The numerical side of chemistry

1
The numerical side of chemistry

• Chapter 2

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Outline

• Precision and Accuracy
• Uncertainty and Significant figures
• Zeros and Significant figures
• Scientific notation
• Units of measure
• Conversion factors and Algebraic manipulations

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Accuracy and Precision
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Precision and Accuracy

• Accuracy refers to the agreement of a particular
  value with the true value.
• Precision refers to the degree of agreement
  among several measurements made in the same
  manner.

Precise but not accurate
Precise AND accurate
Neither accurate nor precise
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Types of Error

• Random Error (Indeterminate Error) - measurement
  has an equal probability of being high or low.
• Systematic Error (Determinate Error) - Occurs in
  the same direction each time (high or low), often
  resulting from poor technique or incorrect
  calibration. This can result in measurements that
  are precise, but not accurate.

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Uncertainty in Measurement

• A digit that must be estimated is called
  uncertain. A measurement always has some degree
  of uncertainty.

• Measurements are performed with
• instruments
• No instrument can read to an infinite
• number of decimal places

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Nature of Measurement
Measurement - quantitative observation
consisting of 2 parts

• Part 1 - number
• Part 2 - scale (unit)
• Examples
• 20 grams
• 34.5 mL
• 45.0 m

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Significant figures or significant digits

• Digits that are not beyond accuracy of measuring
  device
• The certain digits and the estimated digit of a
  measurement

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Rules

• 245
• 0.04
• 0.040
• 1000
• 10.00
• 0.0301
• 103

• 3 significant digits
• 1 significant digit
• 2 significant digits
• 1 significant digit
• 4 significant digit
• 3 significant digit
• 3 significant digit

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Rules for Counting Significant Figures - Details

• Nonzero integers always count as significant
  figures.
• 3456 has
• 4 sig figs.

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Rules for Counting Significant Figures - Details

• Zeros
• - Leading zeros do not count as
• significant figures.
• 0.0486 has
• 3 sig figs.

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Rules for Counting Significant Figures - Details

• Zeros
• - Captive zeros always count as
• significant figures.
• 16.07 has
• 4 sig figs.

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Rules for Counting Significant Figures - Details

• Zeros
• Trailing zeros are significant only if the
  number contains a decimal point.
• 9.300 has
• 4 sig figs.

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Rules for Counting Significant Figures - Details

• Exact numbers have an infinite number of
  significant figures.
• 1 inch 2.54 cm, exactly

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Sig Fig Practice 1
How many significant figures in each of the
following?
1.0070 m ?
5 sig figs
17.10 kg ?
4 sig figs
100,890 L ?
5 sig figs
3.29 x 103 s ?
3 sig figs
0.0054 cm ?
2 sig figs
3,200,000 ?
2 sig figs
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Rules for Significant Figures in Mathematical
Operations

• Addition and Subtraction The number of decimal
  places in the result equals the number of decimal
  places in the least precise measurement.
• 6.8 11.934
• 18.734 ? 18.7 (3 sig figs)

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Sig Fig Practice 2
Calculation
Calculator says
Answer
10.24 m
3.24 m 7.0 m
10.2 m
100.0 g - 23.73 g
76.3 g
76.27 g
0.02 cm 2.371 cm
2.39 cm
2.391 cm
713.1 L - 3.872 L
709.228 L
709.2 L
1821.6 lb
1818.2 lb 3.37 lb
1821.57 lb
0.160 mL
0.16 mL
2.030 mL - 1.870 mL
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Rules for Significant Figures in Mathematical
Operations

• Multiplication and Division sig figs in the
  result equals the number in the least precise
  measurement used in the calculation.
• 6.38 x 2.0
• 12.76 ? 13 (2 sig figs)

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Sig Fig Practice 3
Calculation
Calculator says
Answer
22.68 m2
3.24 m x 7.0 m
23 m2
100.0 g 23.7 cm3
4.22 g/cm3
4.219409283 g/cm3
0.02 cm x 2.371 cm
0.05 cm2
0.04742 cm2
710 m 3.0 s
236.6666667 m/s
240 m/s
5870 lbft
1818.2 lb x 3.23 ft
5872.786 lbft
2.9561 g/mL
2.96 g/mL
1.030 g 2.87 mL
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Why do we use scientific notation?

• To express very small and very large numbers
• To indicate the precision of the number
• Use it to avoid with sig digs

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Scientific Notation
In science, we deal with some very LARGE numbers
1 mole 602000000000000000000000
In science, we deal with some very SMALL numbers
Mass of an electron 0.0000000000000000000000000
00000091 kg
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.
2 500 000 000
1
2
3
4
5
6
7
9
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Step 1 Insert an understood decimal point
Step 2 Decide where the decimal must end
up so that one number is to its left
Step 3 Count how many places you bounce
the decimal point
Step 4 Re-write in the form M x 10n
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2.5 x 109
The exponent is the number of places we moved the
decimal.
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0.0000579
1
2
3
4
5
Step 2 Decide where the decimal must end
up so that one number is to its left
Step 3 Count how many places you bounce
the decimal point
Step 4 Re-write in the form M x 10n
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5.79 x 10-5
The exponent is negative because the number we
started with was less than 1.
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Review
Scientific notation expresses a number in the
form
M x 10n
n is an integer
1 ? M ? 10
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SI measurement

• Le Système international d'unités
• The only countries that have not officially
  adopted SI are Liberia (in western Africa) and
  Myanmar (a.k.a. Burma, in SE Asia), but now these
  are reportedly using metric regularly
• Metrication is a process that does not happen all
  at once, but is rather a process that happens
  over time.
• Among countries with non-metric usage, the U.S.
  is the only country significantly holding out.
  The U.S. officially adopted SI in 1866.

Information from U.S. Metric Association
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The Fundamental SI Units (le Système
International, SI)
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Standards of Measurement

• When we measure, we use a measuring tool to
  compare some dimension of an object to a
  standard.

For example, at one time the standard for length
was the kings foot. What are some problems with
this standard?
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Derived SI units

• Physical quantity Name Abbreviation
• Volume cubic meter m3
• Pressure pascal Pa
• Energy joule J

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Metric System

• System used in science
• Decimal system
• Measurements are related by factors of 10
• Has one standard unit for each type of
  measurement
• Prefixes are attached in front of standard unit

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Metric Prefixes

• Kilo- means 1000 of that unit
• 1 kilometer (km) 1000 meters (m)
• Centi- means 1/100 of that unit
• 1 meter (m) 100 centimeters (cm)
• 1 dollar 100 cents
• Milli- means 1/1000 of that unit
• 1 Liter (L) 1000 milliliters (mL)

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SI Prefixes Common to Chemistry
Prefix Unit Abbr. Exponent
Mega M 106
Kilo k 103
Deci d 10-1
Centi c 10-2
Milli m 10-3
Micro ? 10-6
Nano n 10-9
Pico p 10-12
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Metric Prefixes
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Metric Prefixes
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Conversion Factors

• Fractions in which the numerator and denominator
  are EQUAL quantities expressed in different units
• Example 1 in. 2.54 cm
• Factors 1 in. and 2.54 cm
• 2.54 cm 1 in.

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Learning Check

• Write conversion factors that relate each of the
  following pairs of units
• 1. Liters and mL
• 2. Hours and minutes
• 3. Meters and kilometers

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How many minutes are in 2.5 hours?

• Conversion factor
• 2.5 hr x 60 min 150 min
• 1 hr
• cancel

By using dimensional analysis / factor-label
method, the UNITS ensure that you have the
conversion right side up, and the UNITS are
calculated as well as the numbers!
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Steps to Problem Solving

1. Write down the given amount. Dont forget the
   units!
2. Multiply by a fraction.
3. Use the fraction as a conversion factor.
   Determine if the top or the bottom should be the
   same unit as the given so that it will cancel.
4. Put a unit on the opposite side that will be the
   new unit. If you dont know a conversion between
   those units directly, use one that you do know
   that is a step toward the one you want at the
   end.
5. Insert the numbers on the conversion so that the
   top and the bottom amounts are EQUAL, but in
   different units.
6. Multiply and divide the units (Cancel).
7. If the units are not the ones you want for your
   answer, make more conversions until you reach
   that point.
8. Multiply and divide the numbers. Dont forget
   Please Excuse My Dear Aunt Sally! (order of
   operations)

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Learning Check

• A rattlesnake is 2.44 m long. How long is the
  snake in cm?
• a) 2440 cm
• b) 244 cm
• c) 24.4 cm

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Solution

• A rattlesnake is 2.44 m long. How long is the
  snake in cm?
• b) 244 cm
• 2.44 m x 100 cm 244 cm
• 1 m

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Learning Check

• How many seconds are in 1.4 days?
• Unit plan days hr min
  seconds
• 1.4 days x 24 hr x ??
• 1 day

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Wait a minute!

• What is wrong with the following setup?
• 1.4 day x 1 day x 60 min x 60 sec
• 24 hr 1 hr
  1 min

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Dealing with Two Units

• If your pace on a treadmill is 65 meters per
  minute, how many seconds will it take for you to
  walk a distance of 8450 feet?

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What about Square and Cubic units?

• Use the conversion factors you already know, but
  when you square or cube the unit, dont forget to
  cube the number also!
• Best way Square or cube the ENTIRE conversion
  factor
• Example Convert 4.3 cm3 to mm3

( )
4.3 cm3 10 mm 3 1 cm

4.3 cm3 103 mm3 13 cm3

4300 mm3
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Learning Check

• A Nalgene water bottle holds 1000 cm3 of
  dihydrogen monoxide (DHMO). How many cubic
  decimeters is that?

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Solution

• 1000 cm3 1 dm 3
• 10 cm

( )
1 dm3
So, a dm3 is the same as a Liter ! A cm3 is the
same as a milliliter.
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Temperature Scales

• Fahrenheit
• Celsius
• Kelvin

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Temperature Scales


Celsius
Kelvin
Fahrenheit
Boiling point of water
Freezing point of water
Notice that 1 Kelvin 1 degree Celsius
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Calculations Using Temperature

• Generally require temps in kelvins
• T (K) t (C) 273.15
• Body temp 37 C 273 310 K
• Liquid nitrogen -196 C 273 77 K

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Fahrenheit Formula

• 180F 9F 1.8F 100C
  5C 1C
• Zero point 0C 32F
• F 9/5 C 32

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Celsius Formula

• Rearrange to find TC
• F 9/5 C 32
• F - 32 9/5 C ( 32 - 32)
• F - 32 9/5 C
• 9/5 9/5
• (F - 32) 5/9 C

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Temperature Conversions

• A person with hypothermia has a body temperature
  of 29.1C. What is the body temperature in F?
• F 9/5 (29.1C) 32
• 52.4 32
• 84.4F

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Temperature measurementsKelvin temperature scale
is also called absolute temperature scaleThere
is not negative Kelvin temperature K0C
273.150F 32 9/5 0C 0C 5/9 (0F 32)
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What is temperature?

• Measure of how hot or cold an object is
• Determines the direction of heat transfer
• Heat moves from object with higher temperature to
  object with lower temperature

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Learning Check

• Pizza is baked at 455F. What is that in C?
• 1) 437 C
• 2) 235C
• 3) 221C

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Density m/v

• Density tells you how much matter there is in a
  given volume.
• Usually expressed in g/ml or g/cm3

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Densities of some common materials
Material Density g/cm3 Material Density g/L
Gold 19.3 Chlorine 2.95
Mercury 13.6 CO2 1.83
Lead 11.4 Ar 1.66
aluminum 2.70 Oxygen 1.33
Sugar 1.59 Air 1.20
Water 1.000 Nitrogen 1.17
Gasoline 0.66-0.69 Helium 0.166
Ethanol 0.789 Hydrogen .0084
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Intensive and Extensive properties

• Intensive properties do not depend on amount of
  matter (density, boiling point, melting point)
• Extensive properties do depend on amount of
  matter(mass , volume, energy content).

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Energy

• Capacity to do work
• Work causes an object to move (F x d)
• Potential Energy Energy due to position
• Kinetic Energy Energy due to the motion of the
  object

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The Joule
The unit of heat used in modern thermochemistry
is the Joule
Non SI unit calorie 1Cal1000cal 4.184J 1cal or
4.184kJCal
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Law of conservation of energy

• Energy is neither created nor destroyed it only
  changes form

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Calorimetry
The amount of heat absorbed or released during a
physical or chemical change can be measured
usually by the change in temperature of a known
quantity of water
1 calorie is the heat required to raise the
temperature of 1 gram of water by 1 ?C
1 BTU is the heat required to raise the
temperature of 1 pound of water by 1 ?F
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Calorimeter
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A Cheaper Calorimeter
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Specific heat

• Amount of heat energy needed to warm 1 g of that
  substance by 1oC
• Units are J/goC or cal/goC

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Specific Heat Notes

• Specific heat how well a substance resist
  changing its temperature when it absorbs or
  releases heat
• Water has high s results in coastal areas
  having milder climate than inland areas (coastal
  water temp. is quite stable which is favorable
  for marine life).

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More Specific Heat

• Organisms are primarily water thus are able to
  resist more changes in their own temperature than
  if they were made of a liquid with a lower s

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Specific heats of some common substances

• (cal/g C) (J/g C)
• 1.000 4.184
• 0.107 0.449
• 0.215 0.901
• 0.581 2.43

• Substance
• Water
• Iron
• Aluminum
• Ethanol

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Calculations Involving Specific Heat
OR
s Specific Heat Capacity
q Heat lost or gained
?T Temperature change
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Principle of Heat Exchange

• The amount of heat lost by a substance is equal
  to the amount of heat gained by the substance to
  which it is transferred.
• m x ?t x s m x ?t x s
• heat lost heat gained

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How to calculate amount of heat ?

• H specific heat x mass x change in T
• Example
• Calculate the energy required to raise the
  temperature
• of a 387.0g bar of iron metal from 25oC to 40oC.
  The
• specific heat of iron is 0.449 J/goC