1
Measurements and Uncertainty
Measurement = comparing a value with a unit
Measurement = read between the scale division marks, estimate
the measurement to the nearest one tenth of the space between
scale divisions
Significant Figures = digits read from the scale
+ the last estimated digit
Measurement error = minimum ±1 of the last digit
2
Measurement
32.33 °C 32.3 °CWhat is the
smallest scale
division
3
Reading from a digital display
error = ±1 of the last digit
4
Accuracy and Precision
Every measurement has its error
Repeated measurements - error estimation
Precision = is the degree to which
repeated measurements show the
same results, depends on the
abilities of experimentator
Accuracy = the agreement
between experimental data and a
known value, depends on
instrument quality
5
Weighing
Number of significant figures is given by the instrument quality
6
Significant Figures
• All nonzero digits are significant 3.548
• Zeroes between nonzero digits are significant 3.0005
• Leading zeros to the left of the first nonzero digits are not
significant 0.0034
• Trailing zeroes that are also to the right of a decimal point in a
number are significant 0.003400
• When a number ends in zeroes that are not to the right of a
decimal point, the zeroes are not necessarily significant 1200
Ambiguity avoided by the use of standard exponential, or
"scientific," notation: 1.2 103 or 1.200 103
depending on the number of significant figures
7
Significant Figures
8.75 cm3 8.00 cm3
Not 8 cm3 !!!!
Reading from a scale – number of significant figures is
given by the instrument quality
digits read from the scale + the last estimated digit
8
Significant Figures
Exact numbers = known with complete certainty, infinite
number of significant figures
- Number of people, experiments, …
- conversion factors 1 week = 7 days 7.000000000
1 inch = 2.54 cm
- definitions 0 °C = 273.15 K
can be ignored as a limiting factor in determining the
number of significant figures in the result of a calculation
9
Rules for mathematical operations
Multiplication and Division, the result should be
rounded off so as to have the same number of significant
figures as in the component with the least number of
significant figures.
p V = n R T p = 748 Torr = 99.7 103 Pa
V = 1254 ml = 1.254 10−3 m3
T = 298 K
R = 8.314 J K-1 mol−1
n = pV/RT = 5.0462226 10−2 mol = 5.05 10−2 mol
Rounding off numbers – in the final result of calculation
10
Rules for mathematical operations
Addition and Subtraction, the result is rounded off so that it
has the same number of digits as the measurement having
the fewest decimal places
Measured 2.5 cm with a ruler and 1.2 mm with a micrometer
add 2.5 cm with uncertainty ±0.1 cm
+0.00012 cm with uncertainty ±0.00001 cm
The result is NOT 2.50012 cm
but 2.5 cm
Because the error in the first number is 4 orders of magnitude
bigger than the second number
11
Matter
Matter is made of atoms - little articles that move around
in perpetual motion, attracting each other when they are
a little distance apart, but repelling upon being squeezed
into one another.
Richard P. Feynman
(1918 - 1988)
NP in Physics 1965
Matter is anything that occupies space, has rest mass, is
composed of atoms, is convertible to energy
12
Matter
Field Substance
Mixtures
Homogeneous
Heterogeneous
Pure substance
Element Compound
Molecules
Monoatomic Polyatomic
Atoms
Nucleus
Electrons
Protons
Neutrons
Nuclide
Separation
13
States of Matter
Gas
Liquid
Solid
Ds
14
States of Matter
15
Law of Conservation of Mass
Lavoisier 1785
Matter can be neither created
nor destroyed.
In a chemical reaction, the mass
of the products equals the mass
of the reactants.
The law is a result of precise
weighing reactants and products
(conversely from weighing we
obtain information about
chemical reactions)
Antoine Lavoisier
1743 - 1794
(guilotined)
16
Law of Conservation of Energy
The first law of thermodynamics
Equivalence of mass and energy: E = m c2
u = 1.66 10−27 kg = 931.4 MeV
System:
Isolated = Mass and energy is constant
Closed = Mass is constant, energy is exchanged
with surroundings
Úbytek hmotnosti při uvolnění energie:
• Chemical reactions ng per mol
• Nuclear reactions mg per mol
17
Law of Definite Composition
Proust 1788 / 1799
Proved a constant composition of water.
There are SnO and SnO2
CuCO3 – a compound always contains
the same relative masses of elements
regardless of its origin.
Louis Joseph Proust
(1754 - 1826)
1.000 g of C will always react with 1.333 g of O2 to CO
18
Law of Multiple Proportions
Dalton 1803
When elements combine, they do so in
the ratio of small whole numbers. The
mass of one element combines with a
fixed mass (e.g. 1 g) of another element
according to this ratio (N2O, NO, N2O3,
NO2, N2O5).
Table of relative atomic masses
14 elements relative to H (=1)
John Dalton
(1766 - 1844)
19
Oxides of Chromium
3.0000.92311.000CrO3
2.0000.61541.000CrO2
1.4990.46151.000Cr2O3
1.0000.30771.000CrO
Ratio, rm(O) / gm(Cr) / gCompound
CrOOm
OCrOm
r
yx
)(
)(
=
20
Non-stoichiometric compounds-bertholides
Fe1-xO x = 0.05 – 0.15
3 Fe2+ = 2 Fe3+ + 1 vacancy (Fe)
Compounds of a metal possessing several oxidation
states - Oxides, sulfides, nitrides,...
C. L. Berthollet
(1748 - 1822)
Vacancy = unoccupied position
Fe2+ = blue
Fe3+ = red
21
Dalton's Atomic Theory
• Matter consists of definite particles called atoms.
• Atoms are indestructable. They can rearrange in chemical
reactions but they do not themselves break apart.
• Atoms of a particular element are indistinguishable from
one another. They are all identical in mass, as well as
other properties.
• Atoms of different elements (or types) differ in mass (and
other properties).
• When atoms of different elements combine to form
compounds, new and more complex particles (molecules)
are formed. Their constituent atoms are always present in
a definite numerical ratio.
1805
Law - theory
22
Law of Constant Volumes
1809 Gases combine together in volumes (measured at the
same temperature and pressure) that bear a simple ratio to
each other and to the gaseous products
2 volumes of H2 + 1 volume of O2 → 2 volumes water vapor
Joseph Louis Gay-Lussac
(1778 - 1850)
Gay-Lussac's law
23
Law of Constant Volumes
+
HO
O
H
H
HO
?
2 volumes of H2 + 1 volume of O2 → 2 volumes water vapor
24
Avogadro’s Hypothesis
Volume of 1 mole of gas is 22.4 l
at 0 °C and 101325 Pa
Vm = 22.4 l mol–1 Amadeo Avogadro
(1776 - 1856)
1811 from Dalton atomic theory and Gay-Lussac
Law derived:
Two equal volumes of gas, at the same
temperature and pressure, contain the same
number of molecules.
Gasses are diatomic molecules.
H2, N2, O2
25
Avogadro’s Law
+
H2O
O2
H2
H2
H2O
At a constant temperature and pressure, the volume of a gas is
directly proportional to the number of moles of that gas.
2 volumes of H2 + 1 volume of O2 → 2 volumes water vapor
26
Avogadro’s Molecules
Molecules = smallest particles of matter capable of
independent existence
He, Ne, Ar, .....
N2, P4 (yellow), S8, C60, ......
BCl3, CH4, H2O, NH3......
Not molecules:
NaCl, SiO2, BeF2, C (graphite, diamond), .....
27
Mass – mol – Avogadro’s constant
Elements combine in the constant ratios of small whole numbers:
NaCl = 23.0 g Na and 35.5 g chlorine
Scale of relative atomic masses:
H = 1.0, C = 12.0, O = 16.0
Definition of mole: 12.0 g C = 1 mol
then 23.0 g Na = 1 mol
1 mol of gas = 22.4 litre
Measure the number of particles in 1 mole (Loschmidt, Perrin,...)
NA = 6.022 140 78(18) 1023 mol−1
28
Amount of Substance, n
1 mol = amount of substance that contains as many
elementary entities (e.g., atoms, molecules, ions, electrons) as
there are atoms in 12 g of pure 12C
Avogadro’s constant NA = 6.022 1023 mol–1
Chemical formulae Na2SO4
Stoichiometry in chemical equatins
2 Ca3(PO4)2 + 6 SiO2 + 10 C → 6 CaSiO3 + 10 CO + P4
29
Loschmidt’s Number
Loschmidt’s number = the number of molecules in a
cubic centimetre of a gas under standard conditions.
1865 from kinetic theory of gases calculated
n0 = 2.6 1019 molecules cm–3
Today’s value: 2.686 7775 1025 m–3
Avogadro’s constant
NA = 6.022 141 99 1023 mol–1
Johann Josef Loschmidt
(1821 - 1895)
Počerny near Carlsbad
30
Avogadro’s Constant
Jean Baptiste Perrin
(1870 - 1942)
NP in Physics 1926
Brown motion of particles in a liquid
1908 Proof for the existence of molecules
Introduced term Avogadro’s constant
and experimentally measured
6.82 1023 molecules in 2 g of hydrogen
31
Avogadro’s Constant
From XRD structural analysis of single crystals of Ti
Ti = body centred cubic unit cell
Number of atoms in the unit cell Z = 2
Edge length a = 330.6 pm
Density Ti ρ = 4.401 g cm−3
A(Ti) = 47.88 g mol−1
2 Ti per 1 unit cell with volume V = a3
r a3 = Z A(Ti) / NA
NA = Z A(Ti) / V r
32
Elements in the History of Chemistry
Empedocles (490 - 430 B. C.)
4 basic elements = fire, water, air, earth
and 2 basic forces: attraction and repulsion
(only in 1783 H. Cavendish proved that water is a compound of H
and O)
Aristotle (384 - 322 B. C.) 4 basic elements + aether
an element is the source of properties
Combination of properties
33
Elements in the History of Chemistry
Alexandria: Greek theory + Egyptian practical “chemistry”
Arabic alchemy, transferred to Europe
Alchemist’s elements : fire, water, air, earth and
Au, Ag, Hg, Fe, Sn, Cu, S, salt
Au Sun
Ag Moon
electrum (Sn amalgam) Jupiter
Fe Mars
Cu Venus
Sn Merkur
Pb Saturn
34
Elements in the History of Chemistry
Philippus Aureolus Paracelsus (1493–1541)
3 elementary substances: Hg, S, and salt
Moravský Krumlov - Jan z Lipé
Hg = liquidity and metallic character
S = inflammability
Salt = inert element
35
Elements in the History of Chemistry
1661 Robert Boyle – scientific definition:
an element is any substance that cannot be decomposed
into a simpler substance.
1789 Lavoisier - 21 elements
1808 Dalton - 36 elements – the first connection atom/
element concepts
The same atoms have the same mass, multiples of H
1813-14 Berzelius - 47 elements
1869 Mendelejev table - 63 elements
2012 Periodic table - 118 elements (117 missing)
Elements names - 112
36
Concept of Atom
Leukippos (480-420 B. C. )
Is matter continuous or discontinuous?
World consists of matter and vacuum, indivisible particles.
Demokritos (470-380 B. C.) Atom (atomos = indivisible)
Everything is composed of atoms, which are indivisible;
between atoms lies empty space; atoms are indestructible;
have always been, and always will be, in motion; there are
an infinite number of atoms, and kinds of atoms, which
differ in shape, and size.
Next 2000 years rejected - till 1805 Dalton
37
Dalton's Atomic Theory
• Matter consists of definite particles called atoms.
• Atoms are indestructable. (not nuclear reactions)
• Atoms can rearrange in chemical reactions.
• Atoms of a particular element are indistinguishable
from one another, identical in mass (not nuclides)
and other properties.
• Atoms of different elements differ in mass (not
isobars) and other properties.
• When atoms of different elements combine to form
compounds, new and more complex particles
(molecules) are formed.
• Their constituent atoms are always present in a
definite numerical ratio.
1805
John Dalton
(1766 - 1844)
38
1. Oxygen.
2. Hydrogen.
3. Nitrogen.
4. Carbon.
5. Sulphur.
6. Phosphorus
7. Gold.
8. Platinum.
25. Cerium.
26. Potassium.
27. Sodium.
28. Calcium.
29. Magnesium.
30. Barium.
31. Strontium.
32. Aluminium.
33. Silicon.
34. Yttrium.
35. Beryllium.
36. Zirconium.
Dalton’s Symbols of Atoms/Elements
9. Silver.
10. Mercury.
11. Copper.
12. Iron.
13. Nickel.
14. Tin.
15. Lead.
16. Zinc.
17. Bismuth.
18. Antimony.
19. Arsenic.
20. Cobalt.
21. Manganese.
22. Uranium.
23. Tungsten.
24. Titanium.
39
Atomic Mass
J. Dalton H = 1
J. J. Berzelius O = 100
J. S. Stas O = 16 (natural mixture of isotopes)
chemical scale
physical scale 16O = 16 Mess
1961
Atomic mass unit = 1/12 of mass of atom of nuclide 12C
1 amu = 1 u = 1.6606 10−27 kg
40
Atomic Mass
1814 Table of relative atomic masses of 41 elements
O = 100
1811 Abbreviations as element symbols
Li Lithium
Be Beryllium
Ga Gallium (not Galium)
Y Yttrium
Te Tellur
Tl Thallium
Ds Darmstadtium
(Cp) Copernicium
Jőns Jacob Berzelius
(1779 - 1848)
Compound formulae
Then H2O, today H2O
41
Periodic Table of Elements
42
Definition of an Element
F19
9
A, Mass / Nucleon number
Z, Atomic / Proton number
Nuclide = a set of atoms with identical A and Z
Element = a set of atoms with identical Z
43
Chemical Compounds - composition
Type of atoms A or B - elements
A and B or A and C - compounds
Relative number of atoms AB or AB2
→ empirical formula (CO or CO2)
Absolute number of atoms A2B2 or A6B6
→ molecular formula (C2H2 or C6H6)
[CoN6H15O2]2+
44
Elements – Structure – Allotropy
Structure (bonds between atoms)
→ structural formula
Bonding topology allotropy (elements): O2, O3
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S2
S
S
S
S
n
45
Compounds – Structure – Constitution
Bonding topology
→ structural (constitutional) formula
topological (constitutional, bonding) isomerie
(compounds)
A-B-C or A-C-B
C5H10O
HOCN, HNCO, HONC
[Co(NH3)5NO2]2+ [Co(NH3)5ONO]2+
46
217 isomers of C6H6
Topological (constitutional, bonding) Isomerie
47
Molecular Shape
Molecular Shape → geometrical formula
NH3
Co
NH3
H3N
NH3
NH3N
O
O
2+
NH3
Co
NH3
H3N
NH3
OH3N
N
2+
O
bonding isomers of NO2 groups
48
Compounds – Structure – Constitution
Al4N4C48H40
Al4N4Ph8
[PhAlNPh]4
AlNC12H10
49
Compounds – Structure – Constitution
Al4N4C48H40
Al4N4Ph8
[PhAlNPh]4
AlNC12H10
50
Compounds – Structure – Constitution
Al4N4C48H40
Al4N4Ph8
[PhAlNPh]4
AlNC12H10
51
Molecular Shapes
Molecular Shapes geometrical formula
geometrical isomers
Pt
H3N
Cl
ClH3N Pt
H3N
NH3
ClCl
cis trans
H
R
H
R
H
R
R
H
Z E
Molecular Shape
- physical properties
- chemical reactivity
52
53
Molecular Shapes
Optical isomers – enantiomers
Molecular Shapes → geometrical formulae
Dissymetry
Asymetric atom
54
Optical isomers - enantiomers
C
Cl
CH3
H
Br
C
Cl
H3C
H
Br
55
Optical isomers - enantiomers
56
Molecular Shapes
conformers
R
R
N
Me
N
Me
57
Crystal structures
Polymorphism – only for solids
Same building units (formula), same bonds, different
arrangement in space
Cubic diamond Hexagonal diamond
58
Composition of Atoms
1807 Compounds are held
together by electric forces
Prepared alkali metals from
their melted salts
Electrolysis of K2CO3 melt → K
Electrolysis of NaCl melt → Na
Humphry Davy
(1778 - 1829)
59
Faraday’s Law of Electrolysis
1833 The mass of a substance altered at an electrode is
directly proportional to the quantity of electricity passed.
For a given quantity of electricity (electric charge), the mass of
material altered at an electrode is directly proportional to its
equivalent weight. The equivalent weight is its molar mass
divided the number of electrons required to oxidize or reduce
each unit of the substance
Michael Faraday
(1791 - 1867)
e = 1.602 10−19 C
Faraday Constant = F
Charge of 1 mol of e = 96500 C
1 mol Mz+ ………….96500 C × z
n mol Mz+ …………Q = I t
zF
MIt
m =
60
Composition of Atoms
1758
Two types of electricity: Robert Symmer – socks
1874
Electricity is formed by discreet negatively charged
particles
1894 named electron
George J. Stoney
(1826 - 1911)
61
Composition of Atoms
Cathode Rays, 1898-1903
• A cathode ray tube - glass tube from which most of the air
has been evacuated, electrodes placed at each end, a highvoltage
current passed through the electrodes.
• A ray is produced at the cathode (negative pole) and travels
to the anode (positive pole).
Joseph John Thomson
(1856 - 1940)
• The cathode ray responds to both magnetic
and electric fields. Since the ray is attracted
to a positive electric plate placed over the
cathode ray tube (beam deflected toward the
positive plate), the ray must be composed of
negatively charged particles.
Experimental evidence for the existence of
electron
62
Cathode Rays
Electric field
Magnetic field
Specific charge
q/me = −1.76 108 C g −1
63
Cathode Rays
Specific charge
q/me = −1.76 108 C g −1
Electric field
Magnetic field
64
Electric field Magnetic field
65
Thomson Atomic Model
Electrons
Positive charge diffuse