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STATE OF MATTER, , STATE OF MATTER, , INTRODUCTION, Any substance that has mass and occupies space is called, Matter. Matter is composed of atoms or molecules. The, arrangement of these building blocks gives matter various, states, physical and chemical properties. The force of, interaction between these particles give matter its physical, properties based on which matter can be classified into solid,, liquid or gases. The force of interaction between atoms/, molecules is highest in solids and least in liquids., In this unit, we will learn more about these three physical, states of matter particularly liquid and gaseous states., , 1. INTERMOLECULAR FORCES, The forces of attraction existing among the molecules of a, substance (gaseous, liquid or solid) are called intermolecular, forces., Dipole-dipole, dipole-induced dipole and dispersion forces, are collectively called as van der Waals forces. Ion-dipole, and ion-induced dipole forces are not van der Waals forces., Further, hydrogen bonding is only a special type of dipole-, , Ion-dipole attractions between Na+ and H2O, molecules and Cl– ion and H2O molecules, 1.3 Ion-Induced dipole Interactions, A non-polar molecule may be polarized by the presence of, an ion near it, i.e., it becomes an induced dipole. The, interactions between them are called ion-induced dipole, interactions., , Ion-induced dipole attractions, between NO3 ion and I2 molecule, , For example, in the presence of nitrate ion (NO3 ) , iodine, , dipole attraction shown only by limited number of elements., The different types of intermolecular forces are :, 1.1 Dipole-Dipole Interactions, These forces of attraction occur among the polar molecules., Polar molecules have parmanent dipoles. The positive ple, of one molecule is thus attracted by the negative pole of the, other molecule., HCl in which chlorine being more electronegative acquires, a slight negative charge whereas the hydrogen end becomes, slightly positively charged. The dipole-dipole interactions, then take place among the HCl molecules :, , G, , G, , molecule (I2), which is non-polar, gets polarized as ( I I), as shown in fig., 1.4 Dipole-Induced dipole Interactions, , A non-polar molecule may be polarized by the presence of a, polar molecule (dipole) near it, thereby making it an induced, dipole. The interactions between them are then called dipoleinduced dipole interactions., , Dipole-induced dipole attractions, For example, noble gases get polarized in the presence of, polar molecules., 1.5 London forces or Dispersion forces, 1.2 Ion-Dipole Interactions, 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+ ion as, well as towards Cl– ion., , At any instant of time, the electron cloud of the molecule, may be distorted so that an instantaneous dipole or, momentary dipole (i.e., a dipole for a short while) is produced, in which one part of the molecule is slightly more negative, than the rest. The momentary dipoles induce dipoles in the
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STATE OF MATTER, neighbouring molecules. These are then attracted to each other. The forces of attraction between the induced momentary dipoles, are called London dispersion forces., , Forces of attraction between momentary dipoles and induced, dipoles (London forces) in helium atoms, , 2. INTERMOLECULAR FORCES VERSUS, THERMAL ENERGY, Whether a substance will exist as a solid or a liquid or a gas, is the result of competition between :, (i) intermolecular forces, i.e., the forces of interaction, between the molecules of that substance which try to, bring the molecules closer, and, (ii) thermal energy possessed by the molecules due to, temperature which results into the movement of the, molecules and hence tries to keep them apart., , There are majorly three variables for a given sample of a gas,, i.e. Pressure, Volume and Temperature (P, V and T). When, the values of these three parameters are fixed for a gas, we say, it to be in a fixed state., 4.1 Pressure, A force is exerted on the walls of the container due to the, collisions of the atoms/molecules. This force averaged per, unit area is called the pressure., 4.1.1 Measurement of pressure of a gas, The most common instrument used to measure the pressure, of a gas is called a barometer. Another instrument used to, measure pressure is manometer., 4.2 Volume, , 3. IDEAL GAS, An ideal gas is a hypothetical concept of matter and is treated, as a standard of comparison while studying the various, states of matter. There are various assumptions associated, with an ideal gas. The most notable of these assumptions, are:, , In case of rigid containers, the volume of the gas is same as, the volume of the container it is kept in. However, for containers, which can expand (e.g. balloon), the volume of the gas is, determined by the other two state functions and moles of the, gas taken., 4.3 Temperature, , Volume of the molecules are infinitely small and the force of, interaction between the molecules is zero, , The molecules of the gas undergo random motion colliding, with each other and the walls of the container, , Laws of classical mechanics are applicable on the molecules., 4. STATE OF A GAS AND STATE VARIABLES, “State” of a gas means the physical condition of the system., Certain variables are used to represent physical condition, of the gas which are termed as state variables., , Temperature is a measure of the amount of heat contained, in the gas. When the temperature of the gas equals the, surrounding temperature, no heat flows in or out of the gas, and the gas is said to be in a state of Thermal Equilibrium., 4.3.1 Measurement of Temperature, The instrument used to measure the temperature of a gas is, called a thermometer. There are three units used in measuring, temperature viz. oC, oF and K.
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STATE OF MATTER, , Pressure relations, , Temperature relations, , 1 atm = 1.0132 × 105 Pa, 5, , 1 bar = 10 Pa, , Volume relations, , 1.8 T (0C) = T (0F) – 32, , 1 L = 1000 mL, , 0, , 1 m3 = 1000 L, , T (K) = T ( C) + 273.15, , 76 cm Hg = 1 atm =760 mm Hg, , 1 mL = 1 cc, , 1 torr = 1 mm Hg, , 1 dm3 = 1 L, , 1 kPa = 1000 Pa, , 5. IDEAL GAS LAW, There are four laws which relate the state variables of a gas, in two states. These four laws are :, 5.1 Boyle’s Law (Pressure – Volume Relationship), It states that at constant temperature, the pressure of a fixed, amount (i.e. number of moles n) of gas varies inversely with, its volume. This is known as Boyle’s law Mathematically, , p v, , 1, (at constant T and n), V, , PV = constant, p1V1 = p2V2, Each line of the volume vs temperature graph is called isobar., 5.3 Gay Lussac’s Law (Pressure-Temperature Relationship), It states that at constant volume, pressure of a fixed amount, of a gas varies directly with the temperature. Mathematically,, , pvT, , , P, T, , constant, , Each line of pressure is temperature graph is called isochore., , Graph of pressure, p vs. Volume, V of, a gas at different temperature, Each curve corresponds to a different constant temperature, and is known as an isotherm., 5.2 Charles’s Law (Temperature - Volume Relationship), It states the pressure remaining constant, the volume of a, fixed mass of a gas is directly proportional to its absolute, temperature.
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STATE OF MATTER, , 5.4 Avogadro Law (Volume - Amount Relationship), It states that equal volumes of all gases under the same, conditions of temperature and pressure contain equal, number of molecules., Mathematically, , V v n where n is the number of moles of the gas., , 7. VARIATION OF THE IDEAL GAS EQUATION, Ideal gas equation can be rearranged as follows :, , n, V, , p, RT, , Replacing n by, , m, , we get, M, , 6. IDEAL GAS EQUATION, The above laws can be combined together in a single, equation which is known as ideal gas equation., At constant T and n; V v, , p, , Boyle’s Law, , At constant p and n; V v T Charles’s Law, , At constant p and T; V v n Avogadro Law, , m, MV, d, M, , p, RT, p, (where d is the density), RT, , pM, , dRT, , 8. DALTON’S LAW OF PARTIAL PRESSURES, , Thus,, nT, Vv, p, , , V, , R, , nT, p, , where R is proportionality constant. On rearranging the, equation we obtain, pV = n RT, This equation is called ideal gas equation., , R, , pV, nT, , It states that the total pressure exerted by the mixture of, non-reactive gases is equal to the sum of the partial pressures, of individual gases i.e., the pressures which these gases, would exert if they were enclosed separately in the same, volume and under the same conditions of temperature. In a, mixture of gases, the pressure exerted by the individual gas, is called partial pressure. Mathematically,, pTotal = p1 + p2 + p3 + ..... (at constant T, V), where pTotal is the total pressure exerted by the mixture of, gases and p1, p2, p3 etc. are partial pressures of gases., Partial pressure in terms of mole fraction, , R is called gas constant. It is same for all gases. Therefore it, is also called universal gas constant., , Suppose at the temperature T, three gases, enclosed in the, volume V, exert partial pressure p1, p2 and p3 respectively., then,, , Values of R :, (i) R = 8.314 J K–1 mol–1, (ii) R = 0.0821 L atm K–1 mol–1., , p, , n1RT, V, , p2, , n 2 RT, V, , p3, , n 3RT, V, , (iii) R = 2 cal K–1 mol–1., If temperature, volume and pressure of a fixed amount of, gas vary from T1, V1 and p1 to T2, V2 and p2 then we can, write, , p1V1, T1, , , p1V1, T, , nR and, , p 2V2, T2, , nR, , p2 V2, T2, , This equation is alos known as combined gas law., , where n1 n2 and n3 are number of moles of these gases., Thus expression for total pressure will be, pTotal = p1 + p2 + p3, , n, , RT, RT, RT, n2, n3, V, V, V
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STATE OF MATTER, , (n1 n 2 n 3 ), , Rate of diffusion v P (partial pressure), , RT, V, , Also, v 1/ M, , On dividing p1 by ptotal we get, p1, p total, , §, · RTV, n1, ¨, ¸, © n1 n 2 n 3 ¹ RTV, , n1, n1 n 2 n 3, , n1, n, , x1, , where n = n1 + n2 + n3, x1 is called mole fraction of first gas., , Therefore we can write:, Rate, r v P/ M, Rate of diffusion may be defined in various ways. It may be, number of moles transferred per unit time, Volume, transferred per unit time, distance travelled per unit time, and even pressure drop per unit time. While comparing the, rates of two gases, we should take similar definitions of, rate, it may be n/t, V/t or d/t., , Thus, p1 = x1 ptotal, , r2, r1, , Similarly for other two gases we can write, p2 = x2 ptotal and p3 = x3 ptotal, Thus a general equation can be written as, pi = xi ptotal, , 9. GRAHAM’S LAW OF DIFFUSION, Diffusion is a process of intermixing of gases. This is a, natural tendency of any gas to occupy the whole volume, available to it. So even without pressure difference gases, mix with each other. If the pressure difference is increased, the diffusion process becomes faster., Effusion is flow of a gas through small openings due to, pressure difference that is it is a case of fast diffusion., , P2, P1, , M1, M2, , Graham’s Law can be applied to diffusion and effusion both., , 10. KINETIC THEORY OF GASES, Assumptions or postulates of the kinetic-molecular theory, of gases are given below. These postulates are related to, atoms and molecules which cannot be seen, hence it is said, to provide a microscopic model of gases., (i), , Gases consist of large number of identical particles, (atoms or molecules) that are so small and so far apart, on the average that the actual volume of the molecules, is negligible in comparison to the empty space between, them., , (ii) There is no force of attraction between the particles, of a gas at ordinary temperature and pressure., (iii) Particles of a gas are always in constant and random, motion., , (a) Diffusion is mixing of gas molecules by random motion, under conditions where molecular collisions occur., (b) Effusion is the escape of a gas through a pinhole, without molecular collisions., According to Graham’s Law the rate of diffusion depends, on pressure and molecular weight of a gas. Rate of Diffusion, is directly proportional to Partial Pressure of the gas and, inversely proportional to the square root of molar mass of, the gas. That is, greater the pressure faster is the movement, of molecules and heavier the molecules, slower are their, movement., , (iv) Particles of a gas move in all possible directions in, straight lines. During their random motion, they collide, with each other and with the walls of the container., Pressure is exerted by the gas as a result of collision of, the particles with the walls of the container., (v) Collisons of gas molecules are perfectly elastic. This, means that total energy of molecules before and after, the collision remains same., (vi) At any particular time, different particles in the gas, have different speeds and hence different kinetic, energies., It is possible to show that though the individual speeds, are changing, the distribution of speeds remains, constant at a particular temperature.
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STATE OF MATTER, If a molecule has variable speed, then it must have a, variable kinetic energy. Under these circumstances, we, can talk only about average kinetic energy. In kinetic, theory it is assumed that average kinetic energy of the, gas molecules is directly proportional to the absolute, temperature., The important mathematical results from this Theory are ;, K.E. per mole = 3/2 nRT, K.E. per molecule = 3/2 kT, , 12. REAL GASES, In case of real gases two of assumption taken for ideal gases, become invalid or restricted only to some particular, conditions., (i), , We assumed that there are no interactions between, molecules of an ideal gas., (ii) We assumed that volume of the molecules of a gas is, negligible as compare to entire volume of gases., In case of real gases, we cannot ignore the molecular, interactions any more., , where R = 8.314 and k = R/NA = 1.38 × 10–23 J/K, , 11. Molecular Distribution of speeds, (Max well Boltzmann Distribution), , There are two types of forces of interaction :, Long Ranged attractive forces. &, , The Maxwell Boltzmann Distribution is a plot of fraction of, molecules in the gas sample vs. the speed of the gas, molecules. The distribution is shown below followed by, the salient features of the graph., , Short Ranged repulsive forces., When the molecules of a real gas are far apart, the interactive, forces are negligible. When the molecules are brought closer, to each other attractive forces start to develop and when the, molecules are too close they start repelling each other. The, following curve represents the variation of potential energy, of a system of two molecules of a real gas with distance, between them., , The graph shows that :, , The fraction of molecules having very low or very high, speeds is very less., , Most of the molecules have a speed somewhere in the middle,, this is called the most probable speed. (PMP), , The area covered between any two velocities is the number, of molecules in that velocity range., , The total area covered by the graph gives the total number, 13. COMPRESSIBILITY FACTOR, , of molecules in the sample and is constant., , There are two more molecular speeds defined for a sample, called average speed (uAVG) and root mean square speed, (uRMS), , The deviation from ideal behaviour can be measured in terms, of compressibility factor (Z)., Z = Vm(real)/Vm(ideal), , At very low pressures, there are no interactions between, uRMS, , 3RT, M, , uMP, , 2RT, M, , uAVG, , 8RT, SM, , NB : Always remember to take molecular mass in kg in the, above relations., It’s useful to remember the ratio of uMP : uAVG: uRMS, 1:1.128:1.224 for a given gas at the same temperature., , the molecules of the real gas and Z = 1., , At low or moderate pressure, there are attractive forces, dominant due to which a real gas is compressed to a greater, volume than expected, therefore Z < 1., , At high pressures, repulsions dominate and it is tough to, compress the real gas so it is compressed to smaller volume, Lakshya Educare
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STATE OF MATTER, , than expected thus Z > 1., Z is always 1 for ideal gases., For real gases Z = PV/nRT., , (iii) b { Relates to the volume occupied by the gas molecules, and takes into account the fact that the space actually, occupied by the molecules themselves is unavailable, for the molecules to move in and is given by :, b = 4 × volume of 1 mol of gas molecules., , 13.1 Variation of Z with P and T, The graph of compressibility factor, Z, with pressure for an, ideal gas is a straight line. However, for real gases the value, of Z is <1 for low pressures and then Z becomes >1 as, pressure increases and keeps on increasing. On increasing, the temperature the graph tends more towards Z=1 i.e. ideal, gas., , (iv) For a given gas Van der Waal’s constant ‘a’ is always, greater than ‘b’., (v), , The gas having higher values of ‘a’ can be liquefied, easily., 14.1 Applicability of Vanderwaal’s Equation, Under the conditions of high temperature and low/moderate, pressure and also under very low pressure Z = 1 and the, above equation becomes PVm = RT., 14.2 At low/moderate Pressure, The volume correction factor can be ignored and Z<1 where, the attractive forces dominate. The equation becomes:, §, a ·, Z ¨1 , ¸, © Vm RT ¹, , It can be concluded from the above graphs that real gas, follows ideal behavior at low pressure and high temperature., This does not mean that if you keep on increasing the, temperature a real gas will convert to ideal gas. There is a, characteristic temperature at which a gas follows ideal, behavior most closely; this is called Boyle’s temperature., , 14. VANDERWALL’S EQUATION, This equation was formulated taking into account correction, factors for pressure and volume into the ideal gas equation., , 14.3 At high Pressure, The volume correction factor cannot be ignored but the, pressure correction factor can be ignored. Z > 1 and the, equation is:, P (Vm – b) = RT, , Pb ·, §, Z ¨1 , ¸, © RT ¹, , 15. LIQUEFICATION OF GASES, P an, , 2, , V2, , V nb, , nRT, , Constants a and b are called vander waals constants and, their value depends on the characteristic of a gas., Note :, , 15.1 Critical Temperature, TC, L2 atm, L, ;b{, mol 2, mol, , (i), , Unit of a {, , (ii), , a { Relates to the forces interacting between the gas, molecules and modifies the pressure term., (‘a’ is high if the gas molecules have more attractive, forces), , When the molecules of a gas are brought closer to each, other, due to increase in the attractive forces, a stage may, be reached when the gas changes its phase to liquid. This, phenomenon is called Liquefaction of gases., , The characteristic temperature of a real gas above which it, cannot be liquefied., TC = 8a/27Rb, 15.2 Critical Pressure, PC, It is the minimum pressure required for liquefaction to take, place at critical temperature, PC = a/27b2
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STATE OF MATTER, When the external pressure is equal to 1 bar, the boiling, 15.3 Critical Volume, VC, , point is called standard boiling point of the liquid., , It is the volume occupied by one mole of a gas under critical, temperature and pressure., , Some Applications of Effect of External Pressure on Boiling, , VC = 3b, NB: The compressibility factor at critical point is constant, for all gases and has a value of 0.375., , point., (i), , Obviously, if the external pressure is higher, more heat will, be required to make the vapour pressure equal to the external, pressure and hence higher will be the boiling point. That is, , For liquefication of real gases, we can do either of the, following :, , why in hospitals, surgical instrumnts are sterilized in, , (1), , Increase the pressure on the gas, , a weight to cover the vent., , (2), , Decrease the temperature of gas but temperature is the, dominant factor and pressure assumes a secondary role., , autoclaves in which boiling point of water is raised by using, , (ii), , Similarly, if the external pressure is decreased, the boiling, point is lowered. This is the reason that a liquid boils at a, lower temperature on the top of a mountain (where pressure, , 16. LIQUID STATE, , is low) than on the sea shore. That is why at hills, use of, Intermolecular forces are stronger in liquid state than in, gaseous state., 1., , 2., , 3., , 4., , Properties of liquids : Molecules in liquids are so close that, there is very little empty space between them and under, normal conditions liquids are denser than gases., Molecules of liquids are held together by attractive, intermolecular forces. Liquids have definite volume because, molecules do not separate from each other., Molecules of liquids can move past one another freely,, therefore, liquids can flow, can be poured and can assume, the shape of the container in which these are stored., Vapour pressure of a liquid at any temperature may be, defined as the pressure exerted by the vapour present above, the liquid in equilibrium with the liquid at that temperature., Factors affecting vapour pressure, , pressure cooker is essential for cooking food., 5., , Surface tension is a characteristic property of liquids which, arises due to the fact that the molecules of the liquid at the, surface are in different situation than those in the interior of, the liquid., Surface tension of a liquid is defined as the force acting at, right angles to the surface along one centimetre length of, the surface. Thus, the units of surface tension are dynes, per cm (or Newtons per metre, i.e., N m–1 in the S.I. system., Some important Results, (i) Spherical shape of drops the lowest energy state of a, liquid will be when the surface area is minimum. Surface, tension tries to decrease the surface area of the liquid, to the minimum. The drops of a liquid (or the bubbles of, a gas) are spherical because for a given volume, a sphere, , Two important factors on which the vapour pressure of a, liquids depends are :, (a), , (b), , Nature of the liquid : If the intermolecular forces of attraction, in the liquid are weak, the molecules can easily leave the, liquid and come into the vapour phase and hence the vapour, pressure is higher., , has minimum surface area., (ii) Fire polishing of glass. Sharp glass edges are heated, to make them smooth. This is because on heating, the, glass melts and takes up rounded shape at the edges, which has minimum surface area., , Effect of temperature : As the temperature of a liquid is, increased, the vapour pressure of the liquid increases., , (iii) Rise of a liquid in a capillary tube. This rise is obviously, , Boiling point of a liquid is defined as the temperature at, which the vapour pressure of the liquid becomes equal to, the external pressure (i.e., the atmospheric pressure)., , surface which pushes the liquid into the capillary tube., , When the external pressure is normal atmospheric pressure, (i.e., 760 mm), the boiling point is called the normal boiling, point., , due to the inward pull of surface tension acting on the, , (iv) Effect of nature of the liquid on surface tension. Surface, tension is a property that arises due to the intermolecular, forces of attraction among the molecules of the liquid., Greater are the intermolecular forces of attraction, higher, is the surface tension of that liquid.
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STATE OF MATTER, , 6., , (v) Effect of temperature on surface tension. The surface, tension of liquids generally decreases with increase of, temperature and becomes zero at the critical temperature, (where the meniscus between the liquid and the vapour, disappears). The decrease in surface tension with, increase of temperature is obviously due to the fact, that with increase of temperature, the kinetic energy of, the molecules (and hence the speeds of molecules), increases and, therefore, the intermolecular attraction, decreases., Viscosity is one of the characteristic properties of liquids., Viscosity is a 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., The type of flow in which there is a regular gradation of, velocity in passing from one layer to the next 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 the amount, , du, ., dz, , The pressure of a gas can be measured by various, methods. Mostly it is measured in terms of heights of, liquid column. We know that a liquid exerts pressure on, the bottom of a container or a tube due to gravity., Suppose there is a liquid of density U filled in a tube, (cross sectional area A) up to a height h and there is, vacuum above it., Then :, Volume of the liquid = A × h, Mass of the liquid = U × A × h, Force applied at the bottom = weight of the liquid, = U × g ×A× h, Pressure = F/A = Ugh, If a tube filled with a liquid is kept at an angle T then only, the vertical component of weight is taken., Pressure = Ugh × sinT, , A force is required to maintain the flow of layers. This force, is proportional to the area of contact of layers and velocity, gradient i.e., , A common arrangement to measure pressure of a gas is, , F v A (A is the area of contact), , pressure by determining the height of a mercurry column, , Fv, , du, du, (where,, is velocity gradient; the change in, dz, dz, , velocity with distance), , F v A., , du, dz, , F v KA, , , , 17. MEASUREMENT OF PRESSURE OF A GAS, , du, dz, , ‘ K ’ is proportional constant and is called coefficient of, viscosity. Viscosity coefficient is the force when velocity, gradient is unity and the area of contact is unit area. Thus, ‘ K ’ is measure of viscosity. SI unit of viscosity coefficient, is 1 newton second per square metre (N s m–2) = pascal, second (Pa s = 1kg m–1s–1). In cgs system the unit of, coefficient of viscosity is poise., 1 poise = 1 g cm–1s–1 = 10–1kg m–1s–1, Greater the viscosity, the more slowly the liquid flows., Hydrogen bonding and van der Waals forces are strong, enough to cause high viscosity. Glass is an extremely, viscous liquid., , Viscosity of liquids decreases as the temperature rises, because at high temperature molecules have high kinetic, energy and can overcome the intermolecular forces to slip, past one another between the layers., , called “Barometer” as shown in the figure., A mercury barometer is used to measure atmospheric, supported in a sealed glass tube.
