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The world around us is composed almost entirely
of compounds and mixture of compounds. Most of
the pure elements also contain many atoms bound
together, for example, diamond is a native form
of carbon, in which a large number of carbon
atoms are bound. In compounds, atoms are held
together by forces known as chemical bonds.
Electrons play a key role in chemical bonding.
There are three ideal types of chemical
bonds - ionic bond (between metals and
nonmetals) - covalent bond (between
nonmetals) - metallic bond (between metallic
The ionic bond is a type of chemical bond based
on the electrostatic attraction forces between
ions having opposite charges. It can form
between electropositive and electronegative
elements, e.g. between metal and non-metal ions.
The metal, with a few electrons on the last
shell, donates one or more electrons to get a
stable electron configuration and forms
positively charged ions (cations). These
electrons are accepted by the non-metal to form a
negatively charged ion (anion) also with a stable
electron configuration. The electrostatic
attraction between the anions and cations causes
them to come together and form a bond.
Example the formation of ionic bond between Na
and Cl. For the sodium atom the electron
configuration is 1s22s22p63s1 The first and
second shells of electrons are full, but the
third shell contains only one electron. When
this atom reacts, it gains the configuration of
the nearest rare gas in the periodic table Ne
1s22s22p6 Na atom loses one electron from its
outer shell Na ? Na e-
The chlorine atom has the configuration
1s22s22p63s23p5 It gains one electron and
realizes the stable electron configuration of
Ar 1s22s22p63s23p6 Cl e- ? Cl- When
sodium and chlorine react, the outer electron of
the sodium atoms are transferred to the chlorine
atoms to produce sodium ions Na and chlorine
ions Cl- , which are held together by the
electrostatic force of their opposite charges.
NaCl is an ionic compound.
NaCl formation
1s22s22p6 1s22s22p63s23p6
NaCl formation may be illustrated showing the
outer electrons only (Lewis symbol)
In a similar way, a calcium atom may lose two
electrons to two chlorine atoms forming a calcium
ion Ca2 and two chloride ions Cl-, that is
calcium chloride CaCl2
In sodium chloride, the ionic bonds are not only
between a pair of sodium ion Na an chlorine ion
Cl-, but also between all the ions. These
electrostatic interactions have as a result the
formation of NaCl crystal. We write the formula
of sodium chloride as NaCl, but this is the
empirical formula. The sodium chloride crystal
contains huge and equal numbers of Na and Cl-
ions pocket together in a way that maximizes the
electrostatic forces of the oppositely charged
ions. Figures 3.2 and 3.3 show the crystal
lattice of NaCl and LiBr.
Sodium chloride crystal
Lithium bromide crystal
Covalent bonds
The covalent bond is a type of chemical bond
formed by sharing pairs of electrons between
atoms. When two electronegative atoms react
together, ionic bonds are not formed because both
atoms have a tendency to gain electrons. In such
cases, an stable electronic configuration may be
obtained only by sharing electrons. First,
consider how chlorine atoms Cl react to form
chlorine molecules Cl2
Each chlorine atom shares one of its electrons
with the other atom. The electron is shared
equally between both atoms, and each atom in the
molecule has in its outer shell 8 electrons a
stable electronic configuration corresponding to
that of Ar. In a similar way a molecule of
carbon tetrachloride CCl4 is made up of carbon
and four chloride atoms
The carbon atom shares all its four electrons
and the chlorine atoms share one electron each.
The carbon atom forms 4 covalent bonds with 4
chlorine atoms. In this way, both the carbon and
all four chlorine atoms attain a stable
electronic structure. The sharing of a
single pair of electrons results in a single
covalent bond, often represented by a dash sign,
so chlorine molecule may be written as follow Cl
carbon tetrachloride
For oxygen molecule O2, there are two pairs of
electrons shared between the O atoms (double
covalent bond) O - O In nitrogen molecule
(N2) each nitrogen atom shares three electrons.
The sharing of three pairs of electrons between
two atoms leads to a triple covalent bond N
N Coordinate bond A molecule of
ammonia NH3 is made up of one nitrogen and three
hydrogen atoms
The nitrogen atom forms three bonds and the
hydrogen atoms one bond each. In this case, one
pair of electrons is not involved in bond
formation and this is called a lone pair of
electrons. It is possible to have a shared
electron pair in which the pair of electrons
comes just from one electron and not from both.
Such bond is called coordinate covalent
bond. Even though the ammonia molecule has a
stable configuration, it can react with hydrogen
H by donating the lone pair of electrons,
forming the ammonium ion NH4
Partial ionic character of covalent bonds In the
chlorine molecule Cl Cl the pair of electrons
of the covalent bond is shared equally between
both chlorine atom. Because there is not a charge
separation toward one of the Cl atoms, Cl2
molecule is nonpolar.
On the contrary, in HCl molecule, there is a
shift of electrons toward the chlorine atom which
is more electronegative than hydrogen one. Such
molecules, in which a charge separation exists is
called polar molecule or dipole molecule
The polar molecule of hydrochloric acid
The magnitude of the effect described above is
denoted through the dipole moment µ. The dipole
moment is the product of the magnitude of the
charges (d) and the distance separating them
µ d d
The symbol d suggests small magnitude of charge,
less than the charge of an electron ( 1.602
10-19 C ). The magnitude of 3.34 10-30 Cm
means Debye ( D )
1D 3.34 10-30 C m
The hydrochloric acid molecule has a dipole
moment µ1.03 D and the distance between H and
Cl atoms is 136 pm ( 136 10-12 m ). A charge d
will be
The charge d is about 16 of the electron charge
(1.602 10-19 C ). We can say therefore that
the covalent H Cl bond has about 16
ionic character.
Metallic bond
Metals tend to have high melting and boiling
points suggesting strong bonds between the atoms.
Sodium has the electronic structure
1s22s22p63s1. When sodium atoms come together,
the electron in the 3s atomic orbital of one
sodium atom shares space with the corresponding
electron of a neighbouring atom to form a
molecular orbital in the same way that a covalent
bond is formed. The difference, however, is that
each sodium atom is touched by eight other sodium
atoms, and the sharing occurs between the each
atom and 3s orbitals of all the eight other
atoms. And each oh these eight is in turn touched
by eight sodium atoms and so on.
All of the 3s orbitals of all the atoms overlaps
to give a vast number of molecular orbitals which
extend over the whole piece of metal. There have
to be huge numbers of molecular orbitals because
any orbital can only hold two electrons. The
electron can move freely within these molecular
orbitals and so each electron becomes detached
from its parent atom. The electrons are said to
be delocalised. The metal is held together by the
strong forces of attraction between the positive
nuclei and the delocalised electron. This may be
described as an array of positive ions in a sea
of electrons .
Metallic bond
The free electrons of the metal are
responsible for the characteristic metallic
properties ability to conduct electricity and
heat, malleability (ability to be flattened into
sheets), ductility (ability to be drawn into
wires) and lustrous appearance.
Intermolecular bonds
Van der Waals forces
Intermolecular forces are attractions between
one molecule and neighboring molecules. All
molecules are under the influence of
intermolecular attractions, although in some
cases those attractions are very weak. These
intermolecular interactions are known as van der
Waals forces. Even in a gas like hydrogen
(H2), if you slow the molecules down by cooling
the gas, the attractions are large enough for the
molecules to stick together in order to form a
liquid and then a solid.
In hydrogen s case the attractions are so weak
that the molecules have to be cooled to 21 K
(-252?C) before the attractions, are enough to
consider the hydrogen as a liquid. Helium s
intermolecular attractions are even weaker the
molecules won t stick together to form a liquid
until the temperature drops to 4 K ( -269
?C). Attractions are electrical in nature. In a
symmetrical molecule like hydrogen, however,
these doesnt seem to be any electrical
distortion to produce positive or negative parts.
But that s only true in average. In the next
figure the symmetrical molecule of is
H2 symmetrical molecule
The even shading shows that on average there is
no electrical distraction. But the electrons are
mobile and at any one instant they might find
them selves towards one out if the molecule. This
end of the molecule becomes slightly negative
(charge -?). The other end will be temporarily
short of electrons and so becomes slightly
positive ( ?) as we can see in the next figure.
An instant later the electrons may well have
moved up to the other end, reversing the polarity
of the temporary dipole of molecule.
Temporary dipole of H2
This phenomena even happens in monoatomic
molecules of rare gases, like helium, which
consists of a simple atom. If both the helium
electrons happen to be on one side of the atom at
the same time, the nucleus is no longer properly
covered by electrons for that instant.
Temporary dipole of He
The question is how temporary dipoles give
intermolecular bonds? Imagine a molecule which
has a temporary polarity being approached by one
which happens to be non- polar just at that
Induced dipole
As the right hand molecule approaches, its
electrons will tend to be attracted by the
slightly positive end of the left hand one. This
sets up on induced dipole in the approaching
molecule, which is orientated in such a way that
the ? end of one is attached to the ?- end of
the other.
Dipole-dipole attraction
An instant later the electrons in the left hand
molecule may well have up the other end. In doing
so, they will repel the electrons in the right
hand one.
The polarity of both molecules reverses, but
there is still attraction between ?- end and ?
end. As long as the molecules stay close to each
other, the polarities will continue to fluctuate
in synchronization so that the attraction is
always maintained. This phenomena can occur
over huge numbers of molecules. The following
diagram shows how a whole lattice of molecules
could be held together in a solid.
Molecular distribution in a solid
The interactions between temporary dipoles and
induced dipoles are known as van der Waals
dispersion forces .
Now, let us consider a molecule like HCl. Such a
molecule has a permanent dipole because chlorine
is more electronegative than hydrogen. These
permanent dipoles will cause the HCl molecules to
attract each other rather than if they had to
rely only on dispersion forces. Its important
to realize that all molecules experience
dispersion forces. Dipole-dipole interactions are
not an alternative to dispersion forces. They
occur in addition to them. Molecules which have
permanent dipoles will have boiling points higher
than molecules which have only temporary
fluctuating dipoles. Surprisingly, dipole-dipole
attractions are fairly minor compared with
dispersion forces, and their effect can be seen
if we compare two molecules with the same number
of electrons and the same size.
For example, the boiling points of ethane
(CH3-CH3) and fluoromethane (CH3F) are 184.5 K
(-88.7?C), respectively 194.7 K (-78.5?C). The
molecule of ethane is symmetric while that of
fluoromethane has permanent dipole.
Hydrogen bond
If we plot the boiling points the hydride of the
elements of groups 15, 16 end 17 we find that the
boiling point of the first elements in each
group is abnormally high.
In the cases of NH3, H2O and HF there must be
some additional intermolecular forces of
attraction, requiring significantly more heat
energy to break. These relatively powerful
intermolecular forces are described as hydrogen
  • We can observe that in each of these molecules
  • the hydrogen is attached directly to one of the
    most electronegative elements, causing the
    hydrogen to acquire a significant amount of
    positive charge
  • each of the elements to which the hydrogen atom
    is attached is not only significant, but also has
    one active lone pair of elements.

Lone pairs of the 2nd level have the elements
contained in a relatively small volume of space
which therefore has a high density of negative
charge. Lone pair at higher levels are more
diffuse and not so attractive to positive
Lets consider two water molecules coming close
The slightly ? charge of hydrogen is strongly
attracted to the lone pair end as a result a
coordinate bond is formed. This is a hydrogen
bond . Hydrogen bond is significantly stronger
than a dipole- dipole interaction, but has about
a tenth of the strength of an average covalent
bond. In liquid water, hydrogen bonds are
constantly broken and reformed. In solid water
each water molecule can form hydrogen bond
surrounding water molecules as we can see in the
next figure.
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This is why the boiling pint of water is higher
than of ammonia or hydrogen fluoride. In the case
of ammonia, the amount of hydrogen bonding is
limited by the fact that each nitrogen atom has
only one lone pair. As well, in hydrogen
fluoride, the number of hydrogen atoms is not
enough to form a three- dimensional structure.
In a gas the molecules are in a permanent and
chaotic motion. Each particle travels in random
directions at high speed until it reaches another
one, when it is deflected, or until it collides
with the wall of the vessel. This movement is
called Brownian motion and the gas phase is a
completely disordered state. The thermodynamic
state of a gas is characterized by its pressure,
its volume, and its temperature. The
relationship between the pressure, volume,
temperature and amount of gas are called gas
Pressure is measured as force per unit area.
The SI unit for pressure is Pa (Pascal).
However, several other units are commonly used.
The table below shows the conversion between
these units
Units of Pressure Units of Pressure
1 Pa 1 Nm-21 kgm-1s-2
1 atm 1.01325105 Pa
1 atm 760 torr (mmHg)
1 bar 105 Pa
Volume is related between all gases by
Avogadros hypothesis, which states Equal
volumes of gases, at the same temperature and
pressure contain equal numbers of molecules.
From this, one can derive the molar volume of a
gas, that is the volume occupied by one mole of
gas under certain conditions. This values, at
1atm and 0C is VM 22.41 Lmole-1
Temperature is a measure of how much energy the
particles have in a gas.
1. Boyles law
This law was discovered by Robert Boyle (1662)
and describes the relationship between the gas
pressure and volume. The volume occupied by a
given amount of gas is inversely proportional to
the pressure at constant temperature
where p is the pressure (Pa) V is the
volume (m3) k is a constant.
Boyles law may be written as the relationship
where p1 and V1 are the pressure and the volume
in another state, at the same temperature. If
we represent this relationship we obtain a set of
curves with a shape called equilateral hyperbola,
corresponding to a particular temperature.
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The explanation of Boyles law is based on the
fact that the pressure exerted by a gas arises
from the impact of its molecules to the walls of
the vessel. If the volume is halved, the
density of molecules is doubled. In a given
interval of time twice as many molecules strike
the walls and so, the pressure is doubled in
accord with Boyles law. This law is universal
in the sense that it applies to all gases without
reference to their chemical composition.
2. Charless law
The volume of a given amount of gas, at constant
pressure, increases proportionally to the
where V is the gas volume (m3) T is
the temperature (K) k is a constant. For
two different states, at the same gas pressure,
the relationship becomes
If we represent the relationship, we obtain a
set of straight lines for each pressure
The point of intersection between the straight
lines and the temperature axis is the same
-273.15C. It is the temperature at which the
volume of a gas would become zero , called
absolute zero temperature (0 K).
3. Gay Lussacs law
The pressure of a given amount of gas at
constant volume increases proportionally to the
where p is the pressure at temperature T
T is the temperature (K) k is a
constant. For two different states, at the same
gas volume, the relationship becomes
These three laws were combined to give the
combined gas law
With the addition of Avogadros law we obtain
the ideal gas law
where n is the amount of substance expressed in
mole R universal gas constant (8.314
For a mole of gas, the relationship becomes
VM is the molar volume.
4. Daltons law of partial pressures
Studies of gaseous mixtures showed that each
component behaves independently of the
others. The total pressure exerted by a gaseous
mixture is equal to the sum of the partial
pressures of each component
The partial pressure of a gas is the pressure
that the gas would exert if it were alone in the
Solutions are homogeneous mixtures formed by two
or more components. For one solution, we
distinguish the component that dissolves, called
solvent, and the compound that is dissolved,
called solute. The notion of solution is not
limited to a certain state of aggregation of the
substances. There can be liquid, solid or gaseous
Liquid solutions are
  • a gas dissolved in a liquid carbon dioxide in
  • liquid dissolved in liquid ethanol in water
  • solid dissolved in liquid sodium chloride in
    water, naphthalene in benzene.

Solid solutions the most important are metal
alloys, but in this category are included only
the alloys which are homogenous mixtures.
Gaseous solutions are gas mixtures, like air.
Gases, regardless of their chemical nature, are
miscible in any proportion.
The most common dissolving agent is water it
can dissolve many solid, liquid or gaseous
substances. Other usual dissolving agents are
ethanol, ethyl ether, toluene, chloride
derivatives and others. Substances are
dissolved in solvents differently. For example,
fats are not dissolved in water, but are well
dissolved in petrol iodine is barely dissolved
in water, but is well dissolved in alcohol.
Dissolving is a consequence of molecular
movement. When a solid substance is introduced
in water, its particles (molecules or ions)
interact with the water molecules, are separated
from the solid and diffuse inside the solution.
The higher the number of particles separated in
the time unit, the faster the dissolving process.
The finely divided substances, having a higher
surface area in contact with the solvent, are
dissolved faster than massive substances. Also,
agitation and temperature intensifies the
dissolving process.
The thermal effect of dissolving
  • The dissolving of the substances is accompanied
    by a thermal effect either heat absorption or
    heat release.
  • For example, dissolving one mole of potassium
    nitrate in a large quantity of water requires 36
    kJ absorbed from the environment.
  • The dissolving process of an ionic substance,
    like potassium nitrate, consists of two
    successive processes
  • the separation of K and NO3- ions from the
    crystal lattice, process that requires energy
    from the exterior,
  • the solvation of the ions (hydrating when the
    solvent is water), that takes place with heat

Solvation (hydrating) represents the process of
attaching solvent molecules to the separated
ions from the crystal lattice.
The dissolving process of potassium nitrate in
Because the energy absorbed for the extraction
of the ions from the crystal lattice is higher
than the energy released during the solvation of
the ions, the dissolution of potassium nitrate is
an endothermic process, meaning that dissolving
potassium nitrate in water the solutions will
cool down. In case of other ionic substances,
like copper sulfate, the dissolution is an
exothermic process.
Concentration of the solutions
Concentration expresses the quantitative
relation between the components of the solution.
There are several ways of expressing the
concentration of solutions 1. Mass percentage
represents the mass of substance (g) dissolved in
100 g of solution. The relation of mass percent
Where md is the mass of the dissolved
substance ms the mass of the solution.
2. Volume percentage represents the volume of
substance (m3) dissolved in 100m3 of solution
Where Vd is the volume of the dissolved
substance Vs the volume of the solution.
This way of expressing the concentration of
solutions is used especially in the case of
liquids dissolved in other liquids. 80 (v)
ethanol contains 80 volumes of pure ethanol and
20 volumes of water. 80 alcohol means 80 (v).
3. Molarity represents the number of moles of
substance dissolved in 1L of solution
Where Md is the molecular mass of the dissolved
substance Vs the volume of the solution
4. Molality represents the number of moles of
substance dissolved in 1kg of solvent
Unlike molarity, which depends on temperature,
the molality is independent on temperature.
5. Molar fraction (mole fraction) is the number
of moles of solute divided by the total number of
moles of a solution. For a solution that
contains nA moles of compound A and nB moles of
compound B the mole fraction of compound A in the
solution is
Similarly, the mole fraction of compound B is
From these relations results that the sum of the
mole fractions of compounds A and B is 1. Similar
relations result in the case of solutions that
have several compounds.
6. Titer represents the mass of dissolved
substance (expressed in g) that is found in 1mL
of solution
This way of expressing concentration is commonly
used in analytical chemistry.
Transformation relations between different ways
of expressing concentration
Way of expressing concentration Percentage c Molarity cM Molality cm
Percentage c
Molarity cM
Molality cm
Introducing sodium chloride in a certain amount
of water, in small portions and under stirring,
it can be seen that at a certain moment, the
quantities of NaCl that are added dont dissolve
anymore, they remain in solid state. The
solution that at a certain temperature contains
the maximum proportion of dissolved substance is
called saturated solution. For example, at 20C,
35.8g NaCl is the maximum quantity of NaCl that
can be dissolved in 100g of water. The maximum
concentration of the substance in the saturated
solution represents the solubility.
The solubility of sodium chloride is 35.8 g/100
g of water at the considered temperature.
Solubility depends on the nature of the
substances. Substances that at 20C have the
solubility of more than 1 g solute per 100 g
solvent are considered soluble. Substances
with solubility under this value are considered
slightly soluble. Soluble substances in water
are NaCl, KNO3, AgNO3, KBr, NaOH, sodium
acetate, sulfuric acid, sugar, etc. Slightly
soluble substances in water are AgBr, PbSO4,
Fe(OH)3, CaCO3, BaSO4.
The solubility of substances depends on
temperature. The variation of solubility with
temperature is represented by the solubility
curves. The solubility of salts generally
increases with increasing temperature. For some
solid substances like Ce(SO4)3 or Ca(OH)2 the
solubility decreases with increasing temperature.
The solubility of liquids increases with
increasing temperature. The solubility of gases
decreases with increasing temperature. The
solubility of gases is also influenced by the
pressure of the gas above the solution. The
higher the pressure of the gas, the higher the
Solubility curves for some solid substances
The vapor pressure of solutions Vapor pressure
is the pressure of a vapor in equilibrium with
its non-vapor phases. The transition of a
liquid substance in gaseous state (evaporation)
takes place even before reaching boiling point.
At the liquid air interface the molecules of
the substance are stopped from leaving the liquid
due to the intermolecular forces which are
orientated towards the mass of the liquid.
But, if the kinetic energy of the molecule
becomes very large, this molecule can escape
from the solution and passes in the gaseous
state. This phenomenon is reversible, and at
the interface there is a dynamic equilibrium,
when the number of molecules that passes from
liquid to air is equal to the number of molecules
that passes from air to liquid. This means that
at equilibrium, the gaseous state is saturated
with the molecules of the liquid substance. The
vapor pressure is an indication of a liquid's
evaporation rate. A substance with a high vapor
pressure at normal temperatures is often referred
to as volatile.
The temperature at which the vapor pressure of a
liquid becomes equal to atmospheric pressure (or
in case of closed spaces the pressure above the
liquid) is the boiling temperature.
Vapor pressure of mixtures
If a non-volatile substance is dissolved in a
solvent, the vapor pressure of the solution is
smaller than the one of the pure solvent, at the
same temperature. The relative drop of vapor
pressure is given by
p0 the vapor pressure of the pure solvent p
the vapor pressure of the solvent above the
Raoults law (1877) the relative drop of the
vapor pressure of a diluted solution is equal to
the molar fraction of the solute in solution
Considering x1 as the molar fraction of the
solute and x2 the molar fraction of the solvent,
the relation can be written
from which results
Considering the fact that x1 x2 1, we obtain
p x2?po
The vapor pressure of a solvent in a solution is
directly proportional to its molar fraction. The
solutions that respect the Raoults law are
called ideal solutions. Diluted solutions are
approaching the state of ideal solution. If a
gaseous substance is dissolved in a liquid
solvent, the molecules of gas are dispersed in
the mass of the solvent. They can reach the
liquid gas interface, and if their kinetic
energy is sufficiently high, they pass in the
gaseous state.
Equilibrium is reached at a certain
concentration of the gas in solution, when the
number of the gas molecules that pass from the
solution in gaseous state is equal to the number
of gas molecules that pass the opposite way. At
equilibrium, the solution is saturated in gas.
The variation of the solubility of a gas with
the pressure is expressed by Henrys law the
molar fraction of a gas dissolved in a solvent is
proportional to the pressure of the gas in
equilibrium with the solution
x k?p
Increasing the boiling point of the solutions
According to Raoults law, by dissolving a
non-volatile substance in a solvent, the vapor
pressure of the solvent above the solution is
smaller than the one above the pure solvent.
Thus, the boiling temperature of the solution
will be higher than the one of the solvent. The
increase of the boiling point of the solution
compared to the solvent is proportional to the
decrease of the vapor pressure of the solution
compared to the solvent
The increase of the boiling point is Tf -
the boiling temperature of the solution Tf0 -
the boiling temperature of the solvent The
decrease of the vapor pressure is p0 is the
vapor pressure of the solvent p is the vapor
pressure of the solution.

The variation of the boiling point of the
solution depends also on the concentration of the
dissolved substance.
Vapor pressure and temperature for different
concentrations of the solute expressed in
The increase of the boiling point can be
expressed by the relation
where Keb is the ebullioscopic constant, cm
the molal concentration of the solute.
The ebullioscopic constant, Keb represents the
increase of the boiling point when one mole of
substance is dissolved in 1 kg of solvent.
For diluted solutions, the ebullioscopic
constant does not depend on the nature of the
dissolved substance, as it is a characteristic of
the solvent. This means that solving the same
quantity of substance in a solvent, the increase
of the boiling point of the solution will be the
Ebullioscopic constant for different solvents.
Solvent H2O chloroform ethanol benzene diethyl ether
Keb 0.52 3.88 1.15 2.57 2.11
Replacing the molarity with its expression, it
where md is the mass of solute (kg) msolv
the mass of solvent (kg) M the molar mass
(kgmol-1). This relation is used for
determining the molecular mass of the substances.
The research method, based on the experimental
determination of the increase of the solutions
boiling point, is called ebullioscopy.
Decreasing the freezing point of solutions
Another consequence of Raoults law is the drop
of the freezing point of solutions. The decrease
of the freezing point is proportional with the
molal concentration of the dissolved substance
where Ts is the freezing temperature of the
solution Ts0 the freezing temperature of the
solvent Kcr the cryoscopic constant.
The cryoscopic constant represents the drop of
the freezing point produced by dissolving one
mole of substance in 1 kg of solvent.
Solvent H2O Camphor Naphthalene Benzene Cyclohexane
Kcr 1.8 40.0 7.0 5.12 20.2
The research method based on the experimental
determination of the decrease of the freezing
point of solutions is called cryoscopy. The
relation used in cryoscopy for determining the
molecular masses of substances is
Osmosis and osmotic pressure
If we carefully pour water on a copper sulfate
solution (blue), we will see at the beginning a
clear separation between the blue-coloured copper
sulfate solution and the colorless water. Because
of the Brownian movement the Cu2 and SO42- ions
are dislocated from the solution in the water
layer and the water in the copper sulfate
solution, so that, after a while, a
homogenization of the copper sulfate
concentration is produced.
The effective movement of the chemical species,
ionic or molecular, under the influence of the
difference of concentration is called diffusion.
At equal concentrations the diffusion stops.
The diffusion of some chemical species can be
prevented using membranes. There are
semi-permeable membranes that allow certain
molecules or ions to pass through, but prevent
the passage of other molecules. The osmosis can
be evidenced by the following experience
At the beginning, the liquid from the funnel is
at the same level with the liquid in the vessel.
In time, the liquid ascends in the gradual tube
to a certain level. This happens because water
diffuses through the membrane in the sugar
solution. The membrane is permeable only for the
small water molecules but not for the large sugar
The movement of the solvent through a
semi-permeable membrane from the diluted solution
into the concentrated solution is called osmosis.
The increase of the level stops when the
hydrostatic pressure h is sufficiently high to
prevent the passage of water. The pressure
necessary to stop the diffusion of water is the
osmotic pressure. It can be measured by the
height of the liquid column.
The general osmotic pressure expression was
formulated by vant Hoff
? cRT
where p is the osmotic pressure (Nm-2) c
concentration (molem-3) R universal
constant of gases T thermodynamic
temperature (K). The vant Hoffs equation is
similar to the general equation of ideal gases.
The chemical reaction represents the phenomenon
through which one or more substances are
transformed in other substances, without
affecting the nature of the constituent atoms of
the transformed substances. In the environment
several reactions can be observed, although most
of them have a slow rate. Some examples in this
way are rusting of the steel pieces, alcoholic
fermentation, green turning of leaves due to the
forming of chlorophyll, the ignition of fuels.
Chemical reactions can be emphasized through the
next manifestations
a) Evolution of gas bubbles
If we introduce a piece of zinc in a hydrochloric
acid solution, we may observe the hydrogen
evolution reaction.
Zn 2HCl ? ZnCl2 H2
A more violent reaction occurs between sodium and
water. The reaction product is also hydrogen.
2Na 2H2O ? 2NaOH H2
b) Forming of precipitates
By pouring sodium dichromate solution in a lead
nitrate solution we observe the appearance of a
yellow-coloured precipitate consisting of
slightly soluble lead dichromate.
Pb(NO3)2 Na2Cr2O7 ? 2NaNO3 PbCr2O7
c) Changing of colour Substances absorb light
of different wave lengths, so they appear
differently coloured. Changing the nature of a
substance through a chemical reaction can
sometimes lead to color modifications. So, if in
a colourless solution of ammonium thiocyanate we
pour an iron (III) and ammonia sulphate solution
we observe the colouring of the solution in deep
red because of the forming of the iron (III)
3NH4SCN FeNH4(SO4)2 ? Fe(SCN)3 2(NH4)2SO4
Sometimes the modifying of colour can be the sign
of a physical process, not necessary chemical.
d) Appearance of flame
This is another sign that a chemical reaction
takes place. An example is the ignition reactions
of hydro-carbons. The flame that appears at the
Bunsen bulb is the sign of the oxidation reaction
of methane with oxygen from air.
e) Modification of physical properties of
solutions This is another proof of a chemical
reaction. Such kind of property is conductivity.
If in a vessel with hydrochloric acid solution
we add a sodium hydroxide solution, with the help
of a conductivity meter one can measure the
decreasing of the solutions conductivity until
the complete neutralization of the acid.
Thermal effects The chemical reactions take
place through the breaking of chemical bonds and
the forming of new ones. Therefore, chemical
reactions are accompanied by important thermal
effects (heat release or absorption).
Exothermic reactions reactions that take
place with heat release. Endothermic reactions
reactions that take place with heat absorption.
Chemical reactions are represented using
chemical equations. Reactants substances
initially involved in a chemical reaction. They
are written in the left term of the
equation. Reaction products substances formed
in a chemical reaction. They are written in the
right term of the equation Because in a chemical
reaction, the nature of atoms of the substances
is not changed, the chemical equations are
equalized so that the number of atoms of a
certain element from the left term is equal to
the one from the right term.
Lets consider the chemical reaction between
hydrogen and chlorine, when hydrochloric acid is
H2 Cl2 2HCl
For the hydrochloric acid we chose the
coefficient 2 so that the number of chlorine
atoms, as well as the number of hydrogen atoms is
not modified. The primary signification of this
chemical reaction is that a hydrogen molecule
interacts with a chlorine molecule in order to
form two molecules of hydrochloric acid. During
this transformation, the covalent bonds H H
and Cl Cl are broken, and a new bond is formed
H Cl.
The chemical equations have the same properties
as mathematical equations. Thus, the equation can
be multiplied with Avogadros number, and we
The second signification of the chemical
equation is that 1 mole of hydrogen reacts with
1 mole of chlorine to obtain 2 moles of
hydrochloric acid.
In some situations, in order not to create
confusion, chemical formulas of the reactants and
the reaction products are followed by the symbol
of the aggregation state written between
brackets 2Na (s)
2H2O (l) 2NaOH (aq) H2 (g) The
next symbols are used s solid, l liquid, g
gas, aq aqueous solution.
Classification of chemical reactions
It is very difficult to choose unique and well
defined criteria for the chemical reactions
classification. One criterion can be the way the
reactants interact in order to form the reaction
products. Based on these criteria, we can
  • combination reactions (synthesis),
  • decomposition reactions,
  • single displacement reactions,
  • double displacement reactions.

a) Combination reactions (synthesis) are
reactions in which two substances interact to
form a single compound. There are many examples
for this
N2 3H2 2NH3 Fe S FeS Ca Cl2
CaCl2 SO3 H2O H2SO4
b) Decomposition reactions are transformations in
which from one substance, two or more substances
are formed
CaCO3 CaO CO2 4NH4NO3 3N2 N2O4
8H2O Fe2(SO4)3 Fe2O3 3SO3
c) Single displacement or substitution reactions
are transformations in which one element or one
group of elements from a combination is replaced
with another element or group of elements
Fe CuSO4 Cu FeSO4 Mg 2H2O Mg(OH)2
H2 Zn 2HCl ZnCl2 H2 Cl2 2KI 2KCl I2
d) Double displacement or coupling substitutions
are transformations in which two elements or
groups of elements are exchanged between two
chemical combinations
Pb(NO3)2 2KI PbI2 2KNO3 AgNO3 KCl AgCl
KNO3 H2SO4 BaCl2 BaSO4 2HCl CaCl2 K2CO3
CaCO3 2KCl
A special case of double substitution reactions
is the reaction between acids and bases H2SO4
2NaOH Na2SO4 2H2O
Based on the nature of the reactants or products
there are - combustion reactions - hydrolysis
reaction - precipitation and complexation
reactions a) Combustion reactions oxygen reacts
with a carbon compound containing hydrogen and/or
other element like O, S, N. Example the
combustion of hydrocarbons (toluene, methane,
acetylene), alcohols (methanol) or sulfur
compounds (thiophene) C6H5-CH3 9O2 7CO2
4H2O CH4 2O2 CO2 2H2O
2C2H2 5O2 4CO2 2H2O 2CH3OH 3O2 2CO2
2H2O C4H4S 6O2 4CO2 2H2O SO2 The
burning of carbon can also be considered a
combustion reaction C O2 CO2 b) Hydrolysis
reaction the reactant is water this reactions
are frequent in inorganic chemistry as well as in
organic chemistry Al2(SO4)3 6H2O 2Al(OH)3
c) The precipitation and complexation reactions
the classification criteria is the nature of the
reaction products Pb(NO3)2 K2SO4 PbSO4
2KNO3 CoCl3 6NH3 Co(NH3)6Cl3
In organic chemistry, the chemical reactions
imply usually the breaking and formation of
covalent bonds. There are three fundamental
types of reactions substitution, addition and
elimination. Generally, the organic molecule
that suffers a transformation is called
substrate, and the reactant used in it is called
reagent. The substitution is the reaction in
which an atom or a group of atoms attached to a
carbon atom is replaced with another atom or
group of atoms CH3-CH2-Cl NaOH CH3-CH2-OH
The addition reaction is the transformation that
leads to the increasing of the number of atoms or
groups of atoms attached to the carbon atoms of
the substrate HC?CH HCN gt H2CCH-CN The
elimination is the reverse of the addition and it
leads to the decreases of the number of atoms or
groups of atoms attached to the carbon
atoms CH3-CH2-OH gt H2CCH2 H2O The breaking
of the covalent C C bonds can be interpreted as
an elimination reaction.
It is the part of chemistry that has as aim the
establishment of the quantitative relations
between the reactants and reaction products.
The name stoichiometry derives from Greek
stoicheon that means element and metron that
means measurement. So, stoichiometry is the
science of the elements measuring. As it was
seen before, the atomic mass unit (uam) was
introduced, that represents the 12th part of the
mass of the C 1 uam 1.660510-27 kg
Based on the atomic mass unit the relative
atomic masses of all elements have been
determined. Knowing the atomic masses one can
calculate the (relative) molecular masses, as the
sum of the relative masses of all the atoms in
the molecule. For example, the molecular mass
of water is MH2O 211618 MH2SO4
213241698 MNaCl 2335.558.5 MCuSO4
In the chemical equations, the stoichiometric
coefficients indicate the ratio between the
number of molecules of the reactants and reaction
products. The mole was initially defined as the
mass of substance, expressed in grams, equal to
the molecular mass of the substance. Thus, 1
mole of H2SO4 is the quantity of substance that
contains 98 g H2SO4. The definition of the
mole, as a fundamental unit in the International
System of Units, is the following
The mole is the quantity of substance of a
system that contains 6.0221023 (the Avogadros
number NA) elementary particles. Avogadros
number refers to different elementary particles
that can be molecule, atoms, ions or electrons.
Stoichiometric calculation
Stoichiometric calculation is based on the law
of conservation of mass In a chemical reaction,
the mass of the reactants is equal to the mass of
the reaction products. Let us consider the
reaction between metallic sodium and water that
occurs according to the chemical equation 2Na
2H2O 2NaOH H2 Atomic masses Na 23, H 1,
O 16.
In a vessel filled with sufficiently enough
water we introduce 0.23 g sodium. Calculate the
quantity (mass) of water that has reacted, as
well as the quantities (masses) of sodium
hydroxide and hydrogen that have resulted. The
quantity of water that has reacted with sodium
223g Na218g H2O 0.23g
Nax g H2O ____________________________
Similarly, we calculate the mass of the resulted
NaOH 223g Na240g NaOH 0.23g
Nax g NaOH ___________________________
The resulted hydrogen mass 223g
Na2g H2 0.23g Nax g
H2 _____________________________________
We can calculate directly the volume of H2 that
results from the reaction in normal conditions of
temperature and pressure 223g
Na22.4L H2 (cn) 0.23g Nax
L H2 (cn) ________________________________________
Reversible reactions Reactions that may proceed
in both directions are called reversible
The reversible equation is represented using
arrows in both ways instead of the equality sign.
The law of mass action
The ratio between the product of the reaction
products concentrations and the product of the
reactants concentrations, all taken to the power
of their stoichiometric coefficients, is
We consider the reversible reaction
Kc is the equilibrium constant.
For a general reversible reaction
the expression of the law of mass action is
Le Chateliers principle
If a dynamic equilibrium is disturbed by changing
the conditions (concentrations, temperature and
pressure) the position of equilibrium moves to
counteract the change.
Consequences of Le Chateliers principle
1. Increasing the concentration of one of the
components will shift the equilibrium in the
direction in which this component reacts
2. Increasing the temperature of the system will
shift the equilibrium in the direction of
endothermic reaction, so that the heat will be
3. Increasing the pressure will shift the
equilibrium so that molecules with smaller volume
are being formed.
Electrolytic dissociation of water
The water molecules dissociates according to the
The equilibrium is shifted far to the left.
Experimentally, it was determined that at 25C,
only one molecule of water, out of 556,000,000 is
dissociated, which means the dissociation degree
of water is a 1810-10. The equilibrium
constant for the dissociation reaction of water
Kw is called the ionic product of water
The ionic product of water depends on the
temperature. At 25C, the value of KW is 10-14
mol L-1.
In pure water the concentration of the H3O ions
is equal to that of the HO-, which means that at
In order to express the concentration of the
hydrogen ions in aqueous solutions, the notion of
pH was introduced by Sörensen (1909)

The relation was modified by Bates by replacing
the concentration of the hydronium ions with
their activity
In the case of diluted solutions, the activity
can be considered equal to the concentration
Similar to the pH notion the term of pOH was
introduced, that is a measure of the
concentration of the hydroxyl ions
It is easily demonstrated that, at the
temperature of 25C pH pOH -lg KW 14
Acid base equilibrium
Acids are substances that, in aqueous solutions,
release hydrogen ions H. For example, the
hydrochloric acid dissociates in H and Cl- ions
Bases are substances that, in aqueous solutions,
produce hydroxyl ions, like the case of sodium
hydroxide, that dissociates in Na and HO- ions
In aqueous solutions, acids like HCl, H2SO4 or
HNO3 are completely dissociated, the dissociation
degree is 1. They are called strong acids.
Similarly, bases like KOH or NaOH are completely
dissociated in solution, reason for which they
are called strong bases.
Partially dissociated acids in aqueous solution,
like CH3COOH, HCN or H2S, are called weak acids,
and partially dissociated bases in solution, like
NH3 or organic amines, are called weak bases. The
dissociation degree for weak acids and bases is
less than 1.
The dissociation degree is defined as the ratio
between the number of dissociated molecules and
the total number of dissolved molecules
The reaction between an acid and a base is
called neutralization reaction and it leads to
the formation of a salt and water. For example,
the reaction between nitric acid and potassium
hydroxide can be represented by the equation
Acidity constant
We consider an acid that dissociates according
to the equation
The equilibrium constant is given by the
For diluted solutions, the concentration of
water can be considered constant and it is
included in K. We obtain the acidity constant
Very weak acids the first acidity constant lower
than 10-7.
Acid Constant K1
HClO (hypochlorous acid) 3.210-8
H3BO3 (boric acid) 5.810-10
Weak acids the first acidity constant between
10-7 and 10-2.
Acid Constant K1
H3PO4 (phosphoric acid) 7.510-3
CH3COOH (acetic acid) 1.810-5
H2CO3 (carbonic acid) 0.4510-6
Strong acids are completely dissociated in
aqueous solution one can not distinguish between
their acidity constants.
Base constant For a base that, in aqueous
solution, dissociates according to the reaction
the base constant is given by the relation
Weak bases, like ammonia, aniline, have the
basicity constant below 10-3
Base Constant Kb
Ammonia NH3 1.710-5
Aniline C6H5 NH2 3.810-10
Strong bases, like sodium hydroxide, calcium
hydroxide, are completely dissociated in water,
like in case of strong acids.
Calculation of pH for acid and base solutions
Monoprotic acids are completely dissociated in
aqueous solutions so the hydronium ions
concentration is equal to the concentration of
the acid. For example, for a 10-3 mol L-1
solution of HCl, the concentration of the
hydronium ions is H3O 10-3 mol L-1. The pH
of the solution is
pH -lgH3O -lg 10-3 3
For a strong base, for example 10-3 mol L-1 KOH
the concentration of hydroxyl ions is HO-
10-3 mol L-1. It results that the pOH of the
solution is pOH -lgHO- -lg 10-3 3
Considering the relation between pOH and pH one
obtains pH 14 pOH 14 3 11
For concentrations higher than 10-3 mol L-1 the
pH is calculated using the Bates relation because
the activity differs from the concentration At
very low acid concentrations for the calculation
of pH it is necessary to consider the hydronium
ions coming from the dissociation of both acid as
well as water molecule.
For example, the pH of a 10-7 mol L-1 solution
of HCl is not 7 because the hydronium ions result
not only from the dissociation of the acid, but
from the dissociation of water as well
Considering that the concentration of
hydrochloric acid in the solution is c and the
concentration of hydronium, respectively hydroxyl
ions is x, the total hydronium ions concentration
will be cx. The ionic product of water, at the
temperature of 25C, will be (x c)x 10-14
One obtains a second degree equation x2 cx -
10-14 0
Solving the equation one obtains
The solution with minus in front of the square
root has no meaning, since it is negative. The
concentration of the hydronium ions will
be H3O 10-7 1,12?10-7 2.12?10-7 Thus,
the pH of a 10-7 mol L-1 solution of HCl, will
be pH -lgH3O -lg 2.12?10-7 6.67
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