the seco...
The Meter

• In 1791, the meter was defined to be one tenmillionth of the length of the meridian passing
through Paris fro...
The Meter (continued)

• In 1960, the meter was based on the
wavelength of krypton-86 radiation.
• Finally in 1983, the me...
The Kilogram

• In 1799, a platinum-iridium cylinder was
fabricated to represent the mass of a cubic
deciliter of water at...
The Kilogram Standard
The Mole

• Since the 1960’s, the mole has been based on
the number of atoms in 12.0 g of carbon-12 or
6.022 x 1023 atoms....
Table 1.3

Common Decimal Prefixes Used with SI Units
Units-- Metric System
Use numerical prefixes for larger or smaller
units:
Mega (M) 1000000 times unit (106)
kilo
(k) 1000 ...
Table 1.4 Common SI-English Equivalent Quantities
Quantity

SI to English Equivalent

English to SI Equivalent

Length

1 ...
Figure 1.8

Common laboratory volumetric glassware.
Sample Problem 1.4

Converting Units of Volume

PROBLEM: A graduated cylinder contains 19.9 mL of water. When a
small piec...
Sample Problem 1.4
SOLUTION:
(24.5 - 19.9) mL = volume of galena = 4.6 mL
1 cm3
4.6 mL x
1 mL

= 4.6 cm3

10-3 L
4.6 mL x
...
Sample Problem 1.5

Converting Units of Mass

PROBLEM: Many international computer communications are carried out
by optic...
Sample Problem 1.5
SOLUTION:
8.84 x

103 km

103 m
x
1 km

= 8.84 x 106 m

1.19 x 10-3 lb
8.84 x 106 m x
= 1.05 x 104 lb
1...
Units -- Metric System

• Numerical Prefixes:
–
–
–
–

12.5 m = _______ cm
1.35 kg = _______ g
0.0256 mm = _______ µm
89.7...
Derived Quantities

•
•
•
•
•
•
•

Frequency (cycles/s, hertz)
Density (mass/volume, g/cm3)
Speed (distance/time, m/s)
Acc...
Figure 1.9 Some interesting quantities of length (A), volume (B),
and mass (C).
Density
mass
density =
volume
At a given temperature and pressure, the density of a
substance is a characteristic physical...
Table 1.5

Densities of Some Common Substances*

Substance

Physical State

Density (g/cm3)

Hydrogen

gas

0.0000899

Oxy...
Sample Problem 1.6

Calculating Density from Mass and Length

PROBLEM: Lithium, a soft, gray solid with the lowest density...
Sample Problem 1.6
SOLUTION:
1.49x103 mg x

20.9 mm x

1g
= 1.49 g
3 mg
10

1 cm
= 2.09 cm
10 mm

Similarly the other side...
Dimensional Analysis

• Derived quantities - Density
Determine the density of a substance(g/ml) if
742g of it occupies 97....
Figure 1.10
Some interesting
temperatures.
Figure 1.11 Freezing and boiling points of water in the Celsius,
Kelvin (absolute) and Fahrenheit scales.
Table 1.6 The Three Temperature Scales
Temperature Scales
Kelvin ( K ) - The “absolute temperature scale” begins at
absolute zero and has only positive values. N...
Temperature Conversions
T (in K) = T (in oC) + 273.15
T (in oC) = T (in K) - 273.15

T (in °F) = 9 T (in °C) + 32
5
T (in ...
Sample Problem 1.7

Converting Units of Temperature

PROBLEM: A child has a body temperature of 38.7°C, and normal
body te...
Significant Figures
Every measurement includes some uncertainty. The
rightmost digit of any quantity is always estimated.
...
Figure 1.12

The number of significant figures in a measurement.
Determining Which Digits are Significant
All digits are significant
- except zeros that are used only to position the
deci...
• Zeros that end a number are significant
– whether they occur before or after the decimal point
– as long as a decimal po...
Sample Problem 1.8

Determining the Number of Significant Figures

PROBLEM: For each of the following quantities, underlin...
Sample Problem 1.8
SOLUTION:
(a) 0.0030 L has 2 sf

(b) 0.1044 g has 4 sf

(c) 53,069 mL has 5 sf
(d) 0.00004715 m = 4.715...
Rules for Significant Figures in Calculations
1. For multiplication and division. The answer contains
the same number of s...
Multiplication and Division of Inexact
Numbers
• The result can have no more sig. figs. than the
least number of sig. figs...
Multiplication and Division of Inexact and
Exact Numbers
• Use of exact conversion factors retains the
number of sig figs ...
Rules for Significant Figures in Calculations
2. For addition and subtraction. The answer has
the same number of decimal p...
Addition and Subtraction of Inexact
Numbers
• Result will have a digit as far to the right as all
the numbers have a digit...
Rules for Rounding Off Numbers
1. If the digit removed is more than 5, the preceding
number increases by 1.
5.379 rounds t...
3. If the digit removed is 5 followed by zeros or
with no following digits, the preceding number
increases by 1 if it is o...
Rounding Off Numbers

• Rule 1
• If the first digit to be dropped is less than 5,
that digit and all the digits that follo...
Rounding Off Numbers

• Rule 2
• If the first digit to be dropped is a digit greater
than 5, or a 5 followed by digits oth...
Example of Rule 2

• Thus 62.782 and 62.558 rounded off to 3
significant figures become, respectively, 62.8
and 62.6.
Rounding Off Numbers

• Rule 3
• If the first digit to be dropped is a 5 not followed by
any other digit or a 5 followed o...
Example of Rule 3

• Thus, 62.650 and 62.350 rounded to 3
significant figures become, respectively, 62.6
(even rule) and 6...
Rounding

• Round each of the following numbers to 3
significant figures:
•
•
•
•
•
•

12.36
125.5
89.2532
58.22
12586.365...
Figure 1.13

Significant figures and measuring devices.

The measuring device used determines the number of significant
di...
Exact Numbers
Exact numbers have no uncertainty associated with them.

Numbers may be exact by definition:
1000 mg = 1 g
6...
Sample Problem 1.9

Significant Figures and Rounding

PROBLEM: Perform the following calculations and round each answer
to...
Sample Problem 1.9
SOLUTION:
(a)

16.3521 cm2 - 1.448 cm2

=

7.085 cm

(b)

4.80x104 mg

1g
1000 mg

11.55 cm3

14.904 cm...
Scientific Notation

• Can be used to express very large or
very small numbers
• Expresses value as A x 10n
1≥A<10, n is a...
Scientific Notation

• Is useful for handling significant digits
Express 14,345 to 3 sig. figs.
1.43 x 104
Express 93,000,...
Precision, Accuracy, and Error
Precision refers to how close the measurements in a
series are to each other.
Accuracy refe...
Figure 1.14

Precision and accuracy in a laboratory calibration.

precise and accurate

precise but not accurate
Figure 1.14

Precision and accuracy in the laboratory.

continued

random error

systematic error
Percentage Problems
Percent is the number of items of a specified
type in a group of 100 total items.
Parts per hundred
Pe...
Percentage Problems
A student answered 19 items correctly on a
23 point test. What was his score as a
percentage?
Percenta...
Percentage Problems
Range as a percent of the average is a way
to express precision.
% of average = (highest – lowest) x 1...
Percentage Problems
A technician measured the breaking strength of
three samples of plastic. His results were:
Run 1: 65.8...
Percentage Problems
Percent difference is a way to express
accuracy.
% difference = (measured – actual) x 100%
actual
= (1...
Percentage Problems
A student determined the density of aluminum
metal to be 2.64 g/cm3. The accepted value
is 2.70 g/cm3....
Percentage Problems
A student did three experiments to determine
the density of rubbing alcohol. Her results
were: 0.778 g...
New chm 151 unit 1 powerpoints sp13 s
New chm 151 unit 1 powerpoints sp13 s
New chm 151 unit 1 powerpoints sp13 s
New chm 151 unit 1 powerpoints sp13 s
New chm 151 unit 1 powerpoints sp13 s
New chm 151 unit 1 powerpoints sp13 s
New chm 151 unit 1 powerpoints sp13 s
New chm 151 unit 1 powerpoints sp13 s
New chm 151 unit 1 powerpoints sp13 s
New chm 151 unit 1 powerpoints sp13 s
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New chm 151 unit 1 powerpoints sp13 s

  1. 1. Keys to the Study of Chemistry • Ashton T. Griffin • Wayne Community College • Chapter 1.1-1.6 in Silberberg 5th and 6th editions.
  2. 2. Goals & Objectives • The student will be able to identify the name and symbol of the first 36 elements on the periodic table. (I-1) • The student will understand the common units of length, volume, mass, and temperature and their numerical prefixes. (1.5)
  3. 3. Goals & Objectives • The student will understand the meaning of uncertainty in measurements and the use of significant figures and rounding. (1.6) • The student will understand the distinction between accuracy and precision and between systematic and random error. (1.6)
  4. 4. Master these Skills • The student will be able to: • Use conversion factors in calculations (1.4; SP 1.3-1.5) • Find the density from mass and volume (SP 1.6) • Convert between the Kelvin, Celsius, and Fahrenheit temperature scales (SP 1.7)
  5. 5. Master these Skills • The student will be able to: • Determine the number of significant figures (SP 1.8) and rounding to the correct number of digits. (SP 1.9)
  6. 6. Chemistry Chemistry is the study of matter, its properties, the changes that matter undergoes, and the energy associated with these changes.
  7. 7. Definitions Matter anything that has both mass and volume - the “stuff” of the universe: books, planets, trees, professors, students Composition the types and amounts of simpler substances that make up a sample of matter Properties the characteristics that give each substance a unique identity
  8. 8. Physical Properties properties a substance shows by itself without interacting with another substance - color, melting point, boiling point, density Chemical Properties properties a substance shows as it interacts with, or transforms into, other substances - flammability, corrosiveness
  9. 9. Figure 1.1 The distinction between physical and chemical change.
  10. 10. Table 1.1 Some Characteristic Properties of Copper
  11. 11. Elements • The simplest forms of matter • Cannot be separated by chemical means into simpler stable substances • Represented by symbols on the Periodic Table • Learn the names and symbols for first 36 elements (I-1)
  12. 12. The States of Matter A solid has a fixed shape and volume. Solids may be hard or soft, rigid or flexible. A liquid has a varying shape that conforms to the shape of the container, but a fixed volume. A liquid has an upper surface. A gas has no fixed shape or volume and therefore does not have a surface.
  13. 13. Figure 1.2 The physical states of matter.
  14. 14. Temperature and Change of State • A change of state is a physical change. – Physical form changes, composition does not. • Changes in physical state are reversible – by changing the temperature. • A chemical change cannot simply be reversed by a change in temperature.
  15. 15. Sample Problem 1.2 Distinguishing Between Physical and Chemical Change PROBLEM: Decide whether each of the following processes is primarily a physical or a chemical change, and explain briefly: (a) Frost forms as the temperature drops on a humid winter night. (b) A cornstalk grows from a seed that is watered and fertilized. (c) A match ignites to form ash and a mixture of gases. (d) Perspiration evaporates when you relax after jogging. (e) A silver fork tarnishes slowly in air. PLAN: “Does the substance change composition or just change form?”
  16. 16. Sample Problem 1.2 SOLUTION: (a) Frost forms as the temperature drops on a humid winter night. physical change (b) A cornstalk grows from a seed that is watered and fertilized. chemical change (c) A match ignites to form ash and a mixture of gases. chemical change (d) Perspiration evaporates when you relax after jogging. physical change (e) A silver fork tarnishes slowly in air. chemical change
  17. 17. Energy in Chemistry Energy is the ability to do work. Potential Energy is energy due to the position of an object. Kinetic Energy is energy due to the movement of an object. Total Energy = Potential Energy + Kinetic Energy
  18. 18. Energy Changes Lower energy states are more stable and are favored over higher energy states. Energy is neither created nor destroyed – it is conserved – and can be converted from one form to another.
  19. 19. Figure 1.6 The scientific approach to understanding nature. Observations Natural phenomena and measured events; can be stated as a natural law if universally consistent. Hypothesis Hypothesis is revised if experimental results do not support it. Tentative proposal that explains observations. Experiment Procedure to test hypothesis; measures one variable at a time. Model (Theory) Model is altered if predicted events do not support it. Further Experiment Set of conceptual assumptions that explains data from accumulated experiments; predicts related phenomena. Tests predictions based on model
  20. 20. Chemical Problem Solving • All measured quantities consist of – a number and a unit. • Units are manipulated like numbers: – 3 ft x 4 ft = 12 ft2 – 350 mi = 7h 50 mi 1h or 50 mi.h-1
  21. 21. Conversion Factors A conversion factor is a ratio of equivalent quantities used to express a quantity in different units. The relationship 1 mi = 5280 ft gives us the conversion factor: 1 mi 5280 ft = 5280 ft 5280 ft =1
  22. 22. A conversion factor is chosen and set up so that all units cancel except those required for the answer. PROBLEM: The height of the Angel Falls is 3212 ft. Express this quantity in miles (mi) if 1 mi = 5280 ft. PLAN: Set up the conversion factor so that ft will cancel and the answer will be in mi. SOLUTION: 3212 ft x 1 mi 5280 ft = 0.6083 mi
  23. 23. Systematic Approach to Solving Chemistry Problems • State Problem Clarify the known and unknown. • Plan Suggest steps from known to unknown. Prepare a visual summary of steps that includes conversion factors, equations, known variables. • Solution • Check • Comment • Follow-up Problem
  24. 24. Sample Problem 1.3 Converting Units of Length PROBLEM: To wire your stereo equipment, you need 325 centimeters (cm) of speaker wire that sells for $0.15/ft. What is the price of the wire? PLAN: We know the length (in cm) of wire and cost per length ($/ft). We have to convert cm to inches and inches to feet. Then we can find the cost for the length in feet. length (cm) of wire 2.54 cm = 1 in length (in) of wire 12 in = 1 ft length (ft) of wire 1 ft = $0.15 Price ($) of wire
  25. 25. Sample Problem 1.3 SOLUTION: Length (in) = length (cm) x conversion factor 1 in = 325 cm x = 128 in 2.54 cm Length (ft) = length (in) x conversion factor = 128 in x 1 ft = 10.7 ft 12 in Price ($) = length (ft) x conversion factor = 10.7 ft x $ 0.15 1 ft = $ 1.60
  26. 26. Table 1. 2 SI Base Units Physical Quantity (Dimension) Unit Name Unit Abbreviation Mass kilogram kg Length meter m Time second s Temperature kelvin K Electric Current ampere A Amount of substance mole Luminous intensity candela mol cd
  27. 27. Units -- Metric System  Mass kilogram(kg), gram(g)  Length meter(m), centimeter(cm)  Volume cubic meter(m3), cubic centimeter (cm3) liter(L) = 1000 cm3 (exact) milliliter(mL) = 1 cm3 (exact)
  28. 28. Additional SI Units • Current – Ampere • Amount of Substance – Mole • Luminous Intensity – Candela • Four of these units are of particular interest to chemist.
  29. 29. The Second • Initially the second was tied to the Earth’s rotation. 1/86,400th of the mean solar day. • In 1967, the second was based on the cesium133 atomic clock.
  30. 30. The Meter • In 1791, the meter was defined to be one tenmillionth of the length of the meridian passing through Paris from the equator to the North Pole. • In 1889, a platinum-iridium bar was inscribed with two lines – this became the standard for the meter.
  31. 31. The Meter (continued) • In 1960, the meter was based on the wavelength of krypton-86 radiation. • Finally in 1983, the meter was re-defined as the length traveled by light in exactly 1/299,792,458 of a second.
  32. 32. The Kilogram • In 1799, a platinum-iridium cylinder was fabricated to represent the mass of a cubic deciliter of water at 4 C. In new standard was created in 1879. Due to the changing nature its mass, it was suggested in 2005 that the kilogram be redefined in terms of “fixed constants of nature”.
  33. 33. The Kilogram Standard
  34. 34. The Mole • Since the 1960’s, the mole has been based on the number of atoms in 12.0 g of carbon-12 or 6.022 x 1023 atoms. • New attempts to define the mole include using a new standard Si-28. • New attempts will continue.
  35. 35. Table 1.3 Common Decimal Prefixes Used with SI Units
  36. 36. Units-- Metric System Use numerical prefixes for larger or smaller units: Mega (M) 1000000 times unit (106) kilo (k) 1000 times unit (103) centi (c) 0.01 times unit (10-2) milli (m) 0.001 times unit (10-3) Micro (µ) 0.000001 times unit (10-6) 
  37. 37. Table 1.4 Common SI-English Equivalent Quantities Quantity SI to English Equivalent English to SI Equivalent Length 1 km = 0.6214 mile 1 m = 1.094 yard 1 m = 39.37 inches 1 cm = 0.3937 inch 1 mi = 1.609 km 1 yd = 0.9144 m 1 ft = 0.3048 m 1 in = 2.54 cm Volume 1 cubic meter (m3) = 35.31 ft3 1 dm3 = 0.2642 gal 1 dm3 = 1.057 qt 1 cm3 = 0.03381 fluid ounce 1 ft3 = 0.02832 m3 1 gal = 3.785 dm3 1 qt = 0.9464 dm3 1 qt = 946.4 cm3 1 fluid ounce = 29.57 cm3 Mass 1 kg = 2.205 lb 1 g = 0.03527 ounce (oz) 1 lb = 0.4536 kg 1 oz = 28.35 g
  38. 38. Figure 1.8 Common laboratory volumetric glassware.
  39. 39. Sample Problem 1.4 Converting Units of Volume PROBLEM: A graduated cylinder contains 19.9 mL of water. When a small piece of galena, an ore of lead, is added, it sinks and the volume increases to 24.5 mL. What is the volume of the piece of galena in cm3 and in L? PLAN: The volume of the galena is equal to the difference in the volume of the water before and after the addition. volume (mL) before and after subtract volume (mL) of galena 1 mL = 1 cm3 volume (cm3) of galena 1 mL = 10-3 L volume (L) of galena
  40. 40. Sample Problem 1.4 SOLUTION: (24.5 - 19.9) mL = volume of galena = 4.6 mL 1 cm3 4.6 mL x 1 mL = 4.6 cm3 10-3 L 4.6 mL x 1 mL = 4.6 x 10-3 L
  41. 41. Sample Problem 1.5 Converting Units of Mass PROBLEM: Many international computer communications are carried out by optical fibers in cables laid along the ocean floor. If one strand of optical fiber weighs 1.19 x 10-3 lb/m, what is the mass (in kg) of a cable made of six strands of optical fiber, each long enough to link New York and Paris (8.94 x 103 km)? PLAN: The sequence of steps may vary but essentially we need to find the length of the entire cable and convert it to mass. length (km) of fiber 1 km = 103 m length (m) of fiber 1 m = 1.19 x 10-3 lb mass (lb) of fiber 6 fibers = 1 cable mass (lb) of cable 2.205 lb = 1 kg Mass (kg) of cable
  42. 42. Sample Problem 1.5 SOLUTION: 8.84 x 103 km 103 m x 1 km = 8.84 x 106 m 1.19 x 10-3 lb 8.84 x 106 m x = 1.05 x 104 lb 1m 1.05 x 104 lb 6 fibers x 1 fiber 1 cable 6.30 x 104 lb 1 kg x 1 cable 2.205 lb = 6.30 x 104 lb/cable = 2.86 x 104 kg/cable
  43. 43. Units -- Metric System • Numerical Prefixes: – – – – 12.5 m = _______ cm 1.35 kg = _______ g 0.0256 mm = _______ µm 89.7 megahertz = _______ hertz (1 hertz = 1 cycle per second)
  44. 44. Derived Quantities • • • • • • • Frequency (cycles/s, hertz) Density (mass/volume, g/cm3) Speed (distance/time, m/s) Acceleration (distance/(time)2, m/s2) Force (mass x acceleration, kg•m/s2, newton) Pressure (force/area, kg/(m•s2), pascal) Energy (force x distance, kg•m2/s2, joule)
  45. 45. Figure 1.9 Some interesting quantities of length (A), volume (B), and mass (C).
  46. 46. Density mass density = volume At a given temperature and pressure, the density of a substance is a characteristic physical property and has a specific value.
  47. 47. Table 1.5 Densities of Some Common Substances* Substance Physical State Density (g/cm3) Hydrogen gas 0.0000899 Oxygen gas 0.00133 Grain alcohol liquid 0.789 Water liquid 0.998 Table salt solid 2.16 Aluminum solid 2.70 Lead solid 11.3 Gold solid 19.3 *At room temperature (20°C) and normal atmospheric pressure (1atm).
  48. 48. Sample Problem 1.6 Calculating Density from Mass and Length PROBLEM: Lithium, a soft, gray solid with the lowest density of any metal, is a key component of advanced batteries. A slab of lithium weighs 1.49x103 mg and has sides that are 20.9 mm by 11.1 mm by 11.9 mm. Find the density of lithium in g/cm3. PLAN: Density is expressed in g/cm3 so we need the mass in g and the volume in cm3. lengths (mm) of sides 10 mm = 1 cm mass (mg) of Li lengths (cm) of sides 103 mg = 1 g multiply lengths mass (g) of Li volume (cm3) divide mass by volume density (g/cm3) of Li
  49. 49. Sample Problem 1.6 SOLUTION: 1.49x103 mg x 20.9 mm x 1g = 1.49 g 3 mg 10 1 cm = 2.09 cm 10 mm Similarly the other sides will be 1.11 cm and 1.19 cm, respectively. Volume = 2.09 x 1.11 x 1.19 = 2.76 cm3 density of Li = 1.49 g 2.76 cm3 = 0.540 g/cm3
  50. 50. Dimensional Analysis • Derived quantities - Density Determine the density of a substance(g/ml) if 742g of it occupies 97.3 cubic centimeters. Determine the volume of a liquid having a density of 1.32 g/mL required to have 125 g of the liquid.
  51. 51. Figure 1.10 Some interesting temperatures.
  52. 52. Figure 1.11 Freezing and boiling points of water in the Celsius, Kelvin (absolute) and Fahrenheit scales.
  53. 53. Table 1.6 The Three Temperature Scales
  54. 54. Temperature Scales Kelvin ( K ) - The “absolute temperature scale” begins at absolute zero and has only positive values. Note that the kelvin is not used with the degree sign (°). Celsius ( oC ) - The Celsius scale is based on the freezing and boiling points of water. This is the temperature scale used most commonly around the world. The Celsius and Kelvin scales use the same size degree although their starting points differ. Fahrenheit ( oF ) – The Fahrenheit scale is commonly used in the US. The Fahrenheit scale has a different degree size and different zero points than both the Celsius and Kelvin scales.
  55. 55. Temperature Conversions T (in K) = T (in oC) + 273.15 T (in oC) = T (in K) - 273.15 T (in °F) = 9 T (in °C) + 32 5 T (in °C) = [T (in °F) – 32] 5 9
  56. 56. Sample Problem 1.7 Converting Units of Temperature PROBLEM: A child has a body temperature of 38.7°C, and normal body temperature is 98.6°F. Does the child have a fever? What is the child’s temperature in kelvins? PLAN: We have to convert °C to °F to find out if the child has a fever. We can then use the °C to Kelvin relationship to find the temperature in Kelvin. SOLUTION: Converting from °C to °F 9 (38.7 °C) + 32 = 101.7 °F 5 Yes, the child has a fever. Converting from °C to K 38.7 °C + 273.15 = 311.8 K
  57. 57. Significant Figures Every measurement includes some uncertainty. The rightmost digit of any quantity is always estimated. The recorded digits, both certain and uncertain, are called significant figures. The greater the number of significant figures in a quantity, the greater its certainty.
  58. 58. Figure 1.12 The number of significant figures in a measurement.
  59. 59. Determining Which Digits are Significant All digits are significant - except zeros that are used only to position the decimal point. • Make sure the measured quantity has a decimal point. • Start at the left and move right until you reach the first nonzero digit. • Count that digit and every digit to its right as significant.
  60. 60. • Zeros that end a number are significant – whether they occur before or after the decimal point – as long as a decimal point is present. • 1.030 mL has 4 significant figures. • 5300. L has 4 significant figures. • If no decimal point is present – zeros at the end of the number are not significant. • 5300 L has only 2 significant figures.
  61. 61. Sample Problem 1.8 Determining the Number of Significant Figures PROBLEM: For each of the following quantities, underline the zeros that are significant figures (sf), and determine the number of significant figures in each quantity. For (d) to (f), express each in exponential notation first. (a) 0.0030 L (b) 0.1044 g (c) 53,069 mL (d) 0.00004715 m PLAN: (e) 57,600. s (f) 0.0000007160 cm3 We determine the number of significant figures by counting digits, paying particular attention to the position of zeros in relation to the decimal point, and underline zeros that are significant.
  62. 62. Sample Problem 1.8 SOLUTION: (a) 0.0030 L has 2 sf (b) 0.1044 g has 4 sf (c) 53,069 mL has 5 sf (d) 0.00004715 m = 4.715x10-5 m has 4 sf (e) 57,600. s = 5.7600x104 s has 5 sf (f) 0.0000007160 cm3 = 7.160x10-7 cm3 has 4 sf
  63. 63. Rules for Significant Figures in Calculations 1. For multiplication and division. The answer contains the same number of significant figures as there are in the measurement with the fewest significant figures. Multiply the following numbers: 9.2 cm x 6.8 cm x 0.3744 cm = 23.4225 cm3 = 23 cm3
  64. 64. Multiplication and Division of Inexact Numbers • The result can have no more sig. figs. than the least number of sig. figs. used to obtain the result. 4.242 x 1.23 = 5.21766 12.24/2.0 = 6.12 6.1 5.22
  65. 65. Multiplication and Division of Inexact and Exact Numbers • Use of exact conversion factors retains the number of sig figs in the measured (inexact) value. 22.36 inches x 2.54 centimeters per inch= 56.80 centimeters • Conversion factors involving powers of ten are always exact. 1 kilometer = 1000 meters 3.5 kilometers = 3.5 x 103 meters
  66. 66. Rules for Significant Figures in Calculations 2. For addition and subtraction. The answer has the same number of decimal places as there are in the measurement with the fewest decimal places. Example: adding two volumes 83.5 mL + 23.28 mL 106.78 mL = 106.8 mL Example: subtracting two volumes 865.9 mL - 2.8121 mL 863.0879 mL = 863.1 mL
  67. 67. Addition and Subtraction of Inexact Numbers • Result will have a digit as far to the right as all the numbers have a digit in common 2.02 8.7397 1.234 -2.123 + 3.6923 6.6167 6.9463 6.95 6.617
  68. 68. Rules for Rounding Off Numbers 1. If the digit removed is more than 5, the preceding number increases by 1. 5.379 rounds to 5.38 if 3 significant figures are retained. 2. If the digit removed is less than 5, the preceding number is unchanged. 0.2413 rounds to 0.241 if 3 significant figures are retained.
  69. 69. 3. If the digit removed is 5 followed by zeros or with no following digits, the preceding number increases by 1 if it is odd and remains unchanged if it is even. 17.75 rounds to 17.8, but 17.65 rounds to 17.6. If the 5 is followed by other nonzero digits, rule 1 is followed: 17.6500 rounds to 17.6, but 17.6513 rounds to 17.7 4. Be sure to carry two or more additional significant figures through a multistep calculation and round off the final answer only.
  70. 70. Rounding Off Numbers • Rule 1 • If the first digit to be dropped is less than 5, that digit and all the digits that follow it are simply dropped. • Thus, 62.312 rounded off to 3 significant figures become 62.3.
  71. 71. Rounding Off Numbers • Rule 2 • If the first digit to be dropped is a digit greater than 5, or a 5 followed by digits other than all zeros, the excess digits are all dropped and the last retained digit is increased in value by one unit.
  72. 72. Example of Rule 2 • Thus 62.782 and 62.558 rounded off to 3 significant figures become, respectively, 62.8 and 62.6.
  73. 73. Rounding Off Numbers • Rule 3 • If the first digit to be dropped is a 5 not followed by any other digit or a 5 followed only by zeros, an odd-even rule applies. Drop the 5 and any zeros that follow it and then: • Increase the last retained digit by one unit if it is odd and leave the last retained digit the same if it is even.
  74. 74. Example of Rule 3 • Thus, 62.650 and 62.350 rounded to 3 significant figures become, respectively, 62.6 (even rule) and 62.4 (odd rule). The number zero as a last retained digit is always considered an even number; thus, 62.050 rounded to 3 significant figures becomes 62.0.
  75. 75. Rounding • Round each of the following numbers to 3 significant figures: • • • • • • 12.36 125.5 89.2532 58.22 12586.365 599.68
  76. 76. Figure 1.13 Significant figures and measuring devices. The measuring device used determines the number of significant digits possible.
  77. 77. Exact Numbers Exact numbers have no uncertainty associated with them. Numbers may be exact by definition: 1000 mg = 1 g 60 min = 1 hr 2.54 cm = 1 in Numbers may be exact by count: exactly 26 letters in the alphabet Exact numbers do not limit the number of significant digits in a calculation.
  78. 78. Sample Problem 1.9 Significant Figures and Rounding PROBLEM: Perform the following calculations and round each answer to the correct number of significant figures: (a) 16.3521 cm2 - 1.448 cm2 7.085 cm (b) 4.80x104 mg 1g 1000 mg 11.55 cm3 PLAN: We use the rules for rounding presented in the text: (a) We subtract before we divide. (b) We note that the unit conversion involves an exact number.
  79. 79. Sample Problem 1.9 SOLUTION: (a) 16.3521 cm2 - 1.448 cm2 = 7.085 cm (b) 4.80x104 mg 1g 1000 mg 11.55 cm3 14.904 cm2 7.085 cm = = 2.104 cm 48.0 g 11.55 cm3 = 4.16 g/ cm3
  80. 80. Scientific Notation • Can be used to express very large or very small numbers • Expresses value as A x 10n 1≥A<10, n is an integer 14,345 = 1.4345 x 104 0.009867 = 9.867 x 10-3
  81. 81. Scientific Notation • Is useful for handling significant digits Express 14,345 to 3 sig. figs. 1.43 x 104 Express 93,000,000 to 4 sig. Fig 9.300 x 107 Express 0.009867 to 2 sig. figs. 9.9 x 10-3 or 0.0099
  82. 82. Precision, Accuracy, and Error Precision refers to how close the measurements in a series are to each other. Accuracy refers to how close each measurement is to the actual value. Systematic error produces values that are either all higher or all lower than the actual value. This error is part of the experimental system. Random error produces values that are both higher and lower than the actual value.
  83. 83. Figure 1.14 Precision and accuracy in a laboratory calibration. precise and accurate precise but not accurate
  84. 84. Figure 1.14 Precision and accuracy in the laboratory. continued random error systematic error
  85. 85. Percentage Problems Percent is the number of items of a specified type in a group of 100 total items. Parts per hundred Percent = number of items of interest x 100% total items
  86. 86. Percentage Problems A student answered 19 items correctly on a 23 point test. What was his score as a percentage? Percentage 19 1 23 0 5 10 15 Points on a test 20 25
  87. 87. Percentage Problems Range as a percent of the average is a way to express precision. % of average = (highest – lowest) x 100% average = (20.50 – 19.25) units x 100 % = 6.32% 19.78 units Measurements and the Average Run # 20.50 19.60 1 19.25 19.78 0 1 2 3 4 5 6 7 8 9 10 11 12 Measurement Units 13 14 15 16 17 18 19 20 21
  88. 88. Percentage Problems A technician measured the breaking strength of three samples of plastic. His results were: Run 1: 65.8 MPa Run 2: 72.4 MPa Run 3: 68.3 MPa What was the range of his measurements as a percent of the average? Note: 1 MPa = 145 pounds/in2
  89. 89. Percentage Problems Percent difference is a way to express accuracy. % difference = (measured – actual) x 100% actual = (19.78 – 20.00) units x 100% = –1.1% 20.00 units Measured and True values 20.00 19.78 0 1 2 3 4 5 6 7 8 9 10 11 12 Measurement Units 13 14 15 16 17 18 19 20 21
  90. 90. Percentage Problems A student determined the density of aluminum metal to be 2.64 g/cm3. The accepted value is 2.70 g/cm3. What is the percent difference between her result and the accepted value? Did she do a good job?
  91. 91. Percentage Problems A student did three experiments to determine the density of rubbing alcohol. Her results were: 0.778 g/mL; 0.795 g/mL; 0.789 g/mL. What is her precision as % of average? The true value is 0.785 g/mL. What is her accuracy?

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