ATOMS, MOLECULES AND IONS
To learn chemistry, you must become familiar with the "building
blocks" that chemists use to describe the structure of matter. These
include atoms, molecules and ions.
Atoms and the atomic theory:
In 1808, an English Scientist and schoolteacher, John Dalton,
developed the atomic model of matter that underlies modern
chemistry.
Three of the main postulates of modern atomic theory, all of which
Dalton suggested are:

An element is composed of tiny particles called atoms.
All
atoms of a given element show the same chemical properties.
Atoms of different elements show different properties.

In an ordinary chemical reactions, no atom of any element
disappears or is changed into an atom of another element.

Compounds are formed when atoms of two or more elements
combine. In a given compound, the relative numbers of atoms
of each kind are definite and constant.
In general, these
relative numbers can be expressed as integers or simple
fractions.
On the basis of Dalton,s theory, the atom can be defined as the
smallest particle of an element that can enter into a chemical
reaction.
Components of the atom:
Two future Nobel laureates did pioneer work in this area, J.
Thomson and his student Ernest Rutherford.
Electrons:
Electrons are common to all atoms, carry a unit negative charge (1), and have a very small mass, roughly 1/2000 of that of the light
atom.
Every atom contains a definit number of electrons.
This
number, which runs from 1 to more than 100, is characteristic of a
neutral atom of a particular element.
All atoms of hydrogen contain one electron; all atoms of the element
uranium contain 92 electrons.
Electrons are found in the outer
regions of the atom, where they form what amounts to a cloud of
negative charge.
Protons and Neutrons, the atomic nucleus:
The nucleus of an atom consist of two different types of particles:
1. The proton, which has a mass nearly equal to that of an ordinary
hydrogen atom.
The proton carries a unit positive charge (+1),
equal in magnitude to that of the electron (-1).
2. The neutron, an uncharged particle with a mass slightly greater
than that of a proton.
Properties of subatomic particles:
Particle
Location
Relative charge
Relative mass
Proton
nucleus
+1
1.00728
Neutron
nucleus
0
1.00867
Electron
Outside
nucleus
-1
0.00055
Atomic number:
All the atoms of a particular element have the same number of
protons in the nucleus.
This number is a basic property of an
element, called its atomic number and given the symbol Z ( Z =
number of protons).
In neutral atom, the number of protons in the nucleus is exactly
equal to the number of electrons outside the nucleus. Consider, for
example, the elements hydrogen (Z=1) and uranium (Z = 92). All
hydrogen atoms have one proton in the nucleus; all uranium atoms
have 92.
In a neutral hydrogen atom there is one electron outside
the nucleus; in a uranium atom there are 92.
H atom: 1 proton,
1 electron
U atom: 92 protons,
Z =1
92 electron
Z =92
Mass Number:
The mass number of an atom, given the symbol A, is found by
adding up the number of protons and neutrons in the nucleus.
A = number of protons + number of neutrons
All atoms of a given element have the same number of protons,
hence the same atomic number.
They may, however, differ from
one another in mass and hence in mass number. This can happen
because, although the number of protons in an atom of an element
is fixed, the number of neutrons is not. It may vary and often does.
Consider the element hydrogen (Z = 1). There are three different
kinds of hydrogen atoms. They all have one proton in the nucleus.
A "light" hydrogen atom has no neutrons in the nucleus (A = 1).
Another type of hydrogen atom (deuterium) has one neutron (A =
2). Still a third type (tritium) has two neutrons (A = 3).
Atoms that contain the same number of protons but a different
number of neutrons,
1
1H
,
2
1H
,
3
1H
, are called isotops.
The composition of a nucleus is shown by its nuclear symbol. Here,
the atomic number appears as a subscript at the lower left of the
symbol of the element. The mass number is written as a superscript
at the upper left.
Mass number (A)
X
Element symbol
Atomic number (Z)
The nuclear symbols for the isotopes of uranium referred to above
are
235
92U
238
92U
Quite often, isotopes of an element are distinguished from one
another by writing the mass number after the symbol of the
element. The isotopes of uranium are often referred to as U-235
and U-238.
Note: Ordinary ice floats because the solid phase of water,
1
1H2O
is
less dense than the liquid. In contrast, heavy ice sinks because the
solid form of deuterium oxide,
2
1H2O
is more dense than the liquid.
Example 1 : An isotope of cobalt is used in radiation therapy for
certain types of cancer. Write nuclear symbols for three isotopes of
cobalt (Z = 27) in which there are 29, 31, and 33 neutrons,
respectively.
Solution:
The mass numbers are:
27 + 29 = 56 ,
27 + 31 = 58 ,
27 + 33 = 60
Thus the nuclear symbols are:
56
27Co
58
27Co
60
27Co
Example 2 : One of the most harmful components of nuclear waste
is a radioactive isotope of strontium,
90
38Sr
; it can be deposited in
your bones, where it replaces calcium. How many protons are there
in the nucleus of Sr-90 ? How many neutrons?
Solution: The number of protons is given by the atomic number (left
subscript) and is 38.
The mass number (left superscript) is 90.
The number of neutrons = 90 – 38 = 52
Metals and Nonmetals:
There are more than 80 elements have the properties of metals, in
particular they have high electrical conductivities, e.g., Li. Na, K, Mg,
Ca, Cs, Be, Cr, Mn, Fe, Co, Ni, Au, Ag, Cu, Zn, Cd, Hg, ...
There are about 20 elements are nonmetals, e.g., H, C, N, O, Se, P, S,
halogens,...they have no electrical conductivities.
There are about 6 elements that are difficult to classify exclusively
as metals or nonmetals. They have properties in between those of
elements in the two classes.
In particular, their electrical
conductivities are intermediate between those of metals and
nonmetals. The six elements B, Si, Ge, As, Sb, Te (tellurium) are
often called metaloids
Molecules and ions:
Isolated atoms rarely occur in nature; only the nobel gases (He,
Ne,...) consist of individual, nonreactive atoms.
Atoms tend to
combine with one another in various ways to form more complex
structural units. Two such units, which serve as building blocks for
a great many elements and compounds, are molecules and ions.
Molecules:
Two or more atoms may combine with one another to form an
uncharged molecule.
The atoms involved are usually those of
nonmetallic elements. Within the molecule, atoms are held to one
another by strong forces called covalent bonds, which consist of
shared pairs of electrons. Forces between neighboring molecules, in
contrast, are quite weak.
The
structures
of
molecules
are
sometimes
represented
by
structural formulas, which show the bonding patterns within the
molecule.
The structural formulas of hydrogen chloride, water, ammonia and
methane are:
H
O
H – Cl
H
N
H
H
C
H
H
H
H
H
The dashes represent covalent bonds.
Most commonly, molecular substances are represented by molecular
formulas, in which the number of atoms of each element is indicated
by a subscript written after the symbol of the element.
The
molecular formulas of the substances just described are:
Hydrogen chloride: HCl (1 H atom, 1 Cl atom per molecule)
Water
Ammonia
Methane
: H2O (2 H atoms, 1 O atom per molecule)
: NH3 (1 N atom, 3 H atoms per molecule)
: CH4 (1 C atom, 4 H atoms per molecule)
Sometimes we represent a molecular substance with a formula
intermediate between a structural formula and a molecular formula.
A condensed structural formula suggests the bonding pattern in the
molecule and highlights the presence of a reactive group of atoms
within the molecule. Consider, for example, the organic compounds
commonly known as methyl alcohol and methyl amine.
Methyl alcohol
Molecular formulas
CH4O
Methyl amine
CH5N
Structural formula
H
H – C- O - H
H
Condensed structural formula
H
H- C – N - H
H H
CH3OH
CH3NH2
The condensed structural formulas take up considerably less space
and emphasize the presence in the molecule of
-
The OH group found in all alcohols, including ethyl
alcohol C2H5OH
-
The NH2 group found in one class of amines. Ethyl
amine has the condensed structural formula C2H5NH2
Note: Elements as well as compounds can exist as discrete
molecules. In hydrogen gas, the basic building block is a molecule
consisting of two hydrogen atoms joined by a covalent bond: H - H
Ions:
When an atom loses or gains electrons, charged particles called ions
are formed. Typically, metal atoms tend to lose electrons to form
positively charged ions called cations.
Na atom
(11 p+, 11 e-)
Ca atom
(20 p+, 20 e-)
Na+ ion + e(11 p+, 10 e-)
Ca2+ ion + 2 e(20 p+, 18 e-)
Nonmetal atoms form negative ions (anions) by gaining electrons.
Consider, for example, what happens when atoms of the non-metals
chlorine and oxygen acquire electrons:
Cl atom
+ e-
Cl- ion
(17 p+, 17 e-)
O atom
(17 p+, 18 e-)
+ 2 e-
O2- ion
(8 p+, 8 e-)
(8 p+, 10 e-)
Notice that when an ion is formed, the number of protons in the
nucleus is unchanged. It is the number of electrons that increases
or decreases. In other words, these are not nuclear reactions. They
involve extranuclear electrons, as do all ordinary chemical reactions.
The ions dealt with to this point ( e.g., Na+, Cl- ) are monatomic;
that is, they are derived from a single atom by the loss or gain of
electrons.
Many of the most important ions in chemistry are
polyatomic, containing more than one atom. Examples include the
hydroxide ion (OH-) and the ammonium ion (NH4+). In these and
other polyatomic ions, the atoms are held together by
H
covalent bonds, e.g., ( O
H )-
(H
N
H )+
H
In a very real sense, you can think of a poly atomic ion as a charged
molecule.
Since a bulck sample of matter is electrically neutral, ionic
compounds
always
contain
both
cations
(positively
particles) and anions (negatively charged particles).
charged
Sodium
chloride, is made up of an equal number of Na+ and Cl- ions.
Ionic compounds are held together by strong electrical forces
between oppositely charged ions (e.g., Na+ , Cl-). These forces are
referred to as ionic bonds. Typically, ionic compounds are solids at
room temp. And have relatively high melting points (mp NaCl = 801
°C , CaCl2= 772 °C).
To melt an ionic compound requires that
oppositely charged ions be separated from one another, thereby
breaking ionic bonds.
Formulas of ionic compounds:
The formula of an ionic compound (e.g. NaCl, CaCl2) shows the
simplest ratio between cations and anions (1 Na+ ion for 1 Cl- ion; 1
Ca2+ ion for 2 Cl- ions). In that sense, the formulas of ionic
compounds are simplest formulas.
To determine the formula of an ionic compound, we apply the
principle of electrical neutrality, which requires that the total
positive charge of the cations equal the total negative charge of the
anions. Consider, for example, the ionic compound calcium chloride.
The ions present are Ca2+ and Cl-. Clearly, for the compound to be
electrically neutral, there must be two Cl- ions for every Ca2+ ion.
The formula of calcium chloride must be CaCl2, indicating that the
simplest ratio of Cl- to Ca2+ ions is 2:1.
Nobel gas atoms must have an extremely stable electronic structure,
since they are so unreactive.
Other atoms might be expected to
acquire nobel gas electronic structures by losing or gaining
electrons.
Metals form cations and nonmetals form anions.
Several of
transition metals form more than one cation: Fe2+ and Fe3+; Cu+
and Cu2+.
Note that, in writing the formula of an ionic compound, the positive
ion is always placed first.
Example: Predict the formulas of the ionic compounds formed by:
a) magnesium and sulfur
b) cobalt and chlorine
c) alumminum and oxygen
d) bismuth and fluorine
Solution:
First, identify the charges of the cattion and anion. Then balance positive
with negative charges to arrive at the formula.
a) MgS one magnesium ion Mg2+ requires one S2- ion.
b) CoCl2 one Co2+ ion requires two Cl- ions.
c) Al2O3 two Al3+ ions (total charge=+6) require three
O2- ions (total
charge,-6).
d) BiF3 one Bi3+ requires three F- ions.
Some common polyatomic ions:

Ammonium (NH4+)

Hydroxide (OH-), nitrate (NO3-), chlorate (ClO3-), perchlorate
(ClO4-),
cyanide (CN-), acetate (CH3 Coo-), permanganate
(MnO4-), hydrogen carbonate (HCO3-), dihydrogen phosphate
(H2PO4-).

Carbonate
dichromate

(CO32-),
sulfate
(SO42-),
chromate
(CrO42-),
(Cr2O72-), hydrogen phosphate (HPO42-).
Phosphate (PO43-).
Note that ther is only one common polyatomic cation, Ammonium
(NH4+). All other cations considered in this course are derived
from metal atoms (e.g., Na+ from Na, Ca2+ from Ca, ....). Most of
the polyatomic anions contain one or more oxygen atoms;
collectively these species are called oxoanions.
Example: Predict the formulas of
strontium hydroxide, sodium
carbonate, and ammonium phosphate.
Solution:

Strontium hydroxide: One Sr2+ ion requires two OH- ions.
The formula is Sr(OH)2. Parentheses are used to indicate
that there are two polyatomic OH- ions for every Sr2+.

Sodium carbonate: Two Na+ ions require one CO32- ion. The
formula is Na2CO3.

Ammonium phosphate: Three NH4+ ions are required for
one PO43- ion. The formula is (NH4)3PO4.
Names of compounds:
A compound can be identified either by its formula (e.g. NaCl) or its
name (sodium chloride). You will learn the rules used to name ionic
and simple molecular compounds.
Ions:
Monatomic cations:
They take the name of the metal from which they are derived.
Examples include: Na+ sodium
There is one complication:
, K+ potassium
certain metals, notably those in the
transition series, form more than one type of cation. An example is
iron, which forms both Fe2+ and Fe3+. To distinguish between these
cations, the charge must be indicated in the name. This is done by
putting the charge as a Roman numeral in parentheses after the
name of the metal: Fe2+ , iron (II) ;
and Fe3+ , iron (III).
An
older system used the suffixes -ic for the ion of higher charge and –
ous for the ion of lower charge. These were added to the stem of
the Latin name of the metal, so that the Fe3+ ion was referred to as
ferric and Fe2+ ion as ferrous.
Monatomic anions:
They are named by adding the suffix -ide to the stem of the name of
the nonmetal from which they are derived.
O2- Oxide
S2- sulfide
selenide
I- iodide
Te2- Telluride
Br- bromide
Polyatomic ions:

They are given special names.
H- hydride
Cl- chloride
N3- nitride
F- fluoride
Se2-

When a nonmetal forms two oxoanions, the suffix -ate is used
for the anion with the larger number of oxygen atoms. The
suffix
-ite is used for the anion containing fewer oxygen
atoms.

When a nonmetal forms more than two oxoanions, the
prefixes
per- (largest number of oxygen atoms) and hypo-
(fewest oxygen atoms) are used as well.
Examples:

Oxoanions of nitrogen; NO3- nitrate and NO2- nitrite

Oxoanions of sulfur; SO42- sulfate and SO32- sulfite

Oxoanions of chlorine;
ClO4- perchlorate ,
ClO3- chlorate
ClO2- chlorite , ClO- hypochlorite
Ionic Compounds:
The name of an ionic compound consists of two words. The first
word names the cation and the second names the anion. This is of
course, the same order in which the ions appear in the formula.
Example: Name the following ionic compounds:
CaS
Al(NO3)3
FeCl2
Solution:
CaS
= calcium sulfide
Al(NO3)3
= aluminum nitrate
FeCl2
= iron(II) chloride
Binary Molecular compounds:
When a metal combines with a nonmetal, the product is ordinarily
an ionic compound. When two nonmetals combine with each other,
the product is most often a binary molecular compound.
The systematic name of a binary molecular compound, which
contains two different nonmetals, consists of two words.
1. The first word gives the name of the element that appears first in
the formula; a Greek prefix (di) is used to show the number of
atoms of that element in the formula.
2. The second word consists of :

The appropriate Greek prefix designating the number of atoms
of the second element.

The stem of the name of the second element

The suffix -ide.
To illustrate these rules, consider the names of the served oxides of
nitrogen:

N2O5 dinitrogen pentaoxide

N2O4 dinitrogen tetraoxide

NO2

N2O3 dinitrogen trioxide

NO
nitrogen oxide

N2O
dinitrogen oxide
nitrogen dioxide
The Greek prefixes used in nomenclature are:
Mono (1),
hexa (6),
di (2),
tri (3),
hepta (7),
tetra (4),
octa (8),
nona (9),
penta (5),
and deca
(10)
Example:Give the names of SO2 SO3
PCl3
Cl2O7
Solution:
SO2: Sulfur dioxide
SO3 : Sulfur trioxide
PCl3: Phosphorus trichloride
Cl2O7 : Dichlorine heptaoxide
Many of the best-known binary compounds of the nonmetals have
acquired common names.
exclusively used.
These are widely and in some cases,
Examples include
H2O water
H2O2
PH3 phosphine
NH3
AsH3 arsine
ammonia
NO nitric oxide
N2H4 hydrazine
C2H2
hydrogen peroxide
N 2O
acetylene
nitrous oxide
CH4 methane
Acids:
A few binary molecular compounds containing H atoms ionize in
water to form H+ ions. These are called acids. One such compound
is hydrogen chloride, HCl; in water solution it exists as aqueous H+
and Cl- ions.
The water solution of hydrogen chloride is given a
special name;
it is referred to as hydrochloric acid. A similar
situation applies with HBr and HI
Pure substance
Water solution
HCl(g) hydrogen chloride
H+(aq) , Cl-(aq) hydrochloric acid
HB(g) hydrogen bromide
H+(aq) , Br-(aq) hydrobromic acid
HI(g) hydrogen Iodide
H+(aq) , I-(aq) hydroiodic acid
Most acids contain oxygen in addition to hydrogen atoms. Such
species are referred to as oxoacids. Two oxoacids yhat you are
likely to encounter in the general chemistry laboratory are:
HNO3 nitric acid
H2SO4 sulfuric acid
The names of oxoacids are simply related to those of the
correspondind oxoanions. The –ate suffix of the anion is replaced by
–ic in the acid. Similarly, the suffix -ite is replaced by the suffix ous. The prefixes per- and hypo- found in the name of the anions
are retained in the name of the acid.
ClO4- perchlorate ion
HClO4 perchloric acid
ClO3- chlorate ion
HclO3 chloric acid
ClO2- chlorite ion
HclO2 chlorous acid
ClO- hypochlorite ion
HClO hypochlorous acid
Example: Give the names of the following compounds: HNO2 H2SO3
HIO
Solution:
HNO2
nitrous acid
H2SO3
sulfurous acid
HIO
hypoiodous acid
Mass Relations in Chemistry; Stoichiometry
Atomic masses; the carbon-12 scale:
Relative masses of atoms of different elements are expressed in
terms of their atomic masses (often reffered to as atomic weights).
The atomic mass of an element indicates how heavy, on the
average, one atom of that element is compared with an atom of
another element.
In order to set up a scale of atomic masses, a single scale based on
the most common isotope of carbon,
12
6C.
This isotope is assigned a
mass of exactly 12 atomic mass units (amu).
Mass of C-12 atom = 12 amu (exactly)
It follows that an atom half as heavy as a C-12 atom would weigh 6
amu, an atom twice as heavy as C-12 would have a mass of 24 amu,
and so on.
Hydrogen has an atomic mass of 1.008 amu, helium has an atomic
mass of 4.003 amu. This means that, on the average, a helium atom
has a mass that is about one third that of a C-12 atom: 4.003 amu /
12.00 = 0.3336
or about four times that of a hydrogen atom: 4.003 amu / 1.008 =
3.971
In general, for two elements x and y:
Atomic mass x / atomic mass y = mass of atom of x / mass of atom
of y
Example:
Using the following data for chlorine, calculate its atomic mass.
Isotope
Atomic mass
Abundance
Cl-35
34.97 amu
75.53%
Cl-37
36.97 amu
24.47%
Solution:
Atomic mass y =
(atomic mass Y1) (% Y1 / 100%) + (atomic mass Y2) (% Y2 / 100%) +
Atomic mass of Cl =
(34.97 amu) (75.53% /100%) + (36.97 amu) (24.47% /100%)
=
35.46 amu
Masses of individual atoms; Avogadro,s Number:
Consider the elements helium and hydrogen, A helium atom is about four
times as heavy as a hydrogen atom (He = 4.003 amu, H = 1.008 amu).
It follows that a sample containing 100 helium atoms weighs 4 times as
much as a sample containing 100 hydrogen atoms.
Again, comparing samples of the two elements containing a million atoms
each, the masses will be in a 4 (helium) to 1 (hydrogen) ratio. Turning this
argument around, it follows that a sample of He weighing 4 grams must
contain the same number of atoms as a sample of H weighing 1 gram.
More exactly:
no. of He atoms in 4.003 g helium = no. of H atoms in 1.008 g hydrogen.
A sample of an element with a mass in grams equal to its atomic mass
contains a certain definite number of atoms ( Avogadro,s number, NA).
Avogadro,s number, NA = 6.022 x 1023
Avogadro,s number represents the number of atoms of an element
in a sample whose mass in grams is numerically equal to the atomic
mass of the element. Thus there are
6.022 x 10 23 H atoms in 1.008 g H,
(atomic mass H = 1.008
amu)
6.022 x 10 23 He atoms in 4.003 g He, (atomic mass He = 4.003
amu)
6.022 x 10 23 S atoms in 32.07 g
S,
(atomic mass S = 32.07
amu)
Knowing Avogadro,s number and the atomic mass of an element, it
is possible to calculate the mass of an individual atom. You can also
determine the number of atoms in a weighed sample of any
element.
Example: When selenium Se is added to glass, it gives the glass a
brilliant red color. Taking Avogadro,s number to be 6.022 x 1023 ,
calculate:
A) The mass of a selenium atom.
B) The number of selenium atoms in 1.00 g sample of the
element.
Solution: The atomic mass of Se, from the periodic table, is 78.96
amu
a)
6.022 x 1023 Se atoms = 78.96 g Se
1
Se atom = ? g Se
mass of one Se atom = 1 x 78.96 / 6.022 x 1023 = 1.311 x 10-22 g
b) The number of Se atoms in 1 g sample of Se.
6.022 x 1023 Se atoms = 78.96 g Se
?
Se atom = 1 g Se
Number of Se atoms = 6.022 x 1023 x 1 / 78.96 = 7.627 x 1021 Se
atoms
Formula masses:
The formula mass is the sum of the atomic masses in the formula of
a substance.
Formula
Formula mass
O
16.00 amu
O2
2(16.00 amu) = 32.00 amu
H2O
2(1.008 amu) + 16.00 amu = 18.02 amu
NaCl
22.99 amu + 35.45 amu = 58.44 amu
When the formula unit is a molecule, the formula mass is often
referred to as the molecular mass.
A sample of a substance that has a mass in grams numerically equal
to its formula mass contains Avogadro,s number of formula units.
6.022 x 10 23 O atoms weigh 16.00 g
6.022 x 10 O2 molecules weigh 32.00 g
6.022 x 10 23 H2O molecules weigh 18.02 g
6.022 x 10 23 O (Na+ ions + Cl- ions) weigh 58.44 g
Example: How many molecules are there in a drop of water
weighing 0.050g?
Solution:
6.022 x 10 23 H2O molecules
?
18.02 g H2O
H2O molecules
0.050 g H2O
Number of H2O molecules = 0.050 x 6.022 x 10
23
/ 18.02
= 1.7 x 1021 H2O molecules.
The mole:
The quantity represented by Avogadro,s number is so important that
it is given a special name, the mole.
A mole represents 6.022 x 10
1 mol H atoms
1 mol H2 molecules
23
items, whatever they may be.
= 6.022 x 10
23
H atoms
= 6.022 x 10
23
H2 molecules
1 mol H2O molecules = 6.022 x 10
23
H2O molecules
1 mol electrons
= 6.022 x 10
23
electrons
1 mol dollars
= 6.022 x 10
23
dollars
A mole represents not only a specific number of particles but also a
definite mass of a substance.
In general, the molar mass, M, in
grams per mole, is numerically equal to the formula mass.
Thus:
Formula
Formula mass
Molar Mass, M
O
16.00 amu
16.00 g/mol
O2
32.00 amu
32.00 g/mol
H2O
18.02 amu
18.02 g/mol
NaCl
58.44 amu
58.44 g/mol
Notice that the formula of a substance must be known to find its molar
mass.
Molar-gram conversions: Such conversions are readily made by
using the general relation:
m=Mxn
Where:
m = mass in grams
n= the number of moles
M = molar mass
(g/mol)
Example 1:
Calcium carbonate is the principal ingredient of the chalk used in
most class rooms.
Determine the number of moles of calcium
carbonate in a stick of chalk containing 14.8 g of calcium carbonate.
Solution:
The formula is CaCO3, so the molar mass is :
M = [40.08 +12.01 +3(16.00)] g/mol = 100.09 g/mol
n = m / M = 14.8 / 100.09 = 0.148 mol CaCO3
Example 2:
Acetyl salicylic acid, C9H8O4, is the principal ingredient of asprin.
What is the mass in grams of 0.287 mol of acetyl salicylic acid ?
Solution:
The molar mass of C9H8O4 is:
M= [9(12.01) + 8(1.008)+ 4(16.00)] g/mol = 180.15 g/mol
Hence, mass C9H8O4 = 0.287 x 180.15
= 51.7 g C9H8O4
Note: A mole of H2O, 18.02, weighs considerably more than a mole
of H2, 2.016 g, even though they both contain the same number of
molecules.
Dozen footballs weigh a lot more than a dozen eggs,
even though each involves the same number of items.
Example: Sodium hydrogen carbonate, commonly called bicarbonate
of soda, is used in many commercial products to relieve an upset
stomach. It has the formula NaHCO3. What are the mass percents
of Na, H, C, and O in sodium hydrogen carbonate ?
Strategy: Find the mass in grams of each element in one mole of
NaHCO3. Then find,
% element = mass element x 100% / total
mass compound
The mass of each element in one mole of NaHCO3
Element
N
M
M
Na
1 mole
22.99
22.99 g
H
1 mole
1.008
1.008 g
C
1 mole
12.01
12.01 g
O
3 mole
16.00
48.00 g
Total mass
84.01 g
NaHCO3
Mass % Na = 22.99 x 100% / 84.01 = 27.36 %
Mass % H = 1.008 x 100% / 84.01 = 1.200 %
Mass % C = 12.01 x 100% / 84.01 =
14.30 %
Mass % O = 48.00 x 100% / 84.01 = 57.14 %
The percentages added up to 100, as they should:
27.36 + 1.200 + 14.30 + 57.14% = 100.00 %
In general, the subscripts in a formula represent not only the atom
ratio in which the different elements are combined, but also the
mole ratio.
For example,
Formula
Atom ratio
Mole ratio
H2O
2 atoms H : 1 atom O
2 mol H : 1 mol O
KNO3
1 atom K : 1 atom N : 3 atoms O
1 mol K : 1 mol N : 3 mol O
C12H22O11 12 atoms C : 22 atoms H : 11
atoms O
12 mol C : 22 mol H : 11 mol
O
Example:
An iron-containing mineral responsible for the red color of soils in
many parts of the country is limonite, which has the formula Fe2O3 .
3/2 H2O. What mass of iron in grams can be obtained from a metric
ton (103kg=106g) of limonite ?
Solution:
In one mole of limonite, there is 2 mol Fe : 3 mol O : 3/2 mol (H2O)
Mass of iron (m) = n x M = 2 x 55.85 = 111.7 g Fe.
Mass of limonite = 2(55.85) + 3(16.00) + 3/2(18.02) = 186.7 g /
mol
Thus, % Fe = 111.7 x 100 / 186.7 = 59.83 %
In one metric ton of limonite:
Mass Fe = 1.000 x 106 g limonite x 59.83 Fe / 100 g limonite
= 5.983 x 105 g Fe
To obtain simplest formula from chemical analysis:
Example 1 : A 25 g sample of an orange compound contains 6.64 g
of K, 8.84 g of Cr, and 9.52 g of O. Find the simplest formula ?
Strategy: convert the masses to moles.
Knowing the number of
moles (n) of K, Cr, and O you can then (2) calculate the mole ratios.
Finally (3), equate the mole ratio to the atom ratio, which gives you
the simplest formula.
Number of moles of K = 6.64 g K x 1 mole K / 39.10 g K = 0.170
mol. K
Number of moles of Cr = 8.84 / 52.00 = 0.170 mol. Cr
Number of moles of O = 9.52 / 16.00 = 0.595 mol. O
K
:
0.170
Cr
:
:
0.170
O
:
0.595
Divide through out by the smallest value (0.170)
0.170 / 0.170
:
1
:
0.170 / 0.170
1
:
0.595 / 0.170
:
3.5
:
7
multiply through out by 2
2
:
2
The simplest formula is
K2 Cr2 O7
Example 2 : When a sample of ethyl alcohol is burned in air, it is
found that
5.00 g ethyl alcohol
9.55 g CO2 + 5.87 g H2O
what is the simplest formula of ethyl alcohol ?
Strategy:
(1) Find the mass of each element in the sample:.
All carbon has been converted to carbon dioxide
C
CO2
12.01 g (1 mol) C
?g C
44.01 g (1 mol) CO2
9.55 g CO2
Mass of carbon = 12.01 x 9.55 / 44.01 = 2.61 g C
All hydrogen in ethyl alcohol converted to water
2H
H 2O
2 (1.008) g (2 mol) H
18.02 g (1 mol) H2O
2.016 g H
? g H
18.02 g H2O
5.87 g H2O
Mass of hydrogen = 2.016 x 5.87 / 18.02 = 0.657 g H
Mass of Oxygen is found by difference:
Mass of O = mass of sample – (mass of C + mass of H)
= 5.00 - (2.61 + 0.657) = 1.73 g O
(2) Find the number of moles (n) of each element in the sample:
n =m/M
nC =
2.61 / 12.01 = 0.217 mol C
nH = 0.657 / 1.008 = 0.652 mol H
nO = 1.73 / 16.00 = 0.108 mol O
(3) Find the m0le ratios and then the simplest formula:
C : H: O
0.217
: 0.652
0.217 / 0.108
2
:0.108
:0.652 / 0.108
:6
:0.108 / 0.108
:1
The simplest formula of ethyl alcohol is C2H6O
To obtain molecular formula from simplest formula
Example:
Vitamin C simplest formula is found by analysis to be C3H4O3. From
another, experiment, the molar mass is found to be about 180 g /
mol. What is the molecular formula of vitamin C ?
Solution:
Calculate the molar mass corresponding to the simplest formula, i.e.
M C3H4O3. Then find the multiple by dividing the observed molar
mass, 180 g / mol, by M C3H4O3
M C3H4O3 = 3(12.01) + 4(1.008) + 3(16.00) = 88.06 g / mol.
The ratio of the observed molar mass to that of M C3H4O3 is 180 /
88.06
The ratio = 2.04
The multiple is 2
The molecular formula is C6H8O6