Homework Problems

Chapter 2 Homework Problems: 1, 4, 19, 24, 28 (give the number of protons, neutrons, and electrons), 30, 38, 41, 44, 46, 54, 64, 66, 67, 72, 76, 82, 84, 96, 101, 104, 114, 116, 117, 124

CHAPTER 2

Atoms, Molecules, and Ions

Early Theories of Matter

The ancient Greeks discussed two possibilities for the essential property of matter.

Matter is continuous (no “particles” of matter) - Plato, Aristotle, and a majority of Greek philosophers.

Matter is discrete (composed of particles) - Democritus, Leucippus, and a small number of Greek philosophers.

Does this process have an end?

yes – particles of matter exist

no – matter is continuous

General Properties of Chemical Systems

As scientists began studying chemical systems they discovered several general properties of such systems.

1) Conservation of Mass. The total mass in a closed system remains constant, even if chemical reactions occur.

2) Law of Definite Proportions. All samples of a particular pure chemical substance contain the same relative amounts of each element making up the substance.

Examples: methane 74.9 % C, 25.1 % H

water 88.8 % O, 11.2 % H

copper (II) sulfate 39.8 % Cu, 20.1 % S, 40.1 % O

3) Law of Multiple Proportions. When two elements can combine to form several different chemical compounds, the ratio of the amount of the second element combining with a fixed amount of the first element will be the ratio of small whole numbers.

Example: There are two common compounds of carbon and oxygen

carbon monoxide 1.000 g of C reacts with 1.332 g of O

carbon dioxide 1.000 g of C reacts with 2.664 g of O

g O in carbon dioxide = 2.664 g = 2.000 2g O in carbon monoxide 1.332 g 1

It is easier to calculate the ratios with the larger number on top, but that is not required.

Example: The following pure chemical substances can be formed out of the elements nitrogen and oxygen

nitrogen monoxide 1.000 g of N reacts with 1.142 g of O

nitrogen dioxide 1.000 g of N reacts with 2.285 g of O

nitrous oxide 1.000g of N reacts with 0.5711 g of O

Do these substances demonstrate the law of multiple proportions?

nitrogen monoxide 1.000 g of N reacts with 1.142 g of O

nitrogen dioxide 1.000 g of N reacts with 2.285 g of O

nitrous oxide 1.000g of N reacts with 0.5711 g of O

g O in nitrogen monoxide = 1.142 g = 2.000 2 g O in nitrous oxide 0.5711g 1

g O in nitrogen dioxide = 2.285 g = 4.001 4 g O in nitrous oxide 0.5711 g 1

g O in nitrogen dioxide = 2.285 g = 2.001 2g O in nitrogen monoxide 1.142 g 1

So yes, these data are consistent with the law of multiple proportions.

Dalton’s Atomic Theory

A comprehensive theory that accounted for the above obser-vations was proposed by John Dalton, an English chemist, in 1808. There were four parts to the theory.

1) Elements are composed of particles, called atoms.

a) All atoms of the same element are identical in size, mass, and chemical properties.

b) Atoms of different elements differ in their size, mass, and chemical properties.

Dalton’s Atomic Theory (continued)

2) Chemical compounds are composed of atoms of more than one element.

a) In any particular pure chemical compound the same kinds of atoms are present in the same relative numbers.

3) Chemical reactions can rearrange atoms, but atoms cannot be created, destroyed, or converted from atoms of one element to atoms of a different element.

We now know that some of the hypotheses in Dalton’s atomic theory are not completely correct; however, the theory represents a good starting point in understanding the composition of matter.

Consequences of Dalton’s Atomic Theory

Dalton’s theory can be used to explain the observations cited above.

1) Conservation of mass. Explained by (1) and (3).

2) Law of definite proportion. Explained by (1) and (2).

Example: methane = CH4

Chemical formula - A list of the elements making up a compound, giving the number of atoms of each element per molecule or per formula unit of the compound.

3) Law of multiple proportions. Explained by (1) and (2) .

carbon monoxide (CO) carbon dioxide (CO2)

1 C atom: 1 O atom 1 C atom: 2 O atom

So for a given amount of carbon, carbon dioxide will have twice as many oxygen atoms (and therefore twice the mass of oxygen) as carbon monoxide.

Atomic Structure

In Dalton’s atomic theory the smallest particles (atoms) could not be further broken down. However, a series of experiments, beginning in the mid-19th century, demonstrated that atoms themselves could be broken down into smaller particles.

Radioactivity

In 1895, Antoine Becquerel discovered that some substances (such as radium and uranium) spontaneously emit “radiation”, a process called radioactivity.

Three types of radioactivity were found:

alpha () radiation: positively charged particles, now known to be He2+ nuclei (2 protons + 2 neutrons)

beta () radiation: negatively charged particles, now known to be electrons

gamma () radiation: uncharged, now known to be high energy photons (particles) of light

Electrons

J. J. Thompson (1897) found that when a high voltage was applied across two electrodes at low pressure a beam of particles moved from the negative to the positive electrode. The particles, named electrons, were negatively charged and the same regardless of the gas between the electrodes or the metal used in the electrodes. The charge and mass of an electron were determined experimentally by Millikan (1909).

The “Plum Pudding” Model

Since atoms are electrically neutral, the negative charge of the electrons in an atom had to be balanced by a positive charge. Thompson suggested that most of the space within an atom consisted of a positively charged substance, with electrons embedded within, the “plum pudding” model.

Rutherford and the Nuclear Atom

To test Thompson’s plum pudding model, Ernest Rutherford (1909) carried out an experiment where a beam of positively charged particles (alpha particles) were directed at a thin sheet of gold metal.

The results of this experiment were inconsistent with the plum pudding model. Rutherford proposed a new model, called the nuclear model of the atom, that did account for the experimental results.

Subatomic Particles

particle charge mass

Coulombs elementary kg amu

proton (p+) + 1.60 x 10-19 +1 1.673 x 10-27 1

neutron (n) 0 0 1.675 x 10-27 1

electron (e-) - 1.60 x 10-19 - 1 9.11 x 10-31 0

________

1 amu = 1.6605 x 10-27 kg

mp/me = 1836.

Atomic Structure

nucleus

electron charge cloud

1) The protons and neutrons of the atom are found in a small region in the center of the atom, called the nucleus. This region contains most of the mass of the atom.

2) Electrons in the atom form a diffuse cloud of charge centered on the nucleus and occupying most of the volume of the atom.

3) The size of the charge for the proton and electron is the same. The charge for the proton is positive, and the charge for the electron is negative. Neutrons have no charge.

4) The type of element for an atom is determined by the number of protons in the atomic nucleus.

Element (new definition) - An element is a pure chemical substance composed of atoms, each of which has the same number of protons in the nucleus.

Hydrogen - one proton per atom

Helium - two protons per atom

Lithium - three protons per atom

. .

. .

Similarly, we can now define a compound (new definition) as a pure chemical substance composed of two or more different kinds of atoms.

Atomic Number and Mass Number

1) The atomic number (Z) is equal to the number of protons in the atom.

2) Since atoms are electrically neutral, the number of electrons in an atom is also equal to Z, the atomic number.

3) The mass number (A) is equal to the number of protons + neutrons in the atom.

a) Because protons and neutrons have a mass of approximately 1 (in amu) and electrons have a mass of approximately 0 (in amu) the mass number is equal to the approximate mass of the atom in amu.

b) Based on the above, the number of neutrons in an atom is equal to A - Z. So for an atom: # protons = Z

# electrons = Z

# neutrons = A - Z

Isotopes

The atomic number determines the number of protons and electrons in an atom. This does not place any restrictions on the number of neutrons in the atom.

It is possible for atoms of the same element to have different numbers of neutrons. These different types of atoms are called isotopes.

Isotopes of Hydrogen

normal hydrogen deuterium tritium

1H 2H 3H

Note that to a very good approximation isotopes of a particular element are chemically identical to one another.

Notation For Atoms

We use the following general notation to represent isotopes of atoms.

mass number

atomic number

symbol for element

Since we can use the symbol for the element and the periodic table to determine Z, the atomic number, we often omit Z in giving the symbol for the atom.

Example: 3416S = 34S We can omit the subscript because all

sulfur atoms contain 16 protons.

Notation (Example)

As an example of using the above notation, consider the follow-ing naturally occurring isotopes of oxygen (Z = 8).

protons neutrons electrons mass number symbol

8 8 8 16 16O

8 9 8 17 17O

8 10 8 18 18O

Example: How many protons, neutrons, and electrons are there in one atom of 56Fe? What is the approximate mass of one atom of 56Fe in amu and in kg?

Example: How many protons, neutrons, and electrons are there in one atom of 56Fe? What is the approximate mass of one atom of 56Fe in amu and in kg?

# protons = Z = 26 # neutrons = A – Z = 56 – 26 = 30

# electrons = Z = 26 approximate mass (amu) = A = 56

approximate mass (kg) = 56 amu 1.6605 x 10-27 kg 1 amu

= 9.30 x 10-26 kg

Note that the actual mass of one atom of 56Fe is 55.934939 amu.

Atomic Mass Units (amu)

The mass of a single atom of an element, expressed in SI units, is an extremely small number. For example, the mass of a single atom of 16O is 2.6560 x 10-26 kg. For convenience, we often express values for atomic mass in terms of atomic mass units (amu).

Atomic mass units are defined as follows

12.00 amu = mass of one atom of 12C (exact)

From this we get 1. amu = 1.6605 x 10-27 kg (approximate)

The mass of any other atom (or particle) is found relative to the ratio of its mass to the mass of a 12C atom, which can be measured experimentally.

Mass of particle (amu) = mass particle • (12.00 amu)

mass 12C atom

Example: A mass spectrometer is a device for determining values for mass for atoms and molecules. In a particular experiment, the ratio (mass M/mass 12C) is measured and found to be equal to 7.337. What is the mass of the molecule M (in amu)?

Example: A mass spectrometer is a device for determining values for mass for atoms and molecules. In a particular experiment, the ratio (mass M/mass 12C) is measured and found to be equal to 7.337. What is the mass of the molecule M (in amu)?

mass M = 7.337 mass 12C atom

Mass M = 7.337 (mass 12C atom) = 7.337 (12.00 amu) = 88.04 amu

Note that because of the way we define atomic mass units, the only isotope whose mass is exactly equal to its mass number is 12C.

isotope mass (amu)

1H 1.007825

12C 12.000000... (exact)

238U 238.0508

Atomic Mass in the Periodic Table

Because different isotopes of an element have different masses, the question arises as to which mass should be given in the periodic table.

For short lived radioactive elements the mass number of the most stable isotope of the element is listed.

Element Z A

technetium (Tc) 43 98

radon (Rn) 86 222

plutonium (Pu) 94 244

Average Atomic Mass

For naturally occurring elements, the value for mass given in the periodic table is the average atomic mass, based on the natural abundance of the isotopes that is observed.

In general, we find the average atomic mass as follows:

Mave = f1 M1 + f2 M2 + f3 M3 + … = i=1n fi Mi

where f1, f2,...are the fractions of each isotope observed in nature

M1, M2,…are the corresponding masses for each isotope (in amu)

Note the following

f1 + f2 + f3 + …= 1 fx = % X 100 %

Non-chemical Example

A person has a box of sandwiches. Half of the sandwiches are 6.0 ounces, and half of the sandwiches are 10.0 ounces. What is the average weight of a sandwich?

Average weight = (0.50)(6.0 oz) + (0.50)(10.0 oz)

= 8.0 ounces

We use the same procedure in finding the average mass of an atom. We multiply the fraction of each isotope by the mass of that isotope, and then add the results to find the average mass.

Chemical Example

There are three naturally occurring isotopes of the element magnesium. Based on the information below, find the atomic mass of a magnesium atom.

Isotope percent f M(amu)

24Mg 78.70 % 23.98504

25Mg 10.03% 24.98584

26Mg 11.17% 25.98259

Chemical Example

There are three naturally occurring isotopes of the element magnesium. Based on the information below, find the atomic mass of a magnesium atom.

Isotope percent f M(amu)

24Mg 78.70 % 0.7870 23.98504

25Mg 10.03% 0.1003 24.98584

26Mg 11.17% 0.1117 25.98259

So Mave = (0.7870)(23.98504 amu) + (0.1003)(24.98584 amu)

+ (0.1117)(25.98259 amu)

= 24.30 amu, the value given in the periodic table.

Periodic Table

The periodic table is an arrangement of the chemical elements based on similarities in their physical and chemical properties

The periodic table contains a large amount of useful information about the chemical elements.

Organization

There are several ways in which the elements in the periodic table may be classified.

Rows = Periods

Columns = Groups This is the more important classification. Elements in the same group usually have similar physical and chemical properties.

1A 2A 3A 4A 5A 6A 7A 8A

Simplified Periodic Table

1A 2A 3A 4A 5A 6A 7A 8A

You are responsible for knowing the names/symbols for elements 1-57, 72-86, and 92.

1A 2A 3A 4A 5A 6A 7A 8A

Major Groups in the Periodic Table

Metals, Nonmetals, and Metalloids

Metals: Usually solid at room temperature (exceptions Cs, Fr, Hg)

Shiny metallic luster

Good conductors of electricity and heat

Malleable (can be hammered into thin sheets)

Ductile (can be drawn into thin wires)

Nonmetals: Can be solid, liquid, or gas at room temperature

Dull colored (as solids)

Poor conductors of electricity and heat

Not malleable, not ductile

Metalloids (semimetals): Intermediate between metals and nonmetals

1A 2A 3A 4A 5A 6A 7A 8A

Metals, Nonmetals, Semimetals in the Periodic Table

Examples of Elements (as found in nature)

nickel germanium sulfur

(metal) (metalloid) (nonmetal)

Formation of Ions

Ions are charged particles. Ions can be formed from an atom by either adding electrons (to form an anion) or removing electrons (to form a cation). Ions cannot be formed by changing the number of protons in the atom.

cations anions

particle Z # electrons particle Z# electrons

Na 11 11 Cl 17 17

Na+ 11 10 Cl- 17 18

Ca 20 20 S 16 16

Ca2+ 20 18 S2- 16 18

Note that the charge of an ion is indicated by a superscript to the right of the symbol for the ion.

Metals usually form cations, while nonmetals usually form anions.

Just as we can predict the number of protons, neutrons, and electrons from the symbol for an atom, we can do the same thing for cations and anions formed from atoms. We do this using the atomic number (Z) the mass number (A) and the charge of the ion.

Example: How many protons, neutrons and electrons are there for a 31P3- ion and a 25Mg2+ ion?

Example: How many protons, neutrons and electrons are there for a 31P3- ion and a 25Mg2+ ion?

31P3- # protons = Z = 15 # neutrons = A - Z = 31 - 15 = 16

Charge is 3-, so there are 3 more electrons than protons, and so the number of electrons = 18.

25Mg2+ # protons = Z = 12 # neutrons = A - Z = 25 - 12 = 13

Charge is 2+, so there are two more protons than electrons, and so the number of electrons is 10.

Ion Charges For Main Group Elements

Main group elements tend to form ions by adding or removing electrons so that the number of electrons remaining in the ion is equal to the number of electrons in one atom of the nearest nobel gas.

cations (metals)

group 1A (Li, Na, K, Rb, Cs) form 1+ ions

group 2A (Mg, Ca, Sr, Ba) form 2+ ions

group 3A (Al) form 3+ ions

anions (nonmetals)

group 5A (N) form 3- ions

group 6A (O, S, Se, Te) form 2- ions

group 7A (F, Cl, Br, I) form 1- ions

Transition Metal Ions

Transition metals form cations. Most transition metals, as well as a few main group metals like tin (Sn) and lead (Pb), can form ions with several different charges, but a few transition metals, such as silver, usually form only one type of cation (Ag+ for silver, for example).

Example:

Iron (Fe) Fe2+, Fe3+

Copper (Cu) Cu+, Cu2+

Chromium (Cr) Cr3+, Cr6+

It is generally not easy to predict which cations a transition metal will form.

Chemical Formula

The chemical formula for a substance provides information concerning the composition of the substance.

We can divide substances into two general types.

1) Substances that exist as collections of molecules. In this case the chemical formula indicates the number of atoms of each elements present per molecule.

water phosphorus pentachloride nitrous acid

(H2O) (PCl5) (HNO2)

For organic molecules, the chemical formula is often given in a way that indicates how the molecule is put together.

ethyl alcohol dimethyl ether acetone

CH3CH2OH = C2H6O CH3OCH3 = C2H6O CH3COCH3 = C3H6O

Notice that this longer notation makes it possible to distinguish among different forms (isomers) of organic molecules.

There are several different ways in which molecules can be represented.

The particular representation we use depends on what type of information we are trying to communicate.

2) Substances that exist as collections of atoms or ions in the form of a crystal structure, a regular arrangement of the particles making up the substance.

For these substances, the formula that is given is the empirical formula. An empirical formula gives the relative number of each element making up the compound, reduced to the smallest set of whole number coefficients.

sodium chloride polonium calcium fluoride

NaCl Po CaF2

F-Ca2+

Empirical Formula for Molecular Compounds

The empirical formula for a substance gives the relative number of atoms of each element making up a pure chemical substance, reduced to the smallest set of integer values. For substances that exist as molecules, the molecular formula must be an integer multiple of the empirical formula.

Substance Chemical formula Empirical formula

water H2O H2O

hydrogen peroxide H2O2 HO

benzene C6H6 CH

dichloroethane C2H4Cl2 CH2Cl

acetic acid CH3COOH CH2O

Molecular Compound

A molecular compound is a compound composed of individual particles called molecules. The bonding between atoms is in such compounds is due to the sharing of one or more pairs of electrons. Molecular compounds are usually made up of one or more nonmetallic elements. Note that these compounds are sometimes called covalent compounds since the molecules are held together by covalent bonding.

Examples:

HBr hydrogen bromide SF6 sulfur hexafluoride

CS2 carbon disulfide N2O4 dinitrogen tetroxide

CH3Cl chloromethane SO2 sulfur dioxide

Some elemental substances, such as O2 and N2, exist as indi-vidual molecules, but are not compounds, since they are composed of atoms of a single element.

Ionic Compound

An ionic compound is a compound formed from positive ions (cations) and negative ions (anions) held together by electrostatic attraction. For these compounds we usually give the empirical formula, (sometimes called the formula unit) or smallest electrically neutral collection of ions making up the compound.

Binary ionic compounds (compounds formed from ions of two different elements) are usually a combination of a metal cation and a nonmetal anion.

Examples:

NaCl sodium chloride (Na+ and Cl-)

Fe2O3 iron (III) oxide (Fe3+ and O2-)

Na2O sodium oxide (Na+ and O2-)

CuS copper (II) sulfide (Cu2+ and S2-)

Chemical Formulas For Main Group Ionic Compounds

Because main group elements form ions with a particular charge (depending on which group the element is from) we can predict the chemical formula for a main group ionic compound. We do this by first finding the charges of the ions formed, and then combining them to get an overall neutral compound using the smallest set of whole number coefficients.

Examples: What is the chemical formula for the ionic compound formed from magnesium and chlorine, and from sodium and sulfur?

Examples: What is the chemical formula for the ionic compound formed from magnesium and chlorine, and from sodium and sulfur?

Mg and Cl

Ions are Mg2+ and Cl-, so formula is MgCl2, magnesium chloride.

Na and S

Ions are Na+ and S2-, so formula is Na2S, aluminum sulfide.

magnesium chloride sodium sulfide

Transition Metal Cations

Transition metals can usually form ions with several different charges (this is also true for a few main group metallic elements like tin (Sn) and lead (Pb)). While we cannot easily predict which compounds will form between a transition metal and a main group nonmetal, we can usually figure out the charge of the transition metal cation if we know the chemical formula for the compound. This is indicated in the name of the compound.

Examples:

CuCl

CuCl2

PbS2

MnO2

Examples:

CuCl Cl- ion, so Cu+ ion copper (I) chloride

CuCl2 Cl- ion, so Cu2+ ion copper (II) chloride

PbS2 S2- ion, so Pb4+ ion lead (IV) sulfide

MnO2 O2- ion, so Mn4+ ion manganese (IV) oxide

Polyatomic Ions

A polyatomic ion is a group of atoms which collectively has a charge and acts as an ion in an ionic compound.

ion name example of ionic compound

NO3- nitrate ion NaNO3, Ca(NO3)2, Ni(NO3)2

SO42- sulfate ion CuSO4, K2SO4, Al2(SO4)3

Note that when more than one polyatomic ion is present in a chemical compound the ion is placed in parentheses and the number of ions per formula unit of compound is given as a subscript outside the parentheses.

Hydrates

Some ionic compounds can exist in forms where there is a specific number of water molecules associated with every formula unit of the ionic compound. Such substances are called hydrates.

Cobalt (II) chloride hexahydrate Cobalt (II) chloride

Naming Rules For Simple Compounds

Ionic compounds.

a) [Main group metal (1A, 2A, metals and aluminum (3A)] + [main group nonmetal]:

name of metal + name of nonmetal + ide

Examples: K2S potassium sulfideCaI2 calcium iodideAl2O3 aluminum oxide

b) [Transition group metal (or group 4A metal, or Tl)] + [main group nonmetal]:

name of metal (charge of metal) + name of nonmetal + ide

Examples: FeCl2 iron (II) chlorideFeCl3 iron (III) chlorideCu2S copper (I) sulfide

c) Cation group

NH4+ ammonium ion

Hg22+ mercury (I) ion

Use name of cation group + name of nommetal + ide.

Example: NH4Br ammonium bromideHg2Cl2 mercury (I) chloride (NH4)2S ammonium sulfide

d) Anion group

C2H3O2- is acetate ion CO3

2- is carbonate ionCN- is cyanide ion SCN- is thiocyanate ionOH- is hydroxide ion C2O4

2- is oxalate ionN3

- is azide ion O22- is peroxide ion

CrO42- is chromate ionCr2O7

2- is dichromate ionMnO4

- is permanganate ion

ClO3- is chlorate ion NO3

- is nitrate ionBrO3

- is bromate ion SO42- is sulfate ion

IO3- is iodate ion PO4

3- is phosphate ion

+1 oxygen changes the name to per ________ ate-1 oxygen changes the name to ________ite-2 oxygen changes the name to hypo ________ ite

Example: ClO3- is chlorate ion, so

+1 O ClO4- is perchlorate ion

-1 O ClO2- is chlorite ion

-2 O ClO- is hypochlorite ion

So we get (use name of cation + name of nonmetal group)

NaClO4 sodium perchlorate

NaClO3 sodium chlorate

NaClO2 sodium chlorite

NaClO sodium hypochlorite

If more than one of a group is present, we place the group in parentheses with a number outside indicating how many of the group are present.

Mg(NO3)2 magnesium nitrate

Hydrogen containing anions

HPO42- is hydrogen phosphate ion

H2PO4- is dihydrogen phosphate ion

HCO3- is hydrogen carbonate (bicarbonate) ion

HSO4- is hydrogen sulfate (bisulfate) ion

Examples: NaNO3 sodium nitrateCuSO4 copper (II) sulfateZn(ClO3)2 zinc (II) chlorateZn(ClO2)2 zinc (II) chloriteKH2PO4 potassium dihydrogen phosphate

Acids. A substance that produces H+ ions when added to water (Arrhenius definition).

a) Binary acids (hydrogen + nonmetal)

hydro + nonmetal + ic acid

Examples: HBr hydrobromic acid H2S hydrosulfuric acid

b) Ternary acids (hydrogen + oxygen + nonmetal)

hypo ________ite ion becomes hypo ________ ous acid________ ite ion becomes ________ ous acid________ ate ion becomes ________ ic acidper ________ ate ion becomes per ________ ic acid

So -ate is changed to –ic acid, -ite is changed to -ous acid.

Example: ClO- hypochlorite ion HClO hypochlorous acidClO2

- chlorite ion HClO2 chlorous acidClO3

- chlorate ion HClO3 chloric acidClO4

- perchlorate ion HClO4 perchloric acid

Binary molecular compounds (compounds are usually two non-metals)

a) Left or lower element is named first, second element is given an ide ending, prefix is used to indicate the number of atoms per molecule (but the prefix mono is never used for the first element)

mono = 1 tri = 3 penta = 5 hepta = 7di = 2 tetra = 4 hexa = 6 octa = 8

Example: NO nitrogen monoxideNO2 nitrogen dioxideN2O dinitrogen monoxide (nitrous oxide)

b) A few molecules have common names: H2O is water, NH3 is ammonia, CH4 is methane.

c) If a binary molecular compound forms an acid when added to water the naming of the compound depends on whether it is in the gas phase or aqueous phase.

HCl(g) hydrogen chlorideHCl(aq) hydrochloric acid

Organic molecules - There are systematic rules for naming organ-ic molecules, but you will not be responsible for naming such com-pounds.

CH3CH2CH2CH2CH3 n-pentaneCH3CH2OH ethyl alcoholCH3CH2OCH2CH3 diethyl ether

End of Chapter 2

“…the ultimate particles of all homogeneous bodies are perfectly alike in weight, figure, and so forth.”

- John Dalton, A New System of Chemical Philosophy (1808)

“Elements arranged according to the size of their atomic weights show clear periodic properties.” - D. I. Mendeleev (1869)

“I don’t believe that atoms exist!” - Ernst Mach (1897)

“One of the wonders of this world is that objects so small can have such consequences: Any visible lump of matter - even the merest speck - contains more atoms than there are stars in our galaxy.”

- P. W. Atkins