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STATES OF MATTER

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Intermolecular forces

• Intermolecular forces are the forces of attraction and repulsion between interacting particles.

• Attractive intermolecular forces are known as van der waals forces.

• Only a few elements can participate in hydrogen bond formation.

• Intermolecular forces are further divided into 3 forces.

dispersion or London forces

dipole-dipole forces

dipole-induced dipole forces

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Dispersion forces or London forces

CHARECTERISTICS OF DISPERSION OR LONDON FORCES.

• London forces are exhibited by non polar molecules because of temporarily correlated movements of electrons in interacting molecules.

• This force is a temporary force.• These forces are always attractive.• The interaction energy is inversely proportional to the sixth

power of the distance between two interacting particles.• These forces are important at only very short distances.• Their magnitude depends upon the polarisability of the particle.

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DIPOLE-DIPOLE FORCES• Dipole dipole forces act between the molecules possessing

permanent dipole.• Ends of dipole possess "partial charges”.• Partial charges are always less then the unit electronic charge.• This interaction is stronger than London forces but is weaker

than ion-ion interaction only because partial charges are involved.

• The attractive forces decrease with the increase of distance between the dipoles.

• Interaction energy between stationary polar molecules is

proportional to1/r3

interaction energy between rotating polar molecules is double of stationary polar molecules where r is the distance between the polar molecules.

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Dipole induced dipole forcesCHARECTERISTICS OF DIPOLE-INDUCED DIPOLE FORCES.

• This type of attractive forces operate between polar molecules having permanent dipole and the molecules lacking permanent dipole.

• The interaction energy is inversely proportional to the sixth power of the distance between two interacting particles.

• Induced dipole moment depends upon the dipole moment present in the permanent dipole and the polarisability of the electrically neutral molecule.

• Molecules of larger size can be easily polarised.• High polarisability increases the strength of attractive

interactions.

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THERMAL ENERGY• Thermal energy is the energy of the body arising from the

motion of its atoms and molecules.• It is directly proportional to the temperature of a substance.• It is the measure of the average kinetic energy of the particles

of matter and is thus responsible for the movement of particles.• The movement of particles is called thermal motion.• Intermolecular forces tend to keep the molecules together but

thermal energy of the molecules tends to keep them apart.• The three states of matter are a result of balance between the

intermolecular forces and the thermal energy of the molecules.

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THE GAS LAWS

• There are 4 gas laws we are going to study about :-

Boyle’s law

Charles law

Lussac’s law

Avagadro’s law

Dalton's law of partial pressures

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Boyle’s law

• At constant temperature , the pressure of a fixed amount of gas varies inversely with its volume

• That is

Therefore

On rearranging we get :

we know that :

⇒ =

•  •  

=

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Charles law relationship

• For a fixed mass at constant pressure , volume of a gas increases on increasing temperature and decreases on cooling.

• They found out that for each degree rise in temperature volume of a gas increased by of the original volume of the gas at 0 degree Celsius . Thus if the volume of the gas at 0 degree and at “t” degree Celsius are VO and Vt

⇒

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• ⇒

• At this stage we can define a new scale of temperature such that t degree Celsius on new scale is given by

and 0 degree Celsius will be given by

This new temperature scale is called the Kelvin temperature scale or absolute temperature scale.

This scale is also called the thermodynamic scale of temperature.If we write = 273.15+t and =273.15 in the equation we get

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⇒

Thus we can write this equation as :-

⇒

⇒ = constant =

thus we can write that

Thus the value of is determined by the pressure of the gas, its amount and the units in which volume V is expressed.

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• This is the mathematical representation of Charles law which states that pressure remaining constant , the volume of a fixed mass of a gas is directly proportional to its absolute temperature.

• Each line in the volume vs. temperature graph is called an isobar.

• The lowest hypothetical or imaginary temperature at which all gas are supposed to occupy zero volume is called absolute zero.

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Gay lussac’s law(pressure temperature relationship)

According to lussac:- At constant volume, pressure of a fixed amount of a gas varies directly with the temperature. That is:-

This relationship can be derived from

both boyle’s law and Charle’s law.

Each line in this graph is called an

isochore.

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Avagadro’s law

• It states that equal volumes of all gases under the same condition of temperature and pressure contain equal number of molecules .

• We can say that the volume of the gas depends directly to the number of molecules in it.

• We know that:-• ⇒• We know that one mole is equal to molecules and

is called the Avogadro's constant.

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How to calculate the number of moles in a gas ?

• Number of moles of a gas can be calculated as :-

• Where ‘m’ is equal to the mass of the gas under investigation and ‘M’ is the molar mass.

Therefore

This equation can be rearranged as :-

Here ‘d’ is the density of the gas. Density is directly proportional to its molar mass

Hence this law that follows boyle’s law charles law and Avogadro's law is called an ideal gas

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THE IDEAL GAS EQUATION

• The three laws combined in one single formula is called the ideal gas equation

• According to this:- boyle’s law =

Charles law:

Avogadro's law:-

Combining the equation we get a equation which is called the ideal gas equation.

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• Where R is called the proportionality constant and hence we obtain:-

• Where R is called the gas constant and therefore also called the universal gas constant

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• At STP the value of R is 8.314 K/mol and this equation is called equation of state.

• Now we know that

and hence we get :-

This equation is called the combined gas law.

As it is containing 5 variables and it is also known as the special equation of quartz Lassaigne's.

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Density and molar mass of a gaseous substance

• Ideal gas can be arranged as follows:-

• Replacing ‘n’ by we get :-

• Now m/V=d so we can replace it.⇒

• So for calculating molar mass of a gas we use the formula:-

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Dalton’s law of partial pressures

• It states that that the total pressure exerted by a mixture of non reactive gases is equal to the sum of the partial pressures of individual gases.

• In a mixture of gases, the pressure exerted by an individual gas is called its partial pressure

• Mathematically.• Pressure of a dry gas can be calculated by subtracting vapour

pressure of water from the total pressure of the moist gas which contains water vapour too.

Pressure exerted by a saturated water vapour is called aqueous tension.

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Partial pressure in terms of mole fraction.

• Suppose at temperature T 3 gases enclosed in the volume in the volume V exert partial pressures then

, ,

Where are the number of moles of these gases and the expression will

be:-

=

=

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• On dividing by we get

=

= where

There fore

Where and are the partial pressures of the gases., we

can use these useful formulae to find out partial pressures of individual gases

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Behaviour of real gases : deviation from ideal gas behaviour

• pV value decreases after an increase in pressure and reaches to a minimum value characteristic of gas. After the pV value starts increasing .the curve then crosses the line for ideal gas and after that shows positive deviation continuously . It is thus found that real gases do not follow ideal gas equation perfectly under all the conditions.

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• Deviation from ideal behaviour also becomes apparent when pressure vs. volume plot is drawn. The pressure vs volume plot of experimental data(real gas) and that theoretically calculated from boyle’s law(ideal gas) should coincide. It is apparent that at a very high pressure the measured volume is more than the calculated volume. At low pressures, measured and calculated volumes approach each other.

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• Real gases show deviations from ideal gas law because molecules interact with each other. At very high pressures molecules of gases are very close to each other. Molecular interactions start operating. At high pressure molecules do not strike the walls of the container with full impact because these are dragged back by the other molecules due to molecular attractive forces.

• Thus the pressure exerted by the gas is lower than the pressure exerted by the ideal gas.

observed correction term.

pressure

Here ‘a’ is a constant term.

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• Repulsive forces also become significant. The volume occupied by the molecules because instead of moving in volume ‘V’ these are now restricted to (V-nb) where ‘nb’ is approximately the total volume occupied by the molecules themselves. Here ‘b’ is a constant term. Having taken into account the corrections for pressure and volume , we can rewrite the equation as :-

• This equation is known as the van de Waals equation. Where ‘n’ is number of moles of the gas. Constants a and b are called van der Waals constants and their value depends upon the characteristic of the individual gases.

• The value of ‘a’ is a measure of magnitude of intermoleculer attractive forces within the gas and is independent of temperature and pressure.

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• The deviation from ideal behaviour can be measured in terms of compressibility factor ‘Z’, which is the ratio of the ideal gas that is :-

For an ideal gas Z = 1 at all temperatures and pressures because of the ideal gas relationship, the graph Z vs p will be a straight line parallel to the pressure axis. For gases which deviate from ideality, value of Z deviates from unity.

• At very low pressures all gases have Z=1 and behave as an ideal gas. At high pressures Z>1, these gases are difficultt to compress, whereas Z<1 at intermediate pressures.

• Thus gases show ideal behaviour when the volume occupied is large so that the volume of the molecules can be neglected in comparison to it.

• The temperature at which a real gas obeys all ideal gas laws over an appreciable range of pressure is called boyle temperature or boyle’s point.

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• Boyle’s point depends upon its nature , above boyle’s point real gases show positive deviations from their ideality and Z values are greater than 1. The forces of attraction between the molecules are very feeble. Below Boyle temperature real gases first show decrease in Z value with increasing pressure, which reaches a minimum value. On further increase in pressure, the value of Z increases continuously.

• Derivation:-

if the gas shows an ideal behaviour then, , On putting this value of in the equation we get an equation :-

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• We can see that compressibility factor is actually the ratio of actual molar volume of a gas to the molar volume of it, if it were an ideal gas at that temperature and pressure.

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Liquifaction of gases• The following figure shows the isotherms of carbon dioxide .he

plotted the isotherms of carbon dioxide on various temperatures , later it was found that all real as behaved like carbon dioxide.

• it was noticed that at very high temperatures the gases could not be liquified.

• At 30.98C carbon dioxide remains a gas upto 73 degree Celsius.

At 73 atmospheric pressure liquid carbon dioxide appears for the first time .

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The temperature 30.98oC is called critical temperature.( ) of carbon dioxide.

This is the highest temperature at which a liquid carbon dioxide can be observed.

Volume of one mole of a gas at critical temperature is called critical volume.( )

The pressure at this temperature is called the critical pressure.

( )

The critical temperature, pressure , and volume are called critical constants.

A gas below the critical temperature can be liquified by applying pressure and is called vapour of the substance.

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The liquid state • Vapour pressure:-

Vapour pressure at the stage where an equilibrium is established between liquid phase and vapour phase is known as equilibrium vapour pressure or saturated vapour pressure.

The temperature at which vapour pressure of a liquid is equal to the external pressure is called the boiling temperature at that pressure.

At 1 atm pressure boiling temperature is called normal boiling point.

If pressure is 1 bar then the boiling point is called standard boiling point.

The temperature when the density of a liquid and vapours become the same that is the boundary between liquid and vapour disappears is called critical temperature.

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SURFACE TENSION• When a molecule experiences equal intermolecular forces from

all sides ,the molecule itself does not experience a net force and this phenomenon is called surface tension.

• Liquids tend to minimize their surface area.• The molecules on the surface experience a net downward force

and thus have more energy than the molecules in the bulk.• If surface of the liquid is increased by pulling a molecule from

the bulk attractive forces will have to be overcome.• The energy required to increase the surface area of the

liquid by one unit is defined as the surface energy.• Its SI unit is J/ • Surface tension is defined as the force acting per unit

length perpendicular to the line drawn on the surface of the liquid.

• It is denoted by a Greek letter (ᵞ)

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It has the dimensions as kg s-2 and in the S.I units it can be expressed as Nm-1

The lowest energy state of the liquid will be when surface area is minimum.

Spherical shape satisfies this condition , that is why mercury drops are spherical in shape. This is the reason that sharp glass edges are heated for making the glass smooth.

On heating the glass melts and the surface melts and the surface of the liquid tends to take the rounded shape at the edges , which make the glass edges smooth

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Viscosity• Viscosity is the measure of resistance to flow which arises

due to the internal friction between layers of fluid as they slip past one another while liquid flows.

• When a liquid flows over a fixed surface, the layer of molecules in the immediate contact of surface is stationary. The velocity of upper layers increases as the distance of the layers from the fixed layer increases.

• The type of flow in which there is regular gradation of velocity in passing from one layer to another is called laminar flow.

• If the velocity of the layer at a distance dz is changed by a value du then velocity gradient is given by du/dz. A force is required to maintain the flow of layers. This force is proportional to the area of contact of layers and the velocity gradient i.e

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• We know that

(since A= du/dz)

And we know that ;-

Therefore we can write the following equation as combined as:-

⇒

WHERE THE PORPORTIONALITY CONSTANT IS CALLED THE COEFFICIENT OF VISOCSITY.

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