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States Of Matter (Gases and Liquids), A particular substance may exist in solid, liquid or gaseous states under different, conditions of temperature and pressure. The difference in the physical properties of, a substance in different states is due to the difference in the inter molecular forces, of attraction., Vander Waal’s Forces or intermolecular forces, Intermolecular forces are the forces of attraction and repulsion which exist among, the molecules of a substance. It is different from electrostatic forces. Greater the, strength of intermolecular forces, higher is the boiling and melting points of the, substance., These forces include:, 1., 2., 3., 4., , Dipole-dipole forces, Dispersion or London forces, Instantaneous dipole-induced dipole forces, Ion-dipole interactions, , Dipole-dipole forces: These forces of attraction occur among polar molecules, which have permanent dipoles in which positive pole of the molecule attracts the, negative pole of the other molecule. For example : HCl, HBr, etc. The dipoledipole interactions are stronger., , Dipole-induced dipole interaction: This type of attractive forces operate between, polar molecules having permanent dipole and non-polar molecules having no, permanent dipole. For example: the mixture of acetone and carbon tetrachloride.

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Instantaneous dipole induced dipole interaction: At any given moment, the electron, density of a particle can be unsymmetrical with more negative charge on one side, than on the other. For that particular instant, the particle is dipole and we call it an, instantaneous dipole. This particle with instantaneous dipole causes the electron, density in its neighbouring atom to become a dipole known as induced dipole., These two atoms of temporary dipoles now attract each other., , Ion-dipole interaction: This is the attraction between an ion (cation or anion) and a, polar molecule. For example: when NaCl is dissolved in water, the polar water, molecules are attracted towards Na+ and Cl- ions. The strength of this interaction, depends upon the charge and size of the ion and the magnitude of dipole moment, and size of the polar molecules., Thermal Energy and intermolecular forces, Thermal energy is the heat energy of a substance. It is responsible for the, molecular motions. It is directly proportional to the temperature. The existence of, three states of a matter is due to the balance between thermal energy and, intermolecular force.

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Gas laws:, Boyle’s Law (Pressure-Volume Relationship), Temperature remaining constant, the product of pressure and volume of a given, mass of a gas is constant., P ∝, , 1, 𝑉, , (when temperature is kept constant), , PV = k (constant), The above expression may also be expressed as, P1V1 = P2V2 = constant, , (at constant temperature), , The value of constant depends upon the amount of the gas and the temperature., Boyle’s Law can be verified by any one of the shown ways graphically.

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Relation between Pressure and Density of a gas, Suppose at a constant temperature and for a given mass (m) of the gas at pressure, P1 and volume V1, the density of gas is d1. Similarly at pressure P2 and volume V2,, the density of gas is d2., V1 =, , 𝑚, , and, , 𝑑1, , V2 =, , But according to Boyle’s law,, , 𝑚, 𝑑2, , P1V1 = P2V2, , Putting the above value in this equation, 𝑃1𝑚, 𝑑1, , 𝑃2𝑚, , =, , 𝑑2, , or, , 𝑃1, 𝑑1, , =, , 𝑃2, 𝑑2, , P α d, , or, , At higher altitudes, the air becomes less dense due to low atmospheric pressure., Oxygen becomes insufficient for breathing. This causes headache and uneasiness., It is known as altitude sickness., , Charle’s law(Volume-Temperature Relationship), According to this law, “ At constant pressure, the volume of a given mass of a gas, increases or decreases by 1/273 of its volume at 0˚C for each one degree rise or fall, in temperature”., Let the volume of a given mass of a gas be V0 at 0˚C. The temperature is increased, by t˚C and the new volume becomes Vt. Thus,, Vt = V0 +, Vt = V0 (, , 𝑉0, 273, , ×t, , 273 × 𝑡, 273, , = V0 ( 1 +, ), , 𝑡, 273, , ), , (i), , A new scale called Kelvin scale or absolute scale was introduced.

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At absolute zero or -273˚C, the volume of the gas would become zero. At this, temperature, no substance exists in the gaseous state. The temperature in absolute, is obtained by adding 273 to the temperature in degree celcius., K = (˚C + 273), By substituting T for 273 + t and T0 for 273 in equation (i), Vt =, , 𝑉0 × 𝑇, 𝑇0, 𝑉, 𝑇, , or, , 𝑉1, 𝑇, , =, , 𝑉0, 𝑇0, , = Constant, , The Charle’s law may be stated as follows, “ The volume of a given mass of a gas, at constant pressure is directly proportional to its absolute temperature”., V ∝ T, , (At Constant pressure)

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Avogadro’s Law (Volume-Amount Relationship), Avogadro’s law states that “Equal volumes of all gases under similar conditions of, temperature and pressure contain equal number of molecules”., V ∝ 𝑛, , Mathematically,, Or, , V = kn, , The number of molecules in one mole of a gas is 6.02 × 1023 and is known as, Avogadro’s constant. Volume occupied by one mole of the gas is called molar, volume. Molar volume of gas under different conditions can be summarised as:, i), ii), iii), iv), , At 1 atm pressure and 0˚C, the molar volume is 22.4 L, At 1 bar pressure and 0˚C, the molar volume is 22.711 L, At 1 bar pressure and 25˚C, the molar volume is 24.789 L., At standard ambient temperature and pressure, ie., at 1 bar pressure and, 298.15 K,the molar volume is 24.8 L., , Ideal Gas Equation, Ideal gas equation can be obtained by combining Boyle’s law, Charle’s law and, Avogadro’s law. This equation gives the simultaneous effect of pressure and, temperature on the volume of a gas., On combining Boyle’s, Charle’s and Avogadro’s law, we get,, V ∝, , 𝑛𝑇, 𝑃, , or, , V ∝, , 𝑅𝑛𝑇, 𝑃, , (Here R is proportionality constant or universal gas constant), On rearranging the above equation, we get,, PV = nRT

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Where Ptotal is the total pressure of the mixture and P1, P2, P3, etc are the partial, pressures of components respectively., Graham’s Law of Diffusion and Effusion, Diffusion is the spontaneous mixing of the molecules of one gas with that of, another gas whereas effusion is the gradual movement of gas movement through a, very tiny hole into a vacuum., According to Graham’s law, “At constant temperature and pressure, the rate of, diffusion or effusion of a gas is inversely proportional to the square root of its, density”.ie.,, r ∝, , 1, √𝑑, , where r = rate of diffusion of gas, d = density of gas, For two different gases,, R1 ∝, Combining these, we get :, i), , 1, √𝑑1, 𝑟1, 𝑟2, , r2 ∝, , and, 𝑑2, , = √, , 𝑑1, , or, , 𝑟1, 𝑟2, , 1, √𝑑2, , =√, , 2𝑑1, 2𝑑2, , 𝑀2, , = √, , 𝑀1, , Comparison of time of diffusion taken for the same volume of two gases.

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Behaviour of Real Gases: Deviation from Ideal Gas Behaviour, None of the known gases obey the gas laws or gas equation (PV = nRT) under all, conditions of temperature and pressure. These gases are calles real gases. They, tend towards ideality at low pressure and high temperature. CO2, SO2, NH3 etc.,, are soluble in water and are easily liquified. Such gases show larger deviation than, the gases like H2, O2, N2, etc., which are insoluble in water and are not easily, liquefied., Study of deviations from ideal behaviour, A convenient way of showing the deviation of gas from ideal behaviour is to plot, compressibility factor (Z =, i), ii), , 𝑃𝑉, 𝑛𝑅𝑇, , ) against pressure., , For an ideal gas Z = 1, Real gases have Z ≈ 1 at low pressure and high temperature

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iii), iv), , Z > 1 shows that it is difficult to compress the gas as compared to ideal, gas. In this case repulsive forces dominate., Z < 1 shows that the gas is easily compressible as compared to ideal gas., In this case, attractive forces are dominant., , Causes of deviation from ideal behaviour, Two assumptions of kinetic theory of gases were found to be faulty at high, pressure and low temperature. Under these conditions:, i), ii), , The force of attraction or repulsion between the molecules may not be, negligible., The volume occupied by the gas may be so small that the volume, occupied by the molecules may not be negligible., , Equation for the State of Real Gases (Vander Waal’s Equation)

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The decreased pressure P’ is proportional to density of gas near the wall and the, density of gas inside, ie.,, p ∝ 𝑑2, Again d ∝, , 𝑛, 𝑉, , for n moles of gas., p ∝, , 𝑛2, 𝑉2, , or p = an2 / V2, , Where ‘a’ is a constant depending upon the nature of the gas., Corrected pressure = P + an2 / V2, , Units and their significance of vander Waal’s constants,  Unit and significance of ‘a’

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a = pV2 / n2 = atm L2 mol-2 or bar dm6 mol-2, Greater the value of ‘a’, larger the intermolecular force of attraction among the, molecules.,  Unit and significance of ‘b’, V = nb, b=V/n=, , L / mol or dm3 mol-1, , Its value is a measure of the effective size of the gas molecules. The value of ‘b’ is, four times the actual volume of the molecules., Liquefaction of gases, Increase of pressure and decrease of temperature cause liquefaction of gases., Critical constants, It may be defined as the temperature above which it cannot be liquified however, high pressure may be applied on the gas. The pressure required to liquefy the gas at, the critical temperature is called critical pressure (Pc). The volume occupied by one, mole of the gas at the critical temperature and the critical pressure is called the, critical volume (Vc). For example, the critical constants of CO2 are:, Tc = 31.1˚C, Pc = 73.9 atm, Vc = 95.6 cm3 mol-1