Significant Figures

Laboratory measurements are made by reading all digits on the instrument, and estimating one

digit.

• All the digits of a measurement that you are sure of (markings on the instrument) plus one estimated digit.

• Used to express limitations in a measurement.

Rules for significant digits.• Nonzero digits are always significant.

– Example: 5.67• All final zeros used after the decimal point

are significant. – Example: 5.60

• Zeros between two other significant digits are always significant. – Example: 5006, 5.006

• Zeros used solely for spacing the decimal point are not significant. – Example: 56,100 , 0.566 , .0561

Significant zeros If a zero is used only to place the decimal, it is NOT significant.

Examples:• Desk measures 32.10 cm

– What is the last marking on the instrument?– How many significant figures in this number.

• Counting numbers are exact whole numbers.– 30 people in the room– $20.05 dollars in my pocket

Reading a Measurement

A) 720.29g B) 722.9 g C.) 722.90 g D.) 723 g

A.) 200 g B.) 200.5 g C.) 200.55 g D.) 20.5g

A.) 76.0 ml

B.) 76 ml

C.) 77 ml

D.) 75.00 ml

A.) 47 ml

B.) 47.00 ml

C.) 47.0 ml

D.) 44 ml

A.) 3.44 ml

B.) 3.4 ml

C.) 3.50 ml

D.) 3.5 ml

E.) 3.48 ml

Lec Sup #1 How many significant figures are in

the measurement 405cm?A) 0B) 1C) 2D) 3E) 4

the measurement 3.208 cm?A) 0B) 1C) 2D) 3E) 4

the measurement 3000 cm?A) 0B) 1C) 2D) 3E) 4

the measurement .0045 cm?A) 0B) 1C) 2D) 3E) 4

the measurement .0450 cm?A) 0B) 1C) 2D) 3E) 4

Rules for calculating with significant figures.Addition or subtraction

Your final answer may contain no more places after the decimal than your least known quantity. (Round the answer so that it has the same number of decimal places as the measurement having the fewest decimal places.)

Example: 42.253 mL 125.6 mL 1.75 mL 169.603 mL *Answer can only have as many places to the right of the decimal as that of the known quantity with the least: = 169.6 mL

Multiplication and division Your final answer may have no more total Significant digits than your known quantity with the least number of significant figures.

Example:

62 cm x 33.03 cm = 2047.86 cm2

*only good to 2 figs

2.0 x 10 3 cm2

Rules for rounding off

Look at digit to the right of digit to be rounded. IF:

• Greater than or equal to 5 round up, less than 5 leave.

Lec Sup #6Round to three significant figures.

8.7257cm = A) 8.7300

B) 8.7200

C) 8.72

D) 8.73

E.) 8.73 X 104

Lec Sup #7Round to three significant figures. 125.699cm

=A) 126.00

B) 125

C) 126

D) 125.00

E.) 130.

Lec Sup #8Round to three significant figures.

124,292 = A) 124

B) 124,000

C) 120,000

D) 1.20 X 104

E.) 125,000

Lec Sup #9 Example: If 4.383 g of oxygen combine with 0.0023 g of carbon, what’s the mass of the resulting compound?

4.383 g0.0023 g4.3853 g

A)4.4 gB)4.38 gC)4.385 gD)4.3853 gE)4.39 g

Lec Sup #10 Example: If a line of 1.0 x 108 water molecules is 1.00 inches long, what is the average diameter, in millimeters of a water molecule?

1.00 inch 2.54 cm 1 m 1000 mm1.0 x 108 molecules 1 inch 100 cm 1 m

= 2.54 x 10-7

= 2.5 x 10-7 mm/molecule

A student places 28.70 g of iron, 0.3807 oz of aluminum, and 0.00389 lb of copper in a beaker that weighs 138 g. What is the total mass in grams of the beaker and its contents?

A)179.27 gB) 179.3 gC) 179 gD)180 gE) 200 g

Lec Sup #11

Note: conversions will count in sig fig analysis if the conversion is not exact. For instance metric to english (1lb is approx 454 g). But not in the case of exact conversions (1 lb is exactly 16 oz

A student places 28.70 g of iron, 0.3807 oz of aluminum, and 0.00389 lb of copper in a beaker that weighs 138 g. What is the total mass in grams of the beaker and its contents?

0.3807 oz 1.00 lb 454 g16 oz 1.00 lb

= 10.8 gAl

0.00389 lb 454 g 1.00 lb = 1.77 gCu

28.70 g 10.8 g 1.77 g138 g 179.27 = 179 g

A girl needs to reflux a mixture for 9.85 hours. How long mustthe mixture reflux in minutes?

Lec Sup #12

9.85 h 60 min 1 h

A)= 591 minB)= 600 minC)= 590 min

A girl needs to reflux a mixture for 9.85 hours. How long mustthe mixture reflux in minutes?

Lec Sup #12

9.85 h 60 min 1 h

A) Exact conversions do not dictate the number of significant figures in answer since infinitely significant.

A group of chemistry students are instructed to measure a 0.75 m length of magnesium ribbon and a .100m length of ribbon. How long will the total ribbon be in mm?

A).850mmB)850mmC)8.50 X 102 mm

Lec Sup #13

If multiple operations, calc sig figs through order of operations to see how answer should be reported.

A group of chemistry students are instructed to measure a 0.75 m length of magnesium ribbon and a .100m length of ribbon. How long will the total ribbon be in mm?

0.75 m + .100m = .85m .85m 1000 mm 1 m = 850 mm

Accuracy & PrecisionAccuracy:

how close a measurement is to the true value of the quantity that was measured.

Precision:(1) how closely two or more measurements of the same quantity agree with one another as well as (2) the degree of exactness.

• Chemistry: –Study of matter and

changes in matter • Matter

–Anything that occupies space and has mass

• Pure Substance:–Form of matter that has a

constant composition and distinct properties.

• Mixture:–Combination of 2 or more

substances in which the substances retain their distinct identities.

Types of Mixtures

• Homogeneous:–Composition of mixture is the

same throughout. (solutions)• Heterogeneous:

–Composition is not uniform (suspensions)

Types of Pure Substances• Element:

– Substance which cannot be separated into simpler substances by chemical means.

• Compound:– Composed of atoms of 2 or more

elements chemically fixed in definite proportions. C6H12O6

Na, K, Cl

Classification of Matter

S o lu tion s H ete rog en eou sM ixtu res

M ixtu res

E lem en ts C om p ou n d s

P u re S u b s tan c es

A ll M a tte r

Example 14:

Classify Dry Ice as one of the following (a) an element, (b) a compound, (c) or a mixture:

Example14:

Classify gasoline as one of the following (a) an element, (b) a compound, (c) or a mixture:

Example 14:

Classify air as one of the following (a) an element, (b) a compound, (c) or a mixture:

Example 14:

Classify blood as one of the following (a) an element, (b) a compound, (c) or a mixture:

Example 14:

Classify methane as one of the following (a) an element, (b) a compound, (c) or a mixture:

Example 14:

Classify Iodine as one of the following (a) an element, (b) a compound, (c) or a mixture:

Similar properties on the periodic table

• Families(groups)/Periods• Oxidation numbers• Polyatomic ions• metals, nonmetals, and

metalloids

• Chemical• Physical• Extensive• Intensive

• Macroscopic• Microscopic

Lec Supplement 15: The following are properties of the element silicon; classify them as (a) physical intensive, (b) physical extensive, (c) or chemical properties:

_______ Melting point, 1410oC

_______ Reacts with fluorine to form silicon tetrafluoride

_______ Gray

_______ Not affected by most acids

Matter Changes• Physical change: does not change the

identity (composition) of substance• Chemical change: changes chemical

composition (identity of substance)• both involve energy transformation• endothermic: absorb energy• exothermic: release energy

Lec Sup 15b.)Classify each of the following as a chemical or physical change.

Boiling Water

A) Chemical ChangeB) Physical Change

Tearing Clothes

Lighting a Match

A Rusting Nail

Melting Ice Cream

Metabolizing Food for Energy

Finger Nails Growing

Frying an Egg

Sweat evaporating from your forehead

A balloon pops due to the expansion of air

Dissolving of Toluene in Carbon Tetra Chloride

Terms to know:• Group/Period• Metals/nonmetals/metalloids• Alkali metals, Alkaline earth

metals, Chalcogens, Halogens, and Noble gases (rare gases)

• Molecule:–2 or more atoms tightly bound

together.• Molecular Compound:

–Compounds made up of molecules & contain more than 1 type of atom.

Molecule- A neutral group of atoms that act as a unit. a) In molecules atoms always combine in simple whole number ratios, therefore their proportions by mass must always be the same.

Molecular Compoundscompounds composed of molecules• low melting and boiling points• many exist as gases or liquids at

room temperature• Most are composed of 2 or

more nonmetallic elements

Ionic Compoundscomposed of cations(+) and anions(-)

• Difference in charges holds them together.

• ions are arranged in orderly 3-dimensional pattern.

• Each cation is between two or more anions.

• Most are crystalline solids at room temperature.

• Usually formed from a metallic and nonmetallic element.

Ionic Charges of Elements• You should know the table in your

handout.(grp. 1A,2A,3A,5A,6A,7A)• Also remember:

Ni 2+ Ag1+ Cd 2+ Zn 2+ • Transition metals and group 4A

and 5A metals have multiple ionic charges (oxidation numbers)

Formula writing and compound naming summary

1.) Classify the compound as: ionic or molecular

2.) If the compound is ionic : CATION ANION first name last name

Naming binary Ionic compounds

• Cation(no prefix) then the anion root plus ide.

• HCl (contains cation hydrogen therefore ionic rules)

LS: Name the following

1. CaCl2

2. NaF 3. BaO

A.)Two naming systems for transition metals1.) Stock System

Uses roman numerals i.e. Copper(II) = Cu+2

2.) Classic systemUses suffixes ous and ic.

ous = lower charge; ic = higher

Name the following using the classic naming system

4. FeO5. Fe2O3

6. CuCl2

Name the following using the stock naming system

7. CuF2

8. FeCl3

Polyatomic Ions- Tightly bound groups of atoms that behave as a unit and carry a Charge.

• During reactions, these atoms usually stay together.

• Notice some have ite / ate pairs• ite indicates one less oxygen than

the ate.

Naming Ternary compounds• Contain atoms of 3 different elements-one

is typically a metal• Usually have 1 or more polyatomic ions.

• Name using Ionic procedures. However the ending of the name of the polyatomic ion is not changed.

• Magnesium chloride MgCl2

How do you know the subscript?

Mg+2 Cl-1

• Formula Unit- lowest whole number ratio of ions in an ionic compound. (also called empirical formula)

Magnesium Chloride (MgCl2) 1:2 Ratio Mg to Cl

Molecule must be neutral so balance oxidation states

3.) If the compound is molecular, classify as an acid or nonacid.

4.) If a nonacid, Prefix + element Prefix + root name + -ide first name last name

5.) If an acid, classify as nonoxyacid or oxyacid.

Naming binary molecular

- Element on left preceded by a prefix of how many atoms.

-Element on the right preceded by prefix of how many atoms and ide at the end. P2O5

1=mono etc...

Name the following 9. N2O5

10. PCl3

11. N2O4

-When there is 1 atom of the first element, omit the prefix mono.

-Binary molecular compounds containing hydrogen as the first element are named by the ionic system.

6.) If it is a nonoxoacid, hydro + root name + ic acid HCl, HI, HCN, H2S Hydrochloric acid, Hydroiodic acid, Hydrocyanic acid, hydrosulfuric acid.

7.) If it is an oxoacid,polyatomic anion root + -ic or -ous acid• ate ion = acid with ic / ite ion = ous

• H2SO4,, HNO2, H3PO4

Name the following acids

12. H2SO4

13. HNO314. HI

• Write the chemical formula for Copper (II) Phosphatea.) CuPO4

b.) Cu2PO4

c.) Cu2(PO4)3

d.) Cu3(PO4)2

e.) CuP

• Write the name for Fe(CN)3

a.) Iron Cyanideb.) Iron (I) cyanide (III)c.) Iron (III) Cyanided.) Iron tricyanidee.) Iron Carbon Nitride

• The name for Na2S

a.) sodium sulfideb.) disodium sulfidec.) disodium monosulfided.) sodium sulfatee.) Sodium sulfite

• The name for FeOa.) Iron Oxideb.) diiron trioxide c.) Iron (II) Oxided.) Iron (III) Oxide

• The name for CuCO3

a.) Copper carbideb.) Copper (I) Carbonatec.) Copper Carbonated.) Copper (II) Carbonatee.) Copper monocarbonate

• The formula for nitrogen dioxidea.) N2Ob.) NO2

c.) NOd.) N(I)O(II)

• Name C3H8

• A.) Carbon Hydride• B.) Carbon (IV) Hydride• C.) tricarbon octahydride• D.) propane• E.) butane

• Name HC2H3O2

• A.) Hydrogen Acetate• B.) Hydrogen carbon oxide• C.) ????• D.) Acetous acid• E.) acetic acid

• Name IF5

• A.) Iodine Fluoride• B.) Iodine (I) Fluoride• C.) Iodine pentafluoride• D.) Monoiodine pentafluoride• E.) iodine pentaflourine

• Name Na2SO4•10H2O• A.) Sodium (II) sulfate water• B.) Sodium (I) sulfate water• C.) Sodium sulfite• D.) Disodium sulfate decahydrate• E.) Sodium sulfate decahydrate

Terms You Should Know•atomic number (Z)•mass number (A) •isotopes• •atomic mass•average atomic mass

Particles in the AtomAtoms consist of protons, neutrons and electrons

ElectronsElectrons (-) charge no mass located outside the nucleus

ProtonsProtons (+) charge 1 amu located inside the nucleus

NeutronsNeutrons no charge 1 amu located inside the nucleus

Particles in the Atom

Structure of the Atom

There are two regionsThe nucleus

• With protons and neutrons– Positive charge– Almost all the mass

Electron cloud– Most of the volume of an atom– The region where the electron can be found

Counting the Pieces

Atomic Number (Z) = number of protons in the nucleus of an atom, always the same for a given element

Mass Number (A) = total number of nucleons in an atom (protons+neutrons)

Mass #

Atomic #

IsotopesAtoms of the same element with a different mass

number.

Same # protons, different number of neutrons

C-12 C-13 C-14

Isotope of Magnesium

Atomic symbol Mg Mg Mg

Number of protons 12 12 12

Number of electrons 12 12 12

Mass number 24 25 26

Number of neutronsneutrons 12 13 14

Isotope Notation Mg-24 Mg-25 Mg-26

12e- 12e-

Isotope of Chlorine

• Atomic #• Mass #• # protons• # neutrons• # electrons• Shorthand name

3717 Cl

Mass # - Atomic # = # neutrons

1. How many electrons, protons, neutrons are in an atom of phosphorus with mass number 31?

2. How many electrons, protons, neutrons are in an atom of thorium with mass number 232?

(protons & neutrons) (protons)

CationsNa+

AnionsCl-S2-

IonsAn atom that has become charged by either gaining or losing electrons

Cation- positive ions, loses electrons

Anion - negative ions, gains electrons

I 1– 125

Formation of a Cation

sodium atomNa

loss of one valence

electron

sodium ionNa+

11p+e-

Formation of an Anion

chlorine atomCl

gain of one valence

electron

chloride ionCl1-

17p+e-

Description NetCharge

AtomicNumber

MassNumber

IonSymbol

18 e–

36 e–

128 Te2–

18 e–

Parts of the atom Summary

• # Protons - determine the identity of the atom, atomic number (Z)

• # Neutrons - determine the particular isotope of that element, mass number (A)

• # Electrons - determine the charge on the atom

Average Atomic MassAtomic mass - the average mass of the isotopes in their

relative abundance

Not all isotopes of an element are present in the same amount, so we use a weighted average

Avg.AtomicMass

(mass)(%) + (mass)(%)

Average Atomic Mass• EX: Calculate the avg. atomic mass of oxygen if its

abundance in nature is 99.76% O-16, 0.04% O-17, and 0.20% O-18.

Avg.AtomicMass

= (16)(99.76) + (17)(0.04) + (18)(0.20)

100= 16.00

Average Atomic Mass

• Ex: Find chlorine’s average atomic mass if approximately 8 of every 10 atoms are Cl-35 and 2 are Cl-37

Avg.AtomicMass

(35)(8) + (37)(2)

1035.40 amu= =

:) Atom Jokes :)A neutron walks into a restaurant and orders a couple of drinks. As she is about to leave, she asks the waiter how much she owes. The waiter replies, “For you, No Charge!!!”

Two atoms are walking down the street.One atom says to the other, “Hey! I think I lost an electron!”The other says, “Are you sure??”“Yes, I’m positive!”

IV.)Chemical Formulas• Molecular formula-

shows the kinds and number of atoms present in a molecule of a molecular compound.Ethanol - (C2H6O)1 Molecule of ethanol contains2 carbon, 6 hydrogen, 1 oxygen atom

Ions• Ions are formed by gaining or

losing electrons.• In general,

–Metal atoms tend to lose e-

–Nonmetallic atoms tend to gain e-

Molecular formula:Indicates the actual numbers and types of atoms in a molecule.

Empirical Formula:elements present in simplest whole number ratios of their atoms.H2O2 HOEmpirical formula

Molecular formula

empirical formula: the formula for a compound containing the smallest ratio of the atoms.

molecular formula:the "true" formula of the compound, contains the actual number of atoms of each element present in one molecule of the compound.

EXAMPLES: Molecular Empirical Formula Formula

H2O2 HO

P5O10 PO2

N2O4 NO2

Structure of Ionic Compounds

• Ions arrange in 3-dimensional structures. (see page 54)

• We write an empirical formula: NaCl

• All we can do for ionic compounds is write empirical formulas

Structural FormulaShows which elements are

attached to which in a molecule.

– Types of Models• Ball and Stick models• Space-filling models

•molar mass•chemical formulas•empirical formula•molecular formula•diatomic molecules•polyatomic molecules•allotropes

Significant Figures

Documents

Transcript of Significant Figures

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Significant Figures & Scientific Notation Significant Figures & Scientific Notation.

Significant Figures

SIGNIFICANT FIGURES

Significant Figures and Rounding. Significant Figures Significant figures - show accuracy in measurements & calculations Significant figures in a.

3.1 SIGNIFICANT FIGURES The Concepts. Significant figures pertain to MEASUREMENTS.