STATES OF MATTER

STATES OF MATTER




1. SOME IMPORTANT CONVERSIONS
VOLUME
i.
ii.
iii.
Pressure
i. 1 atm bar
ii.
iii. 1 atm

Temperature
Kelvin temperature (K) = Celsius temperature (0C)+1273. Celsius temperature (0C) =(temperature in Fahrenheit
Thermal Energy
It is the energy of a body arising from motion of its atoms or molecules. Thermal energy is  temperature of substance.
2. GAS LAWS
A. Boyle’s law
The volume of a given mass of gas is inversely proportional to its pressure at constant temperature.
Mathematically,  (at constant temperature)
or PV=constant (at constant T)
or P
By definition, density ‘d’ is related to the mass ‘m’ and volume  by the relation
If we put value of V in above equation from Boyle’s law
Equation, we obtain the relationship. d=
The above equation, shows that at a constant temperature, pressure is directly proportional to the density of fixed mass of gas.
Graphical representation
The graph between
  P and  is a
straight line passing
through origin. At
high pressure,
gases deviate from
Boyle’s law.
Each line of the graph
is called isotherm.
B. Charle’s law
The volume of a given mass of a gas increases or decreases by 1/273 of its volume at  for every one degree rise or fall in temperature at constant pressure.
Mathematically
or  constant (at constant P and m)
Or  (for two different conditions at constant P).
Graphical representation
 The graph of
Volume vs
temperature is a
straight line and on
extending to zero
volume, each line
intercepts the
temperature axis
at  
Each line of graph
Is called isobar.

Note
Absolute zero is the theoretically possible temperature at which the volume of the gas becomes zero. It is equal to 0 K or C. Temperature in Kelvin scale or absolute scale Charle’s law is not applicable to liquids. All gases obey Charle’ law at very low pressure and high temperature.
C. Gay Lussac’s law
The Pressure of a given mass of a gas is directly proportional to the Kelvin temperature at constant volume.
Mathematically
 (At constant volume)
Graphical representation
Pressure vs volume graph at constant volume is a straight line. Each line of this graph is called isochore.










EXAMPLE
EXAMPLE:1 A gas cylinder containing cooking gas can withstand a pressure of 14.9 bar, The pressure gauge of the cylinder indicates 12 bar at . Due to sudden fire in the building, the temperature starts rising. At what temperature will the cylinder explode?
A. B.
C. D.
SOLUTION The gas cylinder containing cooking gas can withstand a pressure of  bar
Let temperature
The pressure gauge of the cylinder indicates  bar
Temperature  K
 Volume remains constatnt.
According to Gay-Lussac’s Law

 Cylinder will explode at a temperature
D. Avogadro’s law
Equal volume of all gases under similar conditions of temperature and pressure contains equal number of molecules.
Mathematically: For each gas, at constant T and P,
V N. Where V=Volume of gas,
Where  is Avogadro number, therefore V
Combined gas law or ideal gas equation
PV=nRT


R is universal gas constant, value of R changes with change in units.
Value of universal gas constant R in different units
Sr.No.
R(Univesal Gas Constant) Unit of
  P V
1. atm L
2. 82.1 mL atm atm mL
3. erg dyne
4. 1.987 cal
5. Pa or
Partial pressure of any component (say A)

Where  mole fraction of A component and  pressure of component when present alone in the same volume.
E. Dalton’s low of partial pressures
If two or more gases which don’t react chemically are enclosed in a vessel, the total pressure of the gaseous mixture is equal to the sum of the partial pressures that each gas will exert when enclosed separately in the same vessel at constant temperature.

Pressure exerted by saturated water vapours is called as aqueous tension.
Aqueous tension.
Note
Diffusion of gas
It is the process of intermixing of gases irrespective of the density relationship and without the effect of external agency.
Red Alert
F. Graham’s law of diffusion
Under similar conditions of temperature and pressure, the rates of diffusion of gases are inversely proportional to the square root of their densities.
Graham’s Law of diffusion:

Since the molar mass of the gas is twice its density,

The Grahma’s law of diffusion may also be started as: under similar condition of temperature and pressure, the rates of diffusion of gases are inversely proportional to the square roots of their molar masses.

=
Effusion: The passage of gases through a small hole under pressure is known as effusion. Graham’s law of diffusion is also applicable to effusion.
EXAMPLE
EXAMPLE:2 An unknown gas diffuses 4 times as fast as oxygen, name the gas
⦁ 1 B. 2
C. 4 D. 3
SOLUTION:
Molar mass of gas
Molar mass of
By Graham’s Law of diffusion=
; Squaring both sides, 16
M (gas
Because molar mass is 2, the gas is hydrogen.
Check Your Grasp
1. Gas equation PV is obeyed by
A. only isothermal processes
B. only adiabatic processes
C. both (A) an (B)
D. none of these.
2. “Equal volumes of all gases at the same temperature and pressure contain equal number of particles.” This statement is a direct consequence of

A. perfect gas law B. partial law of volume
C. Charles’s law D. ideal gas equation
3. The root mean square velocity of an ideal gas at constant pressure varies with density (d) as
A. B. d
C. D. 1
3. KINETIC GAS EQUATION
PV
Here P = Pressure
V = Volume
N = Number of molecules
Square of the root mean square velocity
A. Postulates of kinetic molecular theory of gases:
A. The gases are made up of small particles (atoms or molecules). So the actual volume of the molecules is negligible in comparison to the total volume. Thus gases can be compressed greatly.
B. There is no force of attraction among the particles of gases.
C. The particles of gases are always in constant motion.
D. The pressure exerted by a gas is due to collision of the particles with the walls of container.
E. The collision of gas molecules are perfectly elastic in nature.
F. The particles of the gases have different speeds and hence different kinetic energies.
G. The kinetic energy of gas molecules is directly proportional to the absolute temperature.
B. Relation between average kinetic energy of a gas and temperature:
Here  Aaverage kinetic energy
     Number of moles of the gas
T = Kelvin temperature
R = Universal gas constant
i. At absolute zero (i.e.T=0K), kinetic energy is zero. In another words, thermal motion ceases completely at absolute zero.
ii. The average translational kinetic energy of one molecule of an ideal gas will be given by

Here, k = Known as Boltzmann constant
Red Alert
4. DISTRIBUTION OF MOLECULAR SPEEDS (OR VELOCITIES)
It is denoted by
Average speed :
It is denote by v.


Root mean square velocity
It is denoted by  .

Relation between the different types of speeds
i. Average or mean velocity  velocity
ii. Most probable velocity ( velocity.
iii.
iv.
Where  is the root mean square velocity.

5. DEVIATION OF GASES FROM IDEAL BEHAVIOUR
Deviation from ideal gas behaviour is expressed in. terms of compressibility factor Z, which is given as
TRICK
i. When  this implies that gas is more compressible.
ii. When  this implies that the gas is less compressible.
iii. When Z=1, the gas is an ideal gas.
iv. Z is always greater than 1 for  However, if the temperature is sufficiently low (below, the graph for  can also appear like  and .
Note
i. For  and He, Z is more than 1. This means that gases are less compressible than expected from ideal gas behaviour.
ii. For ,  and  at low pressures. While  1 at high pressure.
iii. At ordinary pressures  Z is almost close to one. It implies that gases tend to become ideal at this pressure.
A. Effect of temperature
Deviation from the ideal gas behaviour goes on decreasing as the temperature of the gas increases. i.e., gases behave ideally at high temperature.
i. Boyle’s temperature: Temperature at which a real gas behave like an ideal gas over appreciable range of pressure is called Boyle’s temperature. For examples:
1. For   the Boyle’s temperature is 323 K
2. For  the Boyle’s temperature is 108 K
B. Effect of pressure
Deviation from the ideal gas behaviour goes on increasing with increase in pressure i.e. gases behave ideally at low pressure.
C. Causes of deviations
The causes of deviation are two wrong assumptions in kinetic gas theory. The assumptions are
i. The Volume occupied by the gas molecules is negligible as compared to the total volume of the gas molecules is not negligible.
ii. The forces of attraction and repulsion among the gas molecules are negligible. But actually, gas molecules attract each other.
Check Your Grasp
4. A gas will approach ideal behaviour at
A. low temperature and law pressure
B. low temperature and high pressure
C. high temperature and low pressure.
D. high temperature and high pressure
5. The compressibility factor for an ideal gas is
A. 1.5 B. 1.0
C. 2.0 D.
6. Gas deviates from ideal gas nature because molecules
A. are colourless B. attract each other
C. contain covalent bond D. show Brownian movement
6. CORRECTION FOR DEVIATIONS (VANDER WAAL’S EQUATION)
for n moles.
Where ‘a’ and ‘b’ are van der Waals’s constants.
‘a’ is a measure of intermolecular forces of attraction in a given gas and ‘b’ is a measure of effective volume occupied by the gas molecule i,e. excluded volume or covolume. Van der Waal’s equation is true for real gases.
Unit of van der Waal’s costant ‘a’:  atm
Unit of van der Waal’s constant ’b’:
Van der Waal’s equation in different conditions
i. At low pressure and high temperature PV=RT
ii. At high pressure
iii. At low pressure, van der Waal’s equation is written as
or
Where Z is known as the compressibility factor.
Check Your Grasp
7. Van der Waal equation is true for
A. Ideal gas B. real gas
C. gaseous substance D. none of the above
8. The van der Waal’s equations of state reduces itself to the ideal gas equation at
A. high pressure and low temperature
B. low pressure and low temperature
C. low pressure and high temperature
D. high pressure and high temperature
7. LOQUEFACTION OF GASES
A. Critical temperature
It is the temperature above which a gas cannot be liquefied however large its pressure may be.
For  gas, the critical temperature

B. Critical pressure
It is the pressure of the gas corresponding to the critical temperature.  
C. Critical volume
It is the volume occupied by one mole of a gas under critical temperature and pressure.
D. Methods of liquefaction
i. In case of gases like  etc the critical temperature are above room temperature  These gases can be liquefied at room temperature by applying pressure alone.
ii. For gases like  etc, the critical temperatures are very low. The gas has to be cooled to critical temperature then pressure is applied to cause the liquefaction of the gas. These gases are called permanent gases.
E. Joule Thomson effect
When a gas after compression is allowed to pass through a fine orifice from a region of high pressure to a region of low pressure, the cooling is caused. The tendency of liquefaction of a gas is related to the value of van der Waal’s constant ‘a’ . Greater the value of ‘a’ , more will be the tendency of a gas to get liquefied. ‘a’ is the measure of intermolecular forces of attraction. The decreasing order of liquefaction of some gases is:
Gas
‘a’   6.71 6.49 4.17 3.59 1.39 1.36

LIQUID STATE OF MATTER
1. KINETIC MOLECULAR THEORY OF LIQUIDS
⦁ Liquids are composed of particles called molecules.
⦁ The intermolecular forces of attraction among the molecules in a liquid are quite appreciable.
⦁ As compared to the gas, the molecules in a liquid are close to each other.
⦁ The molecules are in constant random motion.
⦁ The average kinetic energy of molecules in a liquid is directly proportional to the absolute temperature.
2. PROPERTIES OF LIQUIDS  
A. Volume
A liquid has a definite volume but no definite shape. This is because intermolecular forces of attraction are strong as compared to the gas. Thus, the molecules in a liquid are not free to occupy any volume available to them.
B. Density
Since the molecules in the liquid state are more closely packed as compared to the gaseous state. Hence, density of liquid is more as compared to the gas.
For example: Density of water is maximum at  i.e. 1g/cm3. At 373 K, the density of water is 0.958 g/cm3. Density of water vapours, under similar conditions is 0.000588 g/cm3. This means that density in the liquid state of water is about 1000 times higher as compared to the gaseous state.
C. Compressibility
Liquids are much less compressible than the gases. This is because the intermolecular distance is less as compared to the gases. There is a little for the molecules to come closer. Hence, the liquids are almost incompressible.
D. Diffusion
Diffusion is the movement of the solute particles from higher concentration to the lower concentration in a particular medium. Liquids diffuse at a slower rate as compared to the gases.
E. Evaporation
i. It is the process of conversion of a liquid into its vapours at room temperature.
All molecules in the liquids don’t have same kinetic energy. A certain fraction of the molecules present at the surface of the liquid will have high kinetic energy. This energy is enough to overcome the attractive forces of the neighbouring molecules. They will escape into the space and will appear as vapours.
Red Alert
ii. Evaporation causes cooling: Cooling is caused during exploration. During evaporation, the molecules having higher kinetic energy escape from the surface of the liquid. Therefore, the average kinetic energy of the rest of the molecules decreases. Since, the temperature of the liquid is proportional to the average kinetic energy. Hence temperature gets lowered. Therefore, cooling is caused during evaporation.
ii. Factors affecting the rate of evaporation
1. Nature of the liquid: Greater the Magnitude of the intermolecular forces of attraction, lesser will be the rate of evaporation.
2. Temperature: Rate of evaporation increases with increase in temperature.
3. Surface area: The greater the surface area, the more will be the rate of evaporation.
TRICK  
Rate of evaporation  Temperature
Surface area

F. Heat of vaporisation
It is the quantity of heat required to evaporate a certain mass of given liquid at a constant temperature.
Molar Heat of vaporisation : It is the quantity of heat required to evaporate one mole of given liquid at a constant temperature .
G. Vapour pressure
It is the pressure exerted by the vapours of the liquid in equilibrium with liquid at a given temperature.
Factors affecting vapour pressure
i. Nature of liquid : Vapour pressure decreases with increase in the magnitude of the intermolecular forces.
ii. Temperature of the liquid : Vapour pressure of a liquid increases with the rise in temperature.
TRICK
Vapour presence
  Temperature
H. Boiling point
The temperature at which the vapour pressure of a liquid becomes equal to the atmospheric pressure is called boiling point.
i. Boiling point of a liquid increases with increase in external pressure.
ii. Liquids having weak attractive forces have low boiling points and vice versa.
i. Surface tension of liquid
The temperature of a boiling liquid always remains constant Surface tension is the work that must be done to increase the free surface area of any liquid by one unit at constant temperature. It is presented by gamma () . The units of surface tension is  or .
i. Factors affecting surface tension:
1. Temperature: Surface tension decreases with rise in temperature.
2. Nature of liquid: Surface tension increase with increase in the magnitude of intermolecular forces of attraction.
ii. Measurement of surface tension: Surface tension () is measured with the help of stalagmometer provided with a fine capillary.
Principle: Surface tension of a liquid at a particular temperature is directly proportional to the mass (m) of the spherical drop falling from the capillary of the
Stagmometer held in vertical position.
iii. Important consequences of surface tension
1. Spherical shape of liquid drops: Surface tension tries to decrease the surface of a liquid to the minimum. Since, sphere has the minimum surface area for a particular volume of the liquid. Hence, the drops of liquid are spherical.
2. Capillary action: If the capillary tube is dipped in a liquid which wets glass, the liquid rise into a capillary tube to a certain height. This is known as capillary action. The inward pull acting on the surface molecule pushes the liquid into the capillary tube.
iv. Surfactants : These are surface active agents which decrease the surface tension of water e.g. soaps and detergents.
Red Alert
J. Viscosity
It is resistance offered by one layer of a liquid to the flow of another layer of the liquid.
F = A dv/dx
  F = Force
= Coefficient of viscosity
A = Area of surface in contact (A)
Velocity gradient
Coefficient of viscosity () is the force applied per unit area in order to maintain a unit relative velocity between the two layers of a liquid at unit distance apart.
i. Units of viscosity: CGS unit of viscosity is poise (P).
1 poise  
SI unit of viscosity is
1 poise
ii. Factors affecting viscosity
1. Temperature: Viscosity decreases with increases in temperature.
2. Pressure: Viscosity increases with increase in pressure.
3. Nature of Liquid: Viscosity increases with increase in the magnitude of intermolecular forces of attraction.
TRICK
Viscosity
Pressure
Magnitude of intermolecular forces
Check Your Grasp
9. When temperature is increased, surface tension of water
A. increases B. B. Decreases
C. remains constant D. show irregular behaviour
10. When the temperature is raised, the viscosity of the liquid decreases. This is because of
A. decreased volume of solution
B. increase in temperature increases the average kinetic energy of molecules which overcomes the attractive force between them.
C. decrease in covalent and hydrogen bonds forces
D. Increase attraction between molecules.
11. The relationship between coefficient of viscosity of a liquid and temperature can be expressed as
A. B.
C. D.
12. Which of the following statement is correct if intermolecular forces in liquids A, B and C are in order A<B<C?
A. B evaporates more readily than A
B. B evaporates less readily than A
C. A and B evaporates at the same rate
D. A evaporates more readily than C