Significant Figures

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Honors Chemistry I84.135
Dr. Nancy De Luca Course web site http//faculty.
uml.edu/ndeluca/84.135
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Review Topics

• The following topics should be fairly familiar
  to you, and will not be covered in detail.
• Chapter 1
• Classification of Matter
• Physical and Chemical Changes Properties
• Units of Measurement

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Review Topics

• The following topics should be fairly familiar
  to you, and will not be covered in detail.
• Chapter 2
• Atomic Symbols of Common Elements

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Matter

• Matter is anything that has mass and occupies
  space. It includes everything around us,
  including the air that we breath, our skin and
  bones, and the earth underneath us.

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Properties of Matter

• Matter can be described by its physical or
  chemical properties.
• Physical properties are a description of the
  substance, and include mass, color, physical
  state (solid, liquid or gas) at a specific
  temperature, density, melting or boiling point,
  odor, solubility, etc.

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Properties of Matter
Mercury, a metal that is a liquid at room
temperature, reacts with iodine, a black shiny
solid, to produce mercury (II) iodide, a red
crystalline solid.
mercury
iodine
mercury(II)iodide
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Properties of Matter

• During a physical change, the chemical identity
  of the substance or substances does not change.
• Examples of physical changes include
  evaporation, filtration, and changes of state.

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Properties of Matter

• When ice is melted and the liquid is then
  evaporated, all three forms of water are
  chemically the same, H2O.
• When salt water is boiled, the salt remains,
  and the water is removed as water vapor.
• For either process, there is no change in the
  identity of the substances. This is true for all
  physical changes.

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Physical Changes
When water boils, its chemical composition
remains the same. The molecules are now farther
apart.
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Physical Change

• The dissolving of sugar in water is a physical
  change. The chemical identity of the water and
  the sugar remain unchanged.

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Filtration

• During filtration, liquids are separated from
  solids by physical means. The liquid and solid
  maintain their chemical identity.

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Distillation
During distillation, liquids may be separated
from other liquids, or from solids. The chemical
identity of each component remains unchanged.
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Properties of Matter

• Chemical properties are descriptions of how a
  substance reacts chemically. Examples include
  the rusting of iron in the presence of air and
  water, the souring of milk, or the burning of
  paper to form carbon dioxide and water vapor.

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Chemical Changes

• As iron rusts, the iron atoms combine with
  oxygen in the air to form a new substance, rust,
  or iron (III) oxide.

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Chemical Changes

• During a chemical change, atoms rearrange the
  way they are attached to each other, forming new
  substances with properties that are often quite
  different from the starting materials.

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Intensive Extensive Properties

• Intensive properties do not depend on the
  amount or quantity of matter. Melting point,
  chemical formula and color are intensive
  properties.
• Extensive properties depend upon the quantity
  of matter or sample size. Examples include
  length, mass and volume.

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The Elements

• All matter is composed of approximately 100
  elements, in various combinations, listed on the
  periodic table.
• The table groups elements with similar chemical
  and physical properties.

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The Periodic Table

• Periodic tables group elements with similar
  properties in vertical groups or families.
• Metals are on the left side of the table, and
  non-metals are on the right.
• A bold line resembling a flight of stairs usually
  separated metals from non-metals.

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The Periodic Table
metal/non-metal line
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Measurements

• Scientists needed to establish a system of
  measurement and units before they could reproduce
  or communicate the results of their experiments.
• The Metric System is used, with the units of
  grams (for mass) and milliliters (for volume)
  commonly used in the chemistry laboratory.

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Measurements

• Prefixes Commonly used in Chemistry
• prefix name symbol value exponential notation
• kilo  k 1,000 103
• centi c 1/100 or .01 10-2
• milli m 1/1,000 or .001 10-3
• micro µ .000001 10-6
• nano n 10-9
• pico p 10-12

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Measurements- Units

• SI or International System units are used.
• Quantity Unit Symbol
• Mass kilogram kg
• Length meter m
• Time second s
• Temperature kelvin K

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Measurement- Volume

• Volume is a derived unit. A liter is a volume
  that is 10cm x 10cm x 10cm, or 1000 cm3.
• Therefore, a milliliter (mL) is the same as a
  cubic centimeter (cm3 or cc).

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Measurement - Temperature

• In the chemistry lab, temperature is measured in
  degrees Celsius or Centigrade. The temperature
  in Kelvins is found by adding 273.15
• The Fahrenheit scale has 180 oF/100 oC. This is
  reason for the 5/9 or 9/5 in the conversion
  formulas.

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Measurement - Units

• Common English-Metric Conversion Factors
• 2.54 cm 1 inch
• 1 lb 453.6 g
• 1 qt 943 mL

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Significant Figures

• When writing a number, the certainty with which
  the number is known should be reflected in the
  way it is written.
• Digits which are the result of measurement or
  are known with a degree of certainty are called
  significant digits or significant figures.

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Significant Figures

• The goal of paying attention to significant
  figures is to make sure that every number
  accurately reflects the degree of certainty or
  precision to which it is known.
• Likewise, when calculations are performed, the
  final result should reflect the same degree of
  certainty as the least certain quantity in the
  calculation.

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Significant Figures

• If someone says There are roughly a hundred
  students enrolled in the freshman chemistry
  course, the enrollment should be written as 100
  or 1 x 102.
• Either notation indicates that the number is
  approximate, with only one significant figure.

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Significant Figures

• If the enrollment is exactly one hundred
  students, the number should be written with a
  decimal point, as 100. , or
• 1.00 x 102.
• Note that in either form, the number has three
  significant figures.

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Significant Figures

• The rules for counting significant figures
• 1. Any non-zero integer is a significant figure.

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Significant Figures

• 2. Zeros may be significant, depending upon
  where they appear in a number.
• a) Leading zeros (one that precede any non-zero
  digits) are not significant.
• For example, in 0.02080, the first two zeros
  are not significant. They only serve to place
  the decimal point.

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Significant Figures Zeros (contd)

• b) Zeros between non-zero integers are always
  significant. In the number 0.02080, the zero
  between the 2 and the 8 is a significant digit.
• c) Zeros at the right end of a number are
  significant only if the number contains a decimal
  point. In the number 0.02080, the last zero is
  the result of a measurement, and is significant.

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Significant Figures

• Thus, the number 0.02080 has four significant
  figures.
• If written in scientific notation, all
  significant digits must appear. So 0.02080
  becomes
• 2.080 x 10-2.

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Significant Figures

• 3. Exact numbers have an unlimited number of
  significant figures. Examples are 100cm 1m,
  the 2 in the formula 2pr, or the number of
  atoms of a given element in the formula of a
  compound, such as the 2 in H2O.
• Using an exact number in a calculation will not
  limit the number of significant figures in the
  final result.

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Significant Figures - Calculations

• When calculations are performed, the final
  result should reflect the same degree of
  certainty as the least certain quantity in the
  calculation.
• That is, the least certain quantity will
  influence the degree of certainty in the final
  result of the calculation.

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Significant Figures - Calculations

• There are two sets of rules when performing
  calculations. One for addition and subtraction,
  and the other for multiplication and division.
• For Multiplication and Division
• The result of the calculation should have the
  same number of significant figures as the least
  precise measurement used in the calculation.

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Significant Figures - Calculations

• Multiplication Division
• Example Determine the density of an object
  with a volume of 5.70 cm3 and a mass of 8.9076
  grams.

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Significant Figures - Calculations

• Multiplication Division
• Example Determine the density of an object
  with a volume of 5.70 cm3 and a mass of 8.9076
  grams.
• d mass/volume 8.9076 g/5.70 cm3
• d 1.5627368 1.56 g/cm3

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Significant Figures - Calculations

• Addition and Subtraction
• The result has the same number of places after
  the decimal as the least precise measurement in
  the calculation.
• For example, calculate the sum of
• 10.011g 5.30g 9.7093g 25.0203 25.02g

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Significant Figures - Measurement

• All measurements involve some degree of
  uncertainty. When reading a mass from a digital
  analytical balance, the last digit (usually
  one-ten thousandth of a gram) is understood to be
  uncertain.
• When using other devices in the laboratory, such
  as a ruler, graduated cylinder, buret, etc., you
  should estimate one place beyond the smallest
  divisions on the device.

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Significant Figures - Measurements

• The volume should be estimated to the nearest
  hundredth of a milliliter, since the buret is
  marked in tenths of a milliliter.
• The correct reading is 20.15 (or 20.14 or 20.16)
  mL. It is understood that the last number is
  uncertain.

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Significant Figures - Measurements

• The value of 20.15 mL indicates a volume in
  between 20.1 mL and 20.2 mL.
• If the liquid level were resting right on one of
  the divisions, the reading should reflect this by
  ending in a zero.

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Conversion of Units

• Many chemical calculations involve the
  conversion of units. An example is calculating
  how many grams of a product can be obtained from
  a given mass of a reactant. The calculation
  involves going from mass of reactant to moles of
  reactant to moles of product to grams of product.
  You should write in your units for all
  calculations, and make sure they cancel properly.

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Metric Conversion Factors

• These conversion factors are useful and worth
  learning.
• I inch 2.54 cm
• 1 lb 454.6 g
• 1 L 1.0567 qt

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Problem

• The density of mercury is 13.6 g/mL. What is
  the weight, in lbs, of a quart of mercury?

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Accuracy Precision

• Most experiments are performed several times to
  help ensure that the results are meaningful. A
  single experiment might provide an erroneous
  result if there is an equipment failure or if a
  sample is contaminated. By performing several
  trials, the results may be more reliable.

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Accuracy Precision

• If the experimental values are close to the
  actual value (if it is known), the data is said
  to be accurate.
• If the experimental values are all very similar
  and reproducible, the data is said to be precise.
• The goal in making scientific measurements is
  to that the data be both accurate and precise.

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Accuracy Precision

• Data can be precise, but inaccurate. If a
  faulty piece of equipment or a contaminated
  sample is used for all trials, the data may be in
  agreement (precise), but inaccurate. Such an
  error is called a systematic error. If the
  scientist has good technique, the results will be
  similar, but too high or too low due to the
  systematic error.

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Random Error

• In many experiments, data varies a bit with
  each trial. The variation in the results is due
  to random error. Examples might be estimating
  the last digit for the volume in a buret. Random
  errors have an equal probability of being too
  high or too low. As a result, if enough trials
  are performed, the random error will average
  itself out.