CHAPTER 05 > States of Matter 113
CHAPTER > 05
States of Matter
KEY NOTES
Solid, liquid and gases are three general states of matter. Dipole Induced Dipole Forces
In this chapter, we will discuss different characteristics of These forces exist between the polar molecules having
gaseous and liquid states of matter.
permanent dipole and the molecules lacking permanent
Intermolecular Forces dipole.
Intermolecular forces are the forces of attraction and Permanent dipole of the polar molecule induces dipole on the
repulsion between interacting particles (atoms and electrically neutral molecule by deforming its electron cloud.
molecules). Hydrogen Bond
These are the weak forces and generally affect the physical It is a special case of dipole-dipole interaction. A hydrogen
properties and some chemical properties of matter. bond is formed (or such force exist) when a hydrogen is
Attractive intermolecular forces are known as bonded to a more electronegative atom (like, N, O and F).
van der Waals’ forces. van der Waals’ forces vary δ+ δ− δ+ δ−
considerably in magnitude. They include dispersion forces HF HF
or London forces, dipole-dipole forces and dipole-induced
dipole forces.
H - bond
Dispersion or London Forces Energy of hydrogen bond varies between 10 to 100 kJ mol −1
These forces exist in between neutral atoms and/or i.e. these are strong forces and play a key role in determining
non-polar molecules, as in them electronic charge cloud is the structure and properties of many compounds like
distributed symmetrically and, hence have no dipole proteins, nucleic acid etc.
moment.
The interaction energy of these forces is proportional to Thermal Energy
1 / r 6. (where r is the distance between two particles) The energy of a body which arises because of the motion of its
atoms or molecules, is called the thermal energy.
Dipole-Dipole Forces It is infact, the measure of average kinetic energy of the particles
These forces exists between dipole ends of polar molecules of the matter and, hence is responsible for their motion.
and are the strongest of all van der Waals’ forces. This movement of particles is called thermal motion.
Dipole-dipole interaction energy between stationary polar
molecules is proportional to 1 / r 3 and that between rotating Intermolecular Forces vs Thermal Interactions
polar molecules is proportional to 1 / r 6. The intermolecular forces tend to keep the molecules together
where, is distance between polar molecules. but thermal energy tend to keep them apart.
This interaction is stronger in London forces but weaker Thus, these two compete and the competition between these
ion-ion interactions. two (i.e. intermolecular forces and thermal energy) results in
three states of matter.
,The Gaseous State Ideal Gas Equation
Gases have neither definite shape nor definite volume. A gas that follows Boyle’s law, Charle’s law and
They are characterised by their high diffusibility, Avogadro’s law strictly is called an ideal gas.
large intermolecular space, high kinetic energy, high The combination of various gas laws such as
compressibility and low density. Boyle’s law, Charles’ law and Avogadro’s law leads to the
ideal gas equation.
The Gas Laws
At constant T and n; V ∝ 1/ p (Boyle’s law)
Gas laws are the relationships between measurable properties
of gases. At constant p and n; V ∝ T (Charles’ law)
At constant p and T ; V ∝ n (Avogadro’s law)
Boyle’s Law (Pressure-Volume Relationship)
On combining the above three relations, we get
It states that ‘‘at constant temperature, the pressure of a given
nT nT
mass of a gas is inversely proportional to its volume.’’ V∝ or V = R …(i)
1 p p
i.e. p∝ (At constant T and n)
V (Here, R = proportionality constant or gas constant)
or pV = constant On rearranging the equation (i), we get
or p1V1 = p 2V2 = constant pV = nRT [where, n = w / M]
Graph between p versus V or pV versus p at constant where, R is proportionality constant or universal gas
temperature is called isotherm. constant.
Charle’s Law (Temperature-Volume Relationship) The values of R are
According to this law, “the volume of a given mass of a gas R = 8. 314 Pa m 3 K− 1 mol − 1
is directly proportional to the absolute temperature at = 8. 314 J K− 1 mol − 1
constant pressure”.
= 8.20578 × 10− 2 L atm K− 1 mol − 1
i.e. V ∝ T
V V V Ideal gas equation is a relation between four variables and
(at constant pressure or = constant or 1 = 2 )
T T1 T2 it describes the state of any gas, therefore it is also called
equation of state.
A graph of V versus T at constant pressure is called isobar.
The combined gas law
Gay-Lussac’s Law It is given by,
(Pressure-Temperature Relationship) p1V1 p 2V2
=
According to this law, “at constant volume, the pressure of T1 T2
a given mass of a gas is directly proportional to its absolute Density and molar mass of a gaseous substance is related
temperature”. as,
i.e. p∝T M = dRT / p
p
or = constant (at constant V) Dalton’s Law of Partial Pressure
T
p1 p 2
It states that “the total pressure exerted by the mixture of
or = non-reactive gases is equal to the sum of the partial
T1 T2
pressure of each gas present in the mixture under the same
A graph of p versus T at constant volume is known as conditions of Tand V.”
isochore. p total = p1 + p 2 + p 3 ........... (At constant T and V)
Avogadro’s Law (Volume-Amount Relationship) In terms of mole fraction
It states that, equal volumes of all gases under same Partial pressure, ( p) = mole fraction χ × p total
conditions of temperature and pressure contain equal
number of molecules.” Kinetic Energy and Molecular Speeds
i.e. V ∝n (n = number of moles of gas) Maxwell and Boltzmann have shown that actual
The volume of one mole of a gas at STP is known as distribution of molecular speeds depends on temperature
molar gas volume. and molecular mass of a gas.
The number of molecules in one mole of a gas has been Maxwell derived a formula for calculating the number of
determined 6.022 × 1023 , is known as Avogadro constant. molecules possessing a particular speed.
KEY NOTES
, Average
speed (uav) T2 > T1 The intermolecular forces are negligible and the effect of
Most probable Root mean
gravity on them is also negligible.
speed (ump)
Number of molecules
square speed (urms) The collisions are perfectly elastic, therefore there is no loss
ump uav of kinetic energy during collision. However, there may be
urms redistribution of energy during such a collision.
Curve
at T1 The pressure of a gas is caused by the bombardment of
Curve moving molecules against the walls of the container.
at T2
In a gas, different molecules have different kinetic energies
but the average kinetic energy of molecules is proportional
(0, 0) Speed to absolute temperature of the gas.
Maxwell Boltzmann distribution of speeds
Behaviour of Real Gases :
Kinetic energy of a particle is given by the expression. Deviation from Ideal Gas Behaviour
1
Kinetic energy = mu2 At constant temperature, pV vs p plot for real gases is not a
2 straight line. There is significant deviation from ideal
Average Speed (u or uav ) behaviour.
It is the arithmetic mean of the various speeds of the At very low temperature and high pressure, real gases
molecules. shows deviation from the ideal gas behaviour.
Let there be ‘N’ molecules of gas having velocities The causes of deviation are given below :
u1 , u2 .........., uN . — At low temperature and high pressure, volume of a real
Then, average velocity, gas is larger than that predicted for an ideal gas.
u1 + u2 + .....+ uN 8RT — Intermolecular forces are not negligible.
u or uav = =
N πM The pressure exerted by a real gas is lower than the
Most Probable Speed (ump ) pressure exerted by an ideal gas.
an2
It is the velocity possessed by maximum number of pideal = preal +
molecules. Observed V2
pressure Correction
term
ump = 2RT / M
With the help of kinetic theory of gases, behaviour of gases
Root Mean Square Speed (urms ) can be interpreted mathematically.
It is the square root of the mean of the squares of the velocity The modified form of ideal gas equation is
of molecules of the same gas. van der Waals’ equation as shown below :
u12 + u22 + ..... + uN
2
3 RT n2 a
urms = = p + 2 [V − nb] = nRT
N M V
Root mean square speed, average speed and the most where, a and b are constants.
probable speed have the following relationship. ‘a’ is a measure of magnitude of attractive forces between
urms > uav > ump gaseous molecules and ‘b’ is a measure of effective size of
The ratio between the three speeds are given below : molecules.
ump : uav : urms : : 1 : 1128
. : 1.224 Compressibility Factor
Kinetic Molecular Theory of Gases The extent of deviation of a real gas from ideal behaviour is
expressed in terms of compressibility factor.
Kinetic molecular theory of gases is based on the following
assumptions : pV Vreal
Z= , Z=
A gas consists of extremely small discrete molecules. These nRT Videal
molecules are so small and so far apart that actual volume For ideal gas, Z = 1 at all temperatures and pressures.
of the molecules is negligible as compared to the total At very low pressure, all gases have Z ≈ 1 and behave as
volume of the gas. ideal gas. At high pressure, all gases have Z > 1.
Gas molecules are in constant random motion with high At intermediate pressure, most gases have Z < 1.
velocities that moves in a straight line and changes their Gases show ideal behaviour when the volume occupied is
directions on collision with other molecules or walls of the large, so that the volume of the molecules can be neglected,
container. as comparison to it.
KEY NOTES
CHAPTER > 05
States of Matter
KEY NOTES
Solid, liquid and gases are three general states of matter. Dipole Induced Dipole Forces
In this chapter, we will discuss different characteristics of These forces exist between the polar molecules having
gaseous and liquid states of matter.
permanent dipole and the molecules lacking permanent
Intermolecular Forces dipole.
Intermolecular forces are the forces of attraction and Permanent dipole of the polar molecule induces dipole on the
repulsion between interacting particles (atoms and electrically neutral molecule by deforming its electron cloud.
molecules). Hydrogen Bond
These are the weak forces and generally affect the physical It is a special case of dipole-dipole interaction. A hydrogen
properties and some chemical properties of matter. bond is formed (or such force exist) when a hydrogen is
Attractive intermolecular forces are known as bonded to a more electronegative atom (like, N, O and F).
van der Waals’ forces. van der Waals’ forces vary δ+ δ− δ+ δ−
considerably in magnitude. They include dispersion forces HF HF
or London forces, dipole-dipole forces and dipole-induced
dipole forces.
H - bond
Dispersion or London Forces Energy of hydrogen bond varies between 10 to 100 kJ mol −1
These forces exist in between neutral atoms and/or i.e. these are strong forces and play a key role in determining
non-polar molecules, as in them electronic charge cloud is the structure and properties of many compounds like
distributed symmetrically and, hence have no dipole proteins, nucleic acid etc.
moment.
The interaction energy of these forces is proportional to Thermal Energy
1 / r 6. (where r is the distance between two particles) The energy of a body which arises because of the motion of its
atoms or molecules, is called the thermal energy.
Dipole-Dipole Forces It is infact, the measure of average kinetic energy of the particles
These forces exists between dipole ends of polar molecules of the matter and, hence is responsible for their motion.
and are the strongest of all van der Waals’ forces. This movement of particles is called thermal motion.
Dipole-dipole interaction energy between stationary polar
molecules is proportional to 1 / r 3 and that between rotating Intermolecular Forces vs Thermal Interactions
polar molecules is proportional to 1 / r 6. The intermolecular forces tend to keep the molecules together
where, is distance between polar molecules. but thermal energy tend to keep them apart.
This interaction is stronger in London forces but weaker Thus, these two compete and the competition between these
ion-ion interactions. two (i.e. intermolecular forces and thermal energy) results in
three states of matter.
,The Gaseous State Ideal Gas Equation
Gases have neither definite shape nor definite volume. A gas that follows Boyle’s law, Charle’s law and
They are characterised by their high diffusibility, Avogadro’s law strictly is called an ideal gas.
large intermolecular space, high kinetic energy, high The combination of various gas laws such as
compressibility and low density. Boyle’s law, Charles’ law and Avogadro’s law leads to the
ideal gas equation.
The Gas Laws
At constant T and n; V ∝ 1/ p (Boyle’s law)
Gas laws are the relationships between measurable properties
of gases. At constant p and n; V ∝ T (Charles’ law)
At constant p and T ; V ∝ n (Avogadro’s law)
Boyle’s Law (Pressure-Volume Relationship)
On combining the above three relations, we get
It states that ‘‘at constant temperature, the pressure of a given
nT nT
mass of a gas is inversely proportional to its volume.’’ V∝ or V = R …(i)
1 p p
i.e. p∝ (At constant T and n)
V (Here, R = proportionality constant or gas constant)
or pV = constant On rearranging the equation (i), we get
or p1V1 = p 2V2 = constant pV = nRT [where, n = w / M]
Graph between p versus V or pV versus p at constant where, R is proportionality constant or universal gas
temperature is called isotherm. constant.
Charle’s Law (Temperature-Volume Relationship) The values of R are
According to this law, “the volume of a given mass of a gas R = 8. 314 Pa m 3 K− 1 mol − 1
is directly proportional to the absolute temperature at = 8. 314 J K− 1 mol − 1
constant pressure”.
= 8.20578 × 10− 2 L atm K− 1 mol − 1
i.e. V ∝ T
V V V Ideal gas equation is a relation between four variables and
(at constant pressure or = constant or 1 = 2 )
T T1 T2 it describes the state of any gas, therefore it is also called
equation of state.
A graph of V versus T at constant pressure is called isobar.
The combined gas law
Gay-Lussac’s Law It is given by,
(Pressure-Temperature Relationship) p1V1 p 2V2
=
According to this law, “at constant volume, the pressure of T1 T2
a given mass of a gas is directly proportional to its absolute Density and molar mass of a gaseous substance is related
temperature”. as,
i.e. p∝T M = dRT / p
p
or = constant (at constant V) Dalton’s Law of Partial Pressure
T
p1 p 2
It states that “the total pressure exerted by the mixture of
or = non-reactive gases is equal to the sum of the partial
T1 T2
pressure of each gas present in the mixture under the same
A graph of p versus T at constant volume is known as conditions of Tand V.”
isochore. p total = p1 + p 2 + p 3 ........... (At constant T and V)
Avogadro’s Law (Volume-Amount Relationship) In terms of mole fraction
It states that, equal volumes of all gases under same Partial pressure, ( p) = mole fraction χ × p total
conditions of temperature and pressure contain equal
number of molecules.” Kinetic Energy and Molecular Speeds
i.e. V ∝n (n = number of moles of gas) Maxwell and Boltzmann have shown that actual
The volume of one mole of a gas at STP is known as distribution of molecular speeds depends on temperature
molar gas volume. and molecular mass of a gas.
The number of molecules in one mole of a gas has been Maxwell derived a formula for calculating the number of
determined 6.022 × 1023 , is known as Avogadro constant. molecules possessing a particular speed.
KEY NOTES
, Average
speed (uav) T2 > T1 The intermolecular forces are negligible and the effect of
Most probable Root mean
gravity on them is also negligible.
speed (ump)
Number of molecules
square speed (urms) The collisions are perfectly elastic, therefore there is no loss
ump uav of kinetic energy during collision. However, there may be
urms redistribution of energy during such a collision.
Curve
at T1 The pressure of a gas is caused by the bombardment of
Curve moving molecules against the walls of the container.
at T2
In a gas, different molecules have different kinetic energies
but the average kinetic energy of molecules is proportional
(0, 0) Speed to absolute temperature of the gas.
Maxwell Boltzmann distribution of speeds
Behaviour of Real Gases :
Kinetic energy of a particle is given by the expression. Deviation from Ideal Gas Behaviour
1
Kinetic energy = mu2 At constant temperature, pV vs p plot for real gases is not a
2 straight line. There is significant deviation from ideal
Average Speed (u or uav ) behaviour.
It is the arithmetic mean of the various speeds of the At very low temperature and high pressure, real gases
molecules. shows deviation from the ideal gas behaviour.
Let there be ‘N’ molecules of gas having velocities The causes of deviation are given below :
u1 , u2 .........., uN . — At low temperature and high pressure, volume of a real
Then, average velocity, gas is larger than that predicted for an ideal gas.
u1 + u2 + .....+ uN 8RT — Intermolecular forces are not negligible.
u or uav = =
N πM The pressure exerted by a real gas is lower than the
Most Probable Speed (ump ) pressure exerted by an ideal gas.
an2
It is the velocity possessed by maximum number of pideal = preal +
molecules. Observed V2
pressure Correction
term
ump = 2RT / M
With the help of kinetic theory of gases, behaviour of gases
Root Mean Square Speed (urms ) can be interpreted mathematically.
It is the square root of the mean of the squares of the velocity The modified form of ideal gas equation is
of molecules of the same gas. van der Waals’ equation as shown below :
u12 + u22 + ..... + uN
2
3 RT n2 a
urms = = p + 2 [V − nb] = nRT
N M V
Root mean square speed, average speed and the most where, a and b are constants.
probable speed have the following relationship. ‘a’ is a measure of magnitude of attractive forces between
urms > uav > ump gaseous molecules and ‘b’ is a measure of effective size of
The ratio between the three speeds are given below : molecules.
ump : uav : urms : : 1 : 1128
. : 1.224 Compressibility Factor
Kinetic Molecular Theory of Gases The extent of deviation of a real gas from ideal behaviour is
expressed in terms of compressibility factor.
Kinetic molecular theory of gases is based on the following
assumptions : pV Vreal
Z= , Z=
A gas consists of extremely small discrete molecules. These nRT Videal
molecules are so small and so far apart that actual volume For ideal gas, Z = 1 at all temperatures and pressures.
of the molecules is negligible as compared to the total At very low pressure, all gases have Z ≈ 1 and behave as
volume of the gas. ideal gas. At high pressure, all gases have Z > 1.
Gas molecules are in constant random motion with high At intermediate pressure, most gases have Z < 1.
velocities that moves in a straight line and changes their Gases show ideal behaviour when the volume occupied is
directions on collision with other molecules or walls of the large, so that the volume of the molecules can be neglected,
container. as comparison to it.
KEY NOTES
