States of Matter

Introduction

The classification of matter into three different states, namely solid, liquid and gaseous state is termed as the physical classification of matter. Most properties of solid, liquid and gases that can be observed with our sense organs are called as 'macroscopic' properties. The description of the behaviour of the three states of matter in terms of atomic theory is called 'microscopic' description of matter. From the study of the observable properties of different states of matter one can understand the microscopic nature of matter in terms of the behaviour of constituent particles. The important characteristics of the three states are listed out below: Solid state A solid possesses a definite size (volume) and a definite shape under ordinary conditions; and tends to maintain these even under deforming conditions. The substances in solids are closely packed and bound by strong inter particle attraction, making them rigid and geometrical. Some common examples of solids are iron, silver, common salt, etc. Liquid state A liquid possesses a definite volume but not definite shape. The substances in liquids have particles, which are loosely packed and bound to each other by forces weaker than those of solids. This makes a liquid mobile and shapeless resulting in its taking up the shape of the container in which it is placed. A liquid also has a tendency to flow. For example, water, alcohol, milk, oil, etc. Gaseous state A gas neither possesses a definite volume nor a definite shape. The substances in a gas have particles that are separated by great distance, having virtually no force of attraction between them. A gas occupies the whole of the volume of the vessel in which it is placed. It also takes up the shape of the container. For example, air, carbon dioxide, oxygen, hydrogen, etc. The three states of matter are inter-convertible. This can be done by heating or cooling. Heating increases the inter particle spacing and kinetic energy of the particles. So, a solid on heating gets converted into a liquid, and a liquid into a gas.             The various points of distinction between the three states 

The Gaseous State

Of the three states of matter, the gaseous state is the simplest and shows greatest uniformity in behaviour. Gases show almost similar behaviour irrespective of their chemical nature. This state is characterized by: 

 Gases maintain neither the volume nor the shape. They completely fill the container in which they are placed. 

 They expand appreciably on heating. 

 Gases are highly compressible. The volume of the gas decreases when the pressure increases. 

 They diffuse rapidly into space. 

 Gases exert equal pressure in all directions. 

 All gases are colourless except a few e.g. chlorine (greenish yellow) bromine (reddish brown), nitrogen dioxide (reddish brown) The behaviour of gases can be described by certain quantitative relationships called gas laws. They give the relationship between mass, pressure, volume and temperature. Measurable Properties of Gases The important fundamental properties of gases are mass, volume, pressure and temperature. These are discussed below: Measurement of mass The mass of a gas can be measured by direct weighing. The container in which the gas is enclosed is first weighed. Then the weight of the container, after removing all the gas, is measured again. The difference between the two weights gives the mass of the gas. Units of mass The most common unit for mass is expressed in grams (g) or kilogram (kg) (1 kg = 103g). In chemical measurement, IUPAC prescribes that the mass of a gas (m) be expressed in terms of the number of moles (n). The number of moles can be obtained from the mass of the gas using the relationship 

 Measurement of volume 

The volume of a substance is the space occupied by it. A gas occupies the entire volume of the container available to it. The measurement of the volume of a gas only requires the measurement of the volume of the container enclosing it. Units of volume Generally, volume is expressed in units of litres (L), millilitre (mL) or cubic centimetres (cm3). The different units are related as               1 mL= 1 cm3

              1 L = 103 mL or 1 dm3

 The SI unit of volume is m3. As this unit is too large, volume is generally expressed in smaller units of cubic decimetre (dm3) or cubic centimetre (cm3). These are related to each other as:             1 m3 = 103 dm3 = 106 cm3

 The volume of the gas depends upon its amount, temperature and pressure V = f (amount, temperature, pressure). Measurement of Pressure Gases exert uniform pressure in all the directions on the walls of the container in which they are confined. As pressure is force per unit area, the pressure of the gas is the force exerted by the gas per unit area on the walls of the container. Atmospheric pressure Air is pulled towards the surface by gravity and this exerts pressure on the Earth's surface. The pressure exerted by the gases of the atmosphere on the surface of the Earth is called atmospheric pressure. Measurement of atmospheric pressure Atmospheric pressure is measured by an instrument known as barometer. This consists of a glass tube closed at one end and filled with pure mercury. The tube is then inverted into an open vessel of mercury. The mercury level in the tube drops until the pressure due to the column of mercury in the tube becomes equal to the atmospheric pressure acting outside the tube. The region above the mercury in the tube is almost a perfect vacuum, therefore, the pressure due to mercury column is equal to atmospheric pressure. The pressure (P) is expressed as: P = h..g where 'h' is the height of mercury column in the barometer '' is the density of mercury 'g' is the acceleration due to gravity. 

           Fig: 2.1 - Mercury barometer Units of atmospheric pressure The maximum height of mercury, which can be supported by the atmospheric pressure provides a measure of that pressure. A standard pressure of one atmosphere (1 atm) is defined as the pressure that will support a column of mercury of 76 cm height at 0°C (density of mercury (13.5951 gcm-3) and at standard gravity = 980.665 cm-2. One atmosphere is also referred to as 760 torr. This unit is named after the scientist Torricelli, who invented the Barometer. Thus 1 atm = 76.0 cm of mercury (cm Hg) = 760 mm of mercury (mm Hg) = 760 torr. The S.I. unit of pressure is pascal (Pa), which is the pressure exerted when a force of Newton (1 N) acts on 1m2 area. Pascal is related to atmosphere as: 1 atm = 101.326 x 103 N m-2

 = 101.325 kPa However, for approximate work, one atmosphere is taken to be equal to 102 kPa or 105 Pa or Nm-2. The pressure of gases are measured by a device known as manometer that can be either open end manometer or closed end manometer. These manometers consist of 'U' tube partly filled with a non-volatile liquid like mercury. During measurement, the difference in the levels of the mercury in the two limbs gives the difference in pressure on the two sides. Measurement of Temperature 

Temperature is a measure of hotness or coldness of a body. It is a measure of kinetic energy possessed by the molecules. A hot body is said to be at a higher temperature and a cold body is said to be at a lower temperature. The devices used to measure temperature are called Thermometers. The substance commonly used in the thermometers is mercury. Temperature is commonly measured in Celsius scale (centigrade scale). In this scale, the freezing point of water (0°C) and the boiling point of water (100°C) at one atmospheric pressure are taken as reference points. The range between 0° to 100° is divided into one hundred equal parts, each division corresponding to 1°C. Unit of temperature The S.I. unit of temperature is degrees Kelvin (K) and this scale is known as Kelvin scale. The zero point on the Kelvin scale is known as absolute zero, which is equal to -273.15°C. The temperature on the Celsius scale is converted to temperature on Kelvin scale by the addition of 273.15°. Thus, °C + 273.15 = K Standard temperature and pressure The properties of a gas depends upon the temperature and pressure. Hence, it is convenient to specify a particular temperature and pressure for comparison of different gases. The standard conditions of temperature and pressure are abbreviated as S.T.P. (Standard Temperature and Pressure) and N.T.P. (Normal Temperature and Pressure). Standard Temperature and Pressure (S.T.P. or N.T.P.) values are: Temperature = 0°C or 273.15 K Pressure = 1 atm or 760 mm Hg or 760 torr or 101.325 kPa (S.I. units)

Gas Laws - Boyle's Law

The study of behaviour of gases has led to the formulation of a few important generalisations called as Gas Laws. Boyle's Law Robert Boyle proposed this law in the year 1662, giving the relationship between pressure and volume of given mass of a gas at constant temperature. This law states that volume (V) of a given mass of gas is inversely proportional to the pressure (P) at constant temperature. Mathematically it can be expressed as, 

                                                                                or PV = k = constant 

At a given temperature, when the pressure of the gas is changed from P1 to P2 the relation becomes P1 V1 = P2 V2 = constant where, V2 is the new volume of the gas. The product of volume and pressure for a given mass of a gas at constant temperature is constant. This aspect can be experimentally verified by taking the pressure volume data for a gas like 10g of oxygen at 25oC. It is observed that with the increase in pressure the volume decreases and the product 'PV' remains constant. This data when plotted with 'P' along the x-axis and 'V' long the y-axis gives a curve. 

    Fig: 2.2 - Variation of P and V at constant T The curve shows the inverse relation of 'P' and 'V'. When the pressure is P1, the volume is V1and when the pressure is increased to P2, the volume V2 is smaller than V1. If the graph is plotted between 'P' and 1 / V, a straight line passing through the origin is obtained. On plotting the product 'PV' along y-axis and Pressure 'P' along x-axis, a horizontal line is obtained, indicating 'PV' to be constant even if we change pressure. 

           Fig: 2.3 - Plot of P versus 1/V The P-V curve for a given gas is different at different temperatures. The plot of 'PV' against 'P' at different temperature is known as Isotherms. The higher curve corresponds to higher temperature. Boyle's law expresses the compressible nature of gas, which gives a measure of its increased density. Problem 1. A gas occupies a volume of 250 mL at 745 mm Hg and 25oC. What additional pressure is required to reduce the gas volume to 200mL at the same concentration? Solution P1 = 745 mm Hg V1 = 250 mL P2 = ? V2 = 200mL P1V1 = P2V2

 The additional pressure required is 931.25 - 745 = 186.25 mm.

Charles' Law

Charles formulated this law in 1787 giving the relationship between volume and temperature of a gas. This law stated that at constant pressure, the volume of a given mass of gas increases or decreases by 1/273 of its volume at 0oC for every one degree rise or fall. 

 or 

 A plot of volume along x-axis and temperature along y-axis gives a straight line intercepting the y-axis. When this line is extrapolated to lower temperature, it cuts the x-axis, which represents the zero volume. 

              Fig: 2.4 - Plot of volume versus temperature (P constant) The temperature at which the volume of the gas becomes zero is found to be -273oC, which is independent of the nature and pressure of the gas. The lowest temperature below which volume does not exist (negative), is called the absolute zero. Temperature measurements based on the absolute zero is known as absolute scale of temperature or Kelvin temperature scale. Charles' law is mathematically represented as: 

 273 + t = T (K) and 273 =T0 which corresponds to 0oC on absolute temperature scale 

 Thus, V/T constant = k' 

The volume of a given mass of a gas is directly proportional to the absolute temperature at constant pressure. If V1 is the volume of a certain mass of gas at temperature T1 and V2 is the volume of the same mass of the same gas at temperature T2 at constant pressure, then, 

 The validity of Charles' law can be determined by measuring the volumes of a given mass of a gas at different temperatures, at constant pressure. The value of V/T remains to be constant in this study. The curves obtained by plotting volume temperature ratio against different pressures are called isobars. Charles described the expansive nature of gases with lower density. Problem 2. A sample of helium has a volume of 520 cm3 at 100oC. Calculate the temperature at which the volume will become 26cm3. Assume that pressure is constant? Solution V1 = 520 cm3 V2 = 260 cm3

 T1 = 100 + 273 = 373K T2 = ? 

 or 

 T2 = 186.5 K t = 186.5 - 273 = 86.5oC.

Avogadro's Law

The relationship between the volume of a gas to the number of molecules at constant temperature and pressure is known as Avogadro's law. It states that equal volumes of all gases under similar conditions of temperature and pressure contain equal number of molecules. 22.4 litres of any gas at STP contains 6.023 x 1023 number of molecules irrespective of its nature. Therefore, the volume of a gas is directly proportional to the number of molecules N. V   N (at constant T and P) 

The number of moles 'n' of a gas is also proportional to the number of molecules. 

 n = N/No

 Where, No represents the Avogadro number and is constant. So, n   N, V   N or V   n. Thus, it can be concluded that the volume of gases at constant temperature and pressure is directly proportional to their number of moles.

Dalton's Law of Partial Pressures

Dalton proposed this law on the pressure exerted by a mixture of non-reacting gases in an enclosed vessel. The law of partial pressure states that the total pressure exerted by a mixture of two or more non-reacting gases in a definite volume is equal to the sum of the individual pressures, which each gas would exert if it occupies the same volume at a constant temperature. If p1, p2, p3 are the individual partial pressures of the known gases, then the total pressure 'P' of the mixture of gases at the same temperature and pressure is given by the relation: P = p1 + p2 + p3 + ……. Partial pressure is the pressure exerted by the gas if present alone in the vessel at the same conditions of temperature. For example, A gas 'A' having a pressure of 300 mm Hg is contained in a vessel and another gas 'B' with a pressure of 400 mm Hg is contained in another vessel, are mixed in the third vessel at the same temperature. The total pressure in the third vessel is,                P = PA + PB

                  = 300 + 400 = 700 mm Hg 

               Fig: 2.5 - Dalton's law of partial pressures Dalton's law is used to calculate the pressure of a gas. Problem 3. A 10 L flask at 298 K contains a gaseous mixture of CO and CO2 at a total pressure of 1520 mm of Hg. If 0.20 mole of CO is present, find the partial pressure of CO and that of CO2? Solution According to Dalton's Law: pCO + pCO2 = P = 1520 mm of Hg 

                                                                                                         = 0.49 atm. Partial pressure of CO2, pCO2= P - (pCO) = 2.0 - 0.49 = 1147.6 mm of Hg

Graham's Law of Diffusion

Gases have the tendency to spontaneously intermix and form a homogenous mixture without the help of external agency. This is due to the presence of large amount of empty space between the gas molecules that makes their movement rapid into each other. The gases move from a region of higher concentration to a region of lower concentration until the mixture attains uniform concentration. Graham studied the rate of diffusion of various gases and gave this law. It states that under similar conditions of temperature and pressure, the rates of diffusion of gases are inversely proportional to the square roots of their densities. 

 If r1 and r2 are the rates of diffusion of two gases 'A' and 'B' and 1 and 2 are their densities, then 

 Molecular mass is twice the vapour density, substituting this in the above equation, we have 

 where M1 and M2 are the molecular masses of the two gases. Thus, the rate of diffusion of gases are inversely proportional to the square root of their molecular masses. Rate of diffusion is also equal to the volume of the gas, which diffused per unit time, 

 If V1 and V2 are the volumes of the gases diffusing in time t1 and t2 respectively, then 

 Therefore, 

 If the volume diffused is the same, (V1 = V2) Then,

 Graham's law is useful in: 

 Separation of gases having different densities by diffusion. 

 Determining the densities and molecular masses of unknown gases by comparing their rates of diffusion with known gases. 

 Separating the isotopes of some of the elements. Effusion When the gases contained in a vessel are allowed to escape through a small aperature, it is effusion. 

           Fig: 2.6 - Process of diffusion and effusion Problem 4. An unknown gas diffuses four times as quickly as oxygen. Calculate the molecular mass of the gas. Solution Let the rate of diffusion of oxygen be r(O2) = r1

 The rate of diffusion of the unknown gas r (x) = 4r Molecular mass of O, M(O) = 32 Molecular mass of unknown gas M (x) = M

 From Graham's Law of diffusion, 

 or 

 Squaring on both sides, 

Ideal Gas Equation

By combining Boyle's and Charles' laws, an equation can be derived that gives the simultaneous effect of the changes of pressure and temperature on the volume of the gas. This is known as combined Ideal Gas Equation. A simple and direct method of deriving this equation is as follows: According to Boyle's law, for a given mass of a gas at constant temperature 

 According to Charles' law, 

 Combining (i) and (ii) 

 or 

 or 

 Now, if V1 is the volume of a gas at temperature T1 and pressure P1. V2 is the volume of same amount of gas at temperature T2 and pressure P2, then 

 The above relationship is very useful for converting the volume of a gas from one set of conditions to another. The numerical value of the constant of proportionality (K) depends upon the quantity of gas. The volume of a gas is directly proportional to the number of moles of gas at constant temperature and pressure (Avogadro's law). This means that 'K' is directly proportional to the number of moles, 'n', i.e., K   n or K = nR, where 'R' is the universal gas constant of proportionality. The value of 'R' is same for all gases. However, the numerical value of 'R' varies with the units in which pressure and volume are expressed. Therefore the Ideal gas Equation is derived as: 

 For one mole (n = 1), PV = RT (Ideal Gas Equation) The Ideal Gas Equation is also known as the equation of state for gases as it expresses the quantitative relation ship between the four variables that describe the state of the gas. The word 'ideal' is used here because in reality no gas obeys the above condition and the gases, which deviate from ideality are called as real gases. Universal gas constant (R) From the above ideal gas equation: 

 The universal gas constant is a measure of energy change (work done) per mole of

the gas for one degree change in its temperature. Numerical Value of R The magnitude and unit of 'R' depends upon the units in which pressure, volume and temperature are expressed. Conditions and problems I)When pressure is expressed in atmosphere and volume in litres Under standard condition of temperature and pressure i.e., when P = 1 atm T = 273.15 K V = 22.414 L mol-1

 This gives, 

 II) When pressure is expressed in atmosphere, and volume in mL Here, P = 1 atm T = 273.15 K V = 22414 mL mol-1

 This gives, 

 III) R in energy units When, 

 If 'R' is to be expressed in CGS units, the unit of pressure should be dyne cm-2 and volume in cm3 mol-1. Then, Normal temperature T = 273.15 K Normal pressure, P = (1 x 76 x 13.6 x 981) dyne cm-2

Molar volume under normal temperature and pressure = 22414 cm3mol-1

 Therefore, 

 = 8.314 x 107 erg deg-1 mol-1

 Since, 4.182 x 107erg = 1calorie Hence, 

 IV) In SI units In the SI system of units, under NTP conditions, P = 101325 N m-2

 T = 273.15 K V = 22.414x10-3 m3

 Therefore, 

 = 8.314 J mol-1 K-1

        The value of Gas constant R in different units 

 Problems 5. Calculate the number of moles of hydrogen (H2) present in a 500 cm3 sample of hydrogen gas at a pressure of 760 mm of Hg and 27°C. 

Solution According to ideal gas equation, PV = nRT 

 T = 27 + 273 = 300 K, R=82.1 cm3 atm K-1 mol-1

 n = 0.0203 mol = 2.03 x 10-2 mol. 6. About 200 cm3of a gas is confined in a vessel at 20°C and 740 mm Hg pressure. How much volume will it occupy at S.T.P.? Solution We are given P1 = 740 mm Hg P2 = 760 mm Hg T1 = 20 + 273 = 293K T2 = 273 K V1 = 200 cm3 V2 = ? According to gas equation, 

 Substituting the values, we get 

 = 181.4 cm3. 7. Calculate the volume occupied by 2 moles of an ideal gas at 2.5 x 105 Nm-2 pressure and 300 K temperature. Solution According to ideal gas equation, 

 n = 2 mol, T = 300 K, P = 2.50 x 105 Nm-2

 R = 8.314 Nm K-1 mol-1

 = 19.95 x 10-3m3=19.95dm3.

Ideal and Real Gases

An ideal gas is one, which obeys the general gas equation of PV = nRT and other gas laws at all temperatures and pressures. A real gas, does not obey the general gas equation and other gas laws at all conditions of temperature and pressure. Effect of pressure All gases are known to exist as real gases and show ideal behaviour only to some extent under certain conditions. When PV = nRT for ideal gases, then the ratio 

 For real gases Z may be less or more than one. If Z<1 then it is called negative deviation which means that the gas is more compressible. If Z>1 then the gas is less compressible and it is called positive deviation. It is observed that the deviations are low at low pressures. At high pressures the deviations depends on the nature of the gas. 

 A plot of   versus P for some common gases are shown in the figure.  

   Fig: 2.7 - Plot of compressibility factor as a function of P For H2 and He, 'Z' is greater than one while for N2, CH4 and CO2 'Z' is lesser than one. This means that these gases are more compressible at low pressures and less compressible at high pressures than expected from ideal behaviour. Effect of temperature The effect of temperature on the behaviour of real gases is studied by plotting the value of 'PV' against temperature. It is observed that the deviations from ideal behaviour is less with the increase in temperature. Thus, real gases show ideal behaviour at low pressures and high temperatures. Causes for deviations In order to know the causes for deviations from ideality, Van der Waal pointed out the faulty assumption that were made in formulating the kinetic molecular model of gases. 

 The assumption that the volume occupied by the molecular mass is negligible as compared to the total volume of the gas is invalid. Although this volume is 0.1% volume of the total volume of the gas, the volume of the molecules of gas remain same as compared to the decrease in the total volume of the gas. The decrease in volume occurs with the decrease in temperature and increase in pressure, but the volume of the molecules cannot be neglected. 

 The forces of attraction between the gas molecules were considered to be negligible. This assumption is only valid at low pressures and high temperatures because in these conditions the molecules lie far apart. But at high pressures and low temperatures the volume of the gas is small and so the attractive forces though very small, exist between them. Hence, Van der Waal who incorporated the idea of finite molecular volume and intermolecular forces modified the Ideal Gas Equation as follows: 

 Volume correction was made stating that the free volume of the gas is actually less than the observed volume. A suitable volume term 'b' is subtracted from the observed volume known as the excluded volume or correct volume. The correction term, 'b' is a constant depending upon the nature of the gas. For 'n' moles of gas, the correction term is 'nb' and so the corrected volume is given by, Vcorrected = (V-nb) for 'n' moles. Correction due to intermolecular forces is considered in terms of the pressure. A molecule at the wall of the container experiences an inward pull due to attractive intermolecular force of the neighbours. The molecules strike the wall with a lesser force and so the observed pressure is less than the ideal pressure. The pressure correction term 

Substituting these values for pressure and volume, the ideal gas equation can now be written as: 

 This equation is Van der Waal's equation of state. Here, the constant 'a' measures the forces of attraction between the molecules of the gas and 'b' relates to the incompressible volume of the molecules, measuring the size of the gas molecules. One can now summarize the differences between ideal and real gases as follows: 

Kinetic Molecular Theory of Gases

In order to explain the observed behaviour of gases, a model was proposed based on the molecular and kinetic concept of gas molecules. This model takes into account the particulate nature of matter and the constant movement of particles. Postulates of Kinetic Theory 

 All gases are made up of large number of minute particles called molecules. 

 Large distances separate the molecules so that the actual volume of the molecules is negligible as compared to the total volume of the gas. 

 The molecules are in a state of constant rapid motion in all directions, colliding with one another and also with the walls of the container. 

 The molecular collisions are perfectly elastic with no loss of energy and only redistribution of energy during collision. 

 There are no attractive or repulsive forces between the molecules. 

 The pressure exerted by the gas is due to the bombardment of its molecules on the walls of the container per unit area. 

 The average kinetic energy of the gas molecules is directly proportional to the absolute temperature.     On the basis of these postulates an equation for the pressure of the gas is derived as 

         This is called the Kinetic gas equation where 'N' is the number of molecules in volume 'V', 'm' is the mass of the

    molecule and 'u' is the root mean square velocity of the molecules. 

Liquefaction of Gases

There are large empty spaces (voids) separating the tiny molecules of gases from one another. Each molecule enjoys an almost independent existence. Molecules are in a state of continuous rapid motion and have negligible attractive forces between them due to wide separation. This is particularly so, when temperature is high and pressure is low. When the temperature of the gas is lowered, both the volume of the gas and the kinetic energy of the molecules decrease. The molecular motion becomes slow and molecules become sluggish. The progressive decrease of temperature brings the molecules closer and closer because they are unable to resist the attractive force that starts operating between them. Ultimately, at sufficiently low temperature, the voids between the molecules become less than 10-5cm and the gas changes into liquid state. This process of liquefaction by bringing gas molecules closer can also be achieved by increasing the pressure of the gas: this also decreases the volume of the gas. For example, sulphur dioxide can be liquefied at 265 K if pressure is 760 mm of Hg. It can also be liquefied at 293K if the pressure is increased to 2470 mm of Hg. Thus, liquefaction of gases can be achieved by either decrease of temperature or by increase of pressure. Concept of critical temperature Experimental observations have shown that effect of temperature is more significant in achieving liquefaction than that of pressure. This is due to the fact that for every gas there is a certain temperature above which it cannot be liquefied how so ever high the pressure may be. The kinetic energy of gas molecules above this temperature is sufficient enough to overcome the attractive forces. This temperature is referred to as the critical temperature of the gas. It may be defined as the temperature above which a gas cannot be liquefied by application of pressure. A gas will remain as gas above critical temperature and in order to liquefy it by compression, it has to be cooled to its critical temperature. Critical temperature is denoted by Tc. For example, Tc of CO2 = 304.1 K. 

Critical pressure (Pc) The pressure required to liquefy the gas at its critical temperature is called critical pressure. For example, the value of Pc for CO2 = 55328 mm of Hg. Critical volume (Vc) The volume of one mole of the gas at critical temperature and critical pressure is called critical volume. For example, value of Vc for CO2 = 94.0 cm3 mol-1

 The parameters Tc, Pc and Vc for a gas are collectively called 'critical constants'.

Relationship between Critical Constant and Van der Waal's Constants

The relationship between critical constants of the gases and their Van der Waal constants is as follows: (i) Vc = 3b (ii) Pc = a/27b2

 (iii) Tc = 8a/27Rb (iv) The critical compressibility factor Zc is given by, 

 These relations have been derived from the calculations based on Van der Waal's equation. Boyle's Law When the volume of the gas is reduced, the molecules move with the same speed but in lesser space. As a result, the frequency of collisions with the walls of the container increases and a pressure increase is noticed. This is the statement of Boyle's law and this can be deduced from the kinetic gas equation, 

 and the number of molecules N remain constant. Thus,

 Charle's Law When a gas is heated the molecules move faster increasing the pressure. But to maintain the pressure constant, the force of collision is compensated with an increase in volume. So, at constant pressure the volume of the gas increases with temperature. By kinetic gas equation we have, 

 substituting this we have, 

 This is the statement of Charles' law. Dalton's Law When more than one type of molecule is present (at constant T) then, the total pressure exerted by the mixture should be equal to the sum of their individual pressures when present alone. The pressure exerted by each gas is 

 where 1 and 2 are the average molecular kinetic energies of the two gases containing N1and N2 molecules per unit volume. Since the molecules behave independent of each other,1 and 2 =  , hence 

 = p1 + p2

The total pressure is equal to the sum of the pressures, which each gas would exert if allowed to occupy the entire space. This is Dalton's law of partial pressures. Graham's Law of Diffusion From kinetic theory, 

 Since the rate of diffusion of a gas is determined by the molecular speed, 

 The rate of diffusion of a gas depends inversely on the square root of its density. This is Graham's law of diffusion.

Maxwell's Distribution of Molecular Speeds

On plotting a fraction   of molecules having different speeds against the speeds of the molecules (along x-axis) a curve known as Maxwell's distribution curve is obtained. The important features of which are: 

 The fraction of molecules with very low or very high speeds is very small. 

 The fraction of molecules possessing higher and higher speeds goes on increasing till it reaches a peak and then starts decreasing. 

 The maximum fraction of molecules possess a speed, corresponding to the peak in the curve which is referred to as most probable speed. 

                   Fig: 2.8 - Maxwell-Boltzmann's distribution of speeds The increase in temperature of the gas results in increase in the molecular motion. Consequently, the value of the most probable speed increases with increase in temperature. It may be noted that as long as the temperature of a gas is constant, the fraction having the speed equal to most probable speed remains the same but the molecules having this speed may not be the same. In fact, the molecules keep on changing their speed as a result of collisions. Molecular motions may be described in terms of different types of molecular speeds. These are defined and described below. Most probable speed The most probable speed of a gas is the speed possessed by the maximum fraction of gas molecules at a given temperature denoted by . 

 where, R is the gas constant T is the absolute temperature and M is the molecular mass. Average speed This is the average of speeds possessed by the molecules in a sample of any gas. This is defined as, 

 It can be shown that 

 Root mean square speed The root mean square speed is expressed by the relationship, 

 Root mean square speed in any gas is given by the relationship, 

 The root mean square speed is commonly used and can be calculated from the following relations: 

 Relation between most probable, average and root mean square speeds The three molecular speeds are expressed as 

Thus for gases, the root mean square speed is directly proportional to  , and

inversely proportional to  . Therefore heavier molecules move slower. Average kinetic energy of a gas 

From the kinetic model of gases, 

 For 1 mole of the gas, this equation becomes, 

 For an ideal gas, 

 or 

 Since PV = RT for 1 mole of gas Therefore 

 For 'n' moles of gas, the kinetic energy is 

 The units of Ek depend upon the units of R. Hence the following point holds true: The assumption of kinetic theory that the average kinetic energy or molecular velocity of any gas is directly proportional to its absolute temperature. K.E  u2

 or 

 Problem 8. Calculate the kinetic energy of 2g of oxygen at -23°C. 

Solution Kinetic energy is given as 

 R = 8.314 JK-1mol-1, T= 273 - 23 = 250 K 

 9. Calculate the root mean square speed of methane molecules at 27°C. Solution Root mean square speed, 

 T = 27+ 273 = 300 K, M= 16. R= 8.314 x 107 erg k-1 mol-1

 = 683.9 ms-1

The Liquid State

The liquid state lies between the gaseous and the solid state. Liquids are neither completely disordered nor completely ordered. The cohesive forces between the liquid particles are strong enough to keep them together but these particles do not occupy fixed lattice sites and are relatively more free as compared to the particles in solids. In terms of kinetic molecular model, the nature of the liquid state can be described as follows: 

 Liquids are composed of molecules that are relatively closer than gases. 

 Appreciable intermolecular forces hold the molecules of liquids together. 

 Due to weak intermolecular forces, the molecules are in constant random motion. 

 The average kinetic energy of molecules in a given sample is proportional to the absolute temperature.

 It may be noted that the nature and magnitude of intermolecular forces decide the structure of a liquid and also its characteristic properties.

Properties of Liquids - I

The important properties of liquids are: Volume Liquids have a definite volume under given temperature and pressure conditions. Though they take the shape of the container, they maintain their volume. The intermolecular forces in liquids are strong and therefore, they do not expand to occupy all the space available (as gases do). A given mass of liquid has a fixed volume. For example, 10 cm3 of water always occupies 10 cm3 whether it is placed in a beaker, a conical flask or a large round bottom flask. Shape Liquids have no shape of their own. The molecules in the liquid state are not rigidly fixed to their own sites and take the shape of the container in which they are placed. Density The higher density of liquids compared to gases is due to the fact that molecules of liquids are more closely packed than gases. In general, the density of liquids is higher than gases and it decreases with increase in temperature. It has been found that the densities of liquids are about 1000 times greater than the densities of gases under similar conditions. For example, the density of water at 100oC and 1 atm is 0.958 g cm-3 while the density of water vapours at the same temperature and pressure is 0.000588 gcm-3. Compressibility Liquids are 105 times less compressible than gases but are about 10 times more compressible than solids. This is due to the fact that the molecules in liquid state are not as closely packed as in solids but are closer to each other as compared to gases. Moreover in the case of liquids, the repulsive forces between molecules prevent the compressibility of liquids. Therefore, large pressure is needed to reduce the volume of a liquid to a significant extent. For example, at 25oC, an increase in pressure from 1 atm to 2 atm decreases the volume of an ideal gas by about 50%, whereas the same change in pressure decreases the volume of water by only 0.0045%. Fluidity Liquids flow with greater ease as compared to solids. The ease of flow of liquids depends on the strength of the intermolecular attractive forces e.g. liquids with hydrogen bonding are more viscous and therefore less fluid. Surface tension Due to strong intermolecular cohesive forces in the liquid, the interior of the liquid holds the molecules on the surface inwards. This property is described in terms of

surface tension and the free surface of the liquid acts as a stretched membrane. Diffusion and miscibility Like gases, liquids also diffuse but they diffuse slowly than the gases. The diffusion of liquids is defined as the process of intermixing of the molecules of two or more liquids to form homogeneous mixture solution. This is also the movement of solute particles from higher concentration to lower concentration in a medium. The rate of diffusion is much slower in liquids than in gases. In the liquid state, molecules are quite close to each other. Therefore, a molecule of the liquid has to undergo a number of collisions with the neighbouring molecules. Thus, there is more obstruction for the movement of the molecules of a liquid. As a result, diffusion takes place slowly. In contrast, in gases, there is very less obstruction to the moving molecules because of large empty spaces available for their movement. Moreover, in liquids there are forces of attraction between individual molecules which hold them together. In other words, this slows down the process of diffusion. However raising the temperature increases the kinetic energy of the molecules. This increase the rate of diffusion of a liquid. Quasilattice structure The partially ordered structure of liquids is called the quasilattice structure. They do not have a long-range order. Due to the cohesive forces between the molecules in liquids, molecules appear to be under the influence of each other for short-range order. Evaporation and volatility Evaporation is the process of conversion of a liquid into its vapours at room temperature. When a liquid is placed in an open vessel, it gradually evaporates and is converted into its vapours. The molecules of liquids escape from the surface inspite of strong intermolecular cohesive forces among themselves. The process of evaporation can be explained on the basis of kinetic molecular theory. Different molecules in a liquid have different speeds and therefore, have different kinetic energies. There is a certain fraction of the molecules at the surface, which have very high kinetic energies. These molecules can readily overcome the attractive forces in the liquid and escape from the liquid surface into vapours. This process of escaping of molecules spontaneously from the surface of the liquid to vapour state is called evaporation. It may be noted that during the process of evaporation, cooling always occurs. This is because during evaporation the molecules of higher kinetic energy escape. The slow moving molecules are left behind and therefore, the average kinetic energy of the molecules left in the liquid state is lowered, assuming that no heat is supplied from some outside source. The lowering of the average kinetic energy results in a temperature drop in the liquid. The conversion of a liquid into its vapour at its boiling point is called as vaporization. The tendency of molecules in the liquids to escape from its surface is called volatility. The liquids whose molecules have very little tendency to leave the surface are called non-volatile liquids. Conversely, the liquids whose molecules leave the surface easily are volatile liquids. Volatile liquids evaporate faster.

 Factors Affecting the Rate of Evaporation Rate of evaporation depends upon the following factors: Factors and Heat of Vapourisation Temperature The rate of evaporation increases as the temperature of a liquid is increased, as it is an endothermic process. For example, a glass of hot water evaporates more rapidly than a glass of cold water. Strength of intermolecular forces The ease of evaporation of a liquid is related to the strength of the attractive forces between the molecules in the liquid. In polar liquids cohesive forces are strong while in non-polar liquids the cohesive forces are very weak and the molecules escape easily. For example, ether evaporates more rapidly than ethyl alcohol while ethyl alcohol evaporates quicker than water. Surface area The larger the exposed surface area of the liquid the greater is the number of molecules escaping from its surface. Heat of vapoursation The amount of heat required to evaporate 1 mole of a given liquid at a constant temperature is known as the heat of evaporation or heat of vapourisation. For example, when one mole of water is completely vapourised at 25C, it absorbs 44.180 kJ of energy. This may be written as: 

 Thus, the molar heat of vapourisation of water at 25oC is 44.18 kJ. The heat of vapourisation depends upon the strength of attractive forces between the molecules of a liquid. The relatively high molar heat of vapourisation of water (44.18 kJ mol-1) suggests strong attractive forces in liquid water. Vapour pressure If a liquid is placed in an open vessel, there is complete escape of molecules from the liquid to the atmosphere. If a liquid is allowed to evaporate in a closed vessel, the molecules escaping from the liquid surface are collected in a vapour state, above the surface of the liquid within the container. Due to vapoursation the level of liquid decreases. After some time, the level of liquid does not change further and becomes constant. 

            Fig: 2.9 - Attainment of equilibrium in evaporation of liquid This behaviour of liquid can be explained as follows. Initially, the system contains only liquid, and air above it. The air above the liquid is completely evacuated and the vessel is sealed, so there is nothing above the liquid. As evaporation starts, the molecules from the surface of liquid escape into vapour state, in the confined space above. Therefore, the level of liquid falls. Then starts the process of. This is the reconversion of vapour into liquid. Initially, escaped molecules move randomLy in all directions and collide with one another within the confine of the walls and liquid surface of the container. As more and more molecules enter the confined space, some slow-moving molecules are pushed back. They collide with the surface of the liquid and get recaptured by the intermolecular attraction, to reconvert into liquid. In the initial stages, the rate of evaporation is more than the rate of condensation because only small number of molecules are present in the gaseous state. The rate of condensation thereafter gradually increases as the number of molecules in the gaseous phase increases. Finally, a stage is reached when the rate of the two opposing processes is the same. The state where the rate of evaporation becomes equal to the rate of condensation is called a state of dynamic equilibrium. In such a state, although the amount of liquid level in the vessel does not change, evaporation has not stopped and the system is not at rest. In fact, the number of molecules, which escape from the liquid to the gaseous phase (due to evaporation), becomes equal to the number of vapour molecules that return to the liquid. The molecules in the vapour phase begin to exert pressure. As evaporation reaches the equilibrium state, the concentration of the molecules in the vapour state becomes constant. The pressure exerted by the molecules in the gaseous phase in equilibrium with its liquid is called equilibrium vapour pressure of the liquid or its vapour pressure. may be defined as 'the pressure exerted by the vapours in equilibrium with its liquid at a given temperature'. Vapour pressure is a characteristic property of a liquid at a given temperature. It does not depend upon the amount of the liquid or the vapour phase. The magnitude of vapour pressure depends upon the following three factors: 

 Nature of liquid The vapour pressure of a liquid depends upon the nature of the liquid. When intermolecular forces are weak, the molecules tend to escape readily and therefore,

the equilibrium vapour pressure is high. Vapour pressure of liquids provides an indication of the magnitude of intermolecular forces. Ether and alcohol evaporate faster than water. Hence, ether and alcohol have higher vapour pressure than water at a given temperature. The higher vapour pressure of ether and alcohol as compared to water is due to the fact that there are weaker attractive forces in ether and alcohol. 

Temperature of the liquid The vapour pressure of a liquid increases with increasing temperature. As the temperature increases, the number of molecules, which have larger kinetic energy to overcome the intermolecular cohesive forces, increases. As a result more molecules escape from the surface of the liquid and concentration of molecules in the vapour phase increase. Hence, vapour pressure of the liquid increases. 

 Presence of impurities Impurities affect the vapour pressure of a liquid appreciably. The non-volatile impurities lower the vapour pressure of a liquid. 

Properties of Liquids - II

Boiling Vapour pressure measures the tendency for the molecules to escape from liquid to the gas phase. At lower temperatures the vapour pressure of a liquid is much lower than the pressure on the surface of the liquid. When the temperature of the liquid is gradually increased, its vapour pressure also increases. Ultimately a stage is reached when the vapour pressure of the liquid equals the pressure of the air above it. At this point, molecules and vapours formed within the liquid can easily rise through the liquid in the form of bubbles and escape into the air. This phenomenon is known as boiling and the temperature at which this occurs is known as boiling point. Boiling point is the temperature at which the vapour pressure of a liquid becomes equal to the atmospheric pressure. The boiling point, therefore, depends upon the atmospheric pressure and it changes with the change in the pressure above the liquid. As the atmospheric pressure increases, it is necessary to heat the liquid to a higher temperature to make its vapour pressure equal to atmospheric pressure. At high altitudes like Ooty, having lower atmospheric pressure, water boils at a much lower temperature than in the plains like Bangalore where atmospheric pressure is higher. Generally, boiling points for most of the liquids are specified as normal boiling points. The normal boiling point of a liquid is the temperature at which the vapour pressure of the liquid becomes equal to one atmospheric pressure (standard pressure). It may be noted that once the boiling starts, the temperature of the liquid remains constant, until the whole of the liquid has vaporized, even though heating is continued. Problem 10. Why does the temperature of the boiling liquid remains constant even though heating is continued ?

 Solution When a liquid is heated, the heat supplied is consumed to pull the liquid molecules apart against strong attractive forces, which hold them together in the liquid form. The heat energy goes to compensate the loss of energy due to escaping molecules, which have to overcome the attractive forces between the molecules of the liquid. As a result, there is no change in the average kinetic energy of the molecules remaining in the boiling liquid. Since the average kinetic energy is proportional to the temperature (1/2mV2   T), therefore, the temperature of the liquid does not change till the whole of liquid has been converted into the vapour state. Effect of change in external pressure on the boiling point A liquid may be made to boil at any desired temperature by changing the external pressure. For example, a liquid may be made to boil at higher temperature by increasing the pressure on its surface, as is done in a pressure cooker. It may be made to boil at a lower temperature than the normal boiling point by reducing the external pressure on it. It is observed that some substances decompose at their normal boiling points and therefore, they cannot be heated up to their normal boiling points. They are made to boil at reduced temperatures. This principle is used in purifying less stable liquids by distillation under reduced pressure. This process is called vacuum distillation.. Difference between evaporation and boiling Although boiling and evaporation are similar processes, yet they differ in few aspects. The main points of difference between evaporation and boiling are given below: 

 Surface tension Surface tension is also related to the intermolecular forces in the liquid. The molecules in liquids are held closely and hence attract each other. A molecule in the bulk of the liquid is attracted equally on all sides so that the net attractive pull on the molecule is zero. However, a molecule at the surface is subjected only to the attractive forces of the molecules below it, as there are no molecules above it. Therefore, surface molecules experience a resultant downward attractive force from within the liquid, which tends to make the surface area of the liquid as small as possible. This causes the molecules at the surface to be pulled inwards and so there is always some residual imbalance force acting on the surface of the liquids. This is called surface tension. Whenever we want to stretch the surface, work has to be

done against surface tension. Surface tension may be defined as: 'Force per unit length acting perpendicular to the tangential line on the surface'. It may also be defined as 'the work done to increase the free surface area of any liquid by one unit at constant temperature and pressure.' The SI unit of surface tension or force per unit length is Nm-1. Since this unit is too big for any practical purpose we use a smaller unit mN m-1 (millinewton meter-1). 

 Fig: 2.10 - Forces at the surface and interior of the liquid Effect of temperature Surface tension decreases with rise in temperature, almost linearly. The decrease of surface tension with increase in temperature results because the kinetic energy (or speeds) of the molecules increases. Thus, the strength of intermolecular forces decreases resulting in the decrease of surface tension also. For example, clothes are washed more efficiently in hot water than in cold water due to decreased surface tension in hot water. The effect of temperature on surface tension is given by Eotvas equation 

 where,  = surface tension, k = constant, d = density M = Molecular mass, Tc = critical temperature; T= temperature As 'T' approaches critical temperature, the surface tension becomes zero. At this stage the meniscus between the liquid and vapour disappears. Nature of liquid Primarily surface tension of a liquid is governed by the strength of intermolecular attractive forces. Therefore, the magnitude of surface tension is a measure of intermolecular attractive forces. For instance the order of strength between inter molecular forces as well as the surface tensions of water, ethyl alcohol and ether are in their respective orders:Water (72.8)> Ethyl alcohol (22.3) > Ether (17.0). 

Impurities present in the liquid Impurities affect surface tension appreciably. It is observed that impurities, which tend to concentrate on the surface of liquids, compared to its bulk lower the surface tension. Substances like detergents, soaps, alcohol lower the surface tension of water, while inorganic impurities present in the bulk of a liquid such as NaCl tend to increase the surface tension of water. Pressure Increase of pressure on the surface of a liquid increases the surface tension. Such effects are not large. The following two important phenomena are due to surface tension: Spherical shape of drops The liquid drops have nearly spherical shapes. Because of surface tension, the free surface of a liquid tends to attain minimum surface area. Since the sphere has minimum surface area for a given volume of liquid, the liquid tries to adopt spherical shape. Examples are water droplets or mercury globules. Capillary action When one end of a capillary tube is put into a liquid that wets glass, the liquid rises into the capillary tube to a certain height and then stops. The rise of liquid in a capillary is due to the inward pull of surface tension acting on the surface, which pushes the liquid into the capillary tube. This phenomenon is called capillary action. The rise of liquid in the capillary is very important. For example, water below the surface of the Earth rising to the plants through the roots, oil rising into the wick of an oil lamp, ink rising in a blotting paper, are all examples of capillary action. Viscosity Certain liquids flow faster than others. Water and kerosene oil flow rapidly while honey and castor oil flow slowly. The cause of different rates of flow of liquids may be easily understood by considering flow of liquid in a beaker. If water is stirred in a beaker with a rod and left undisturbed for some time, its swirling motion stops after some time. The faster moving outer layer adjacent to the edge of the beaker comes to stop first. The slower moving layer near the center, which stops last, is pulling it back. Different layers in a liquid move over one another with different speeds in the direction of the flow of the liquid. However, due to intermolecular forces, there is resistance of one layer to the other layer. These internal self-governing forces tend to oppose any free motion. This resistance to the flow of a liquid is termed as viscosity. 'The internal resistance to flow in liquids, which, one layer offers to another layer trying to pass over it is called viscosity'. The viscosities of liquids are compared in terms of coefficient of viscosity (). This is defined as the tangential force per unit area required to maintain a unit difference in velocities. The units of viscosity are poise (P), where 1P = 1 g cm-1 s-1. In S.I. unit, 1P = 0.1 Nsm-

2. 

Viscosity is also related to the intermolecular forces in the liquid. If the intermolecular forces are large, viscosity will be high. For example, water has higher viscosity than methyl alcohol because intermolecular forces in water are more than that in methyl alcohol. 

With rise in temperature viscosity of a liquid decreases. This increases the average kinetic energy and so the intermolecular forces can be easily overcome. Liquids with extensive hydrogen bonding show higher viscosity due to an increase in size and mass of the molecule. For example, glycerol and sulphuric acid show higher viscosity than water due to hydrogen bonding. Problem 11. Which of the liquids in each of the following pairs has a higher vapour pressure. (a) Alcohol, glycerine (b) Mercury, water (c) Petrol, kerosene. Solution Liquids having higher vapour pressure are: (a) Alcohol (b) Water (c) Petrol. 

The Solid State

Solids are substances having definite volume and definite shape. In terms of kinetic molecular model, in solids there is a regular order in the arrangement of the constituting particles (atoms, molecules or ions) i.e. the particles constituting the solids occupy fixed positions These particles are held together by fairly strong forces. Characteristics of Solids Some of the common properties of solids, which distinguish them from other two states of matter, are: 

 Solids are rigid and have definite shapes. 

 Solids have definite volume irrespective of the size or shape of the container in which they are placed. 

 Solids are almost incompressible, having compressibility, which is approximately 106times more than gases. 

 Many solids have a crystalline appearance and have definite pattern of angles and planes. 

 Solids diffuse very slowly as compared to liquids and gases. Constituent particles are very closely packed in solids permitting very little space for their movement. 

 Solids have a much higher density (mass to volume ratio) than that of gases and

liquids. 

 Most solids become liquids when heated. Some undergo sublimation on heating. The temperature at which a solid changes into liquid is called the melting point and the process is called as melting. Due to the varying natures of solids their melting temperatures vary considerably.

Classification of Solids

The above properties suggest that the properties of the solids not only depend upon the nature of the constituents, but also on their arrangements. Based on their structural features solids can be classified into three categories: 

 Crystalline solids 

 Amorphous solids 

 Polycrystalline solids  Crystalline Solids The substances whose constituents are arranged in definite orderly arrangements are called crystalline solids. Many naturally occurring solid substances occur in the crystalline form. Some common examples of crystalline solids are sodium chloride, sulphur, diamond, sugar, etc. They have the following characteristics: 

 They posses characteristic geometric shapes. The constituent particles in crystals are usually held by strong inter atomic, inter-ionic or intermolecular forces. Particles vibrate about their equilibrium positions and do not posses translational motion. 

 Crystalline solids have sharp melting points, indicating the presence of a long range order arrangement in them. The long-range order is due to the regular arrangement of the constituents (molecules, atoms or ions) throughout the three dimensional network of crystals. For example, experiments (X-ray diffraction method) show that in a crystal of sodium chloride, the constituents Na+ and Cl- ions are present at alternate sites as shown below:                           Na+ Cl- Na+ Cl- Na+ Cl-

                            Cl- Na+ Cl- Na+ Cl- Na+

                          Na+ Cl- Na+ Cl- Na+ Cl-

                           Cl- Na+ Cl- Na+ Cl- Na+

 Though shown in two dimensions this systematic long-range order is also found in three dimensions, with each Na+ surrounded by six ions and vice versa. This order is due to strong coulombic forces of attraction between Na+ and Cl- ions. Similar regular arrangements are found in other solids too. 

 Crystalline solids are anisotropic by nature i.e., their mechanical, electrical and

optical properties depend upon the direction along which they are measured. 

 When cut or hammered gently they show a clean fracture along a smooth surface. Amorphous Solids Substances whose constituents are not arranged in an orderly manner are called amorphous solids. They are also called pseudo solids and differ from crystalline solids in many respects. The common examples of amorphous solids are glass, rubber, fused silica, plastics, etc. 

They have the following characteristics: 

 They do not occur in characteristic geometric shapes. They posses properties of incompressibility and rigidity to some extent. 

 Their mechanical, electrical and optical properties do not depend upon the direction along which they are measured. They are isotropic and in this respect resemble liquids and are sometimes referred to as super cooled liquids. 

 Amorphous solids do not have sharp melting points. They have some orderly arrangement but it is not extended to more than a few Angstrom units. Thus, amorphous solids are said to have short-range order. On heating they melt and begin to flow like liquids. 

 When cut or hammered they break in an irregular manner. Polycrystalline Solids These are crystalline solids, constituted of very fine crystals, not seen by the naked eye. These solids appear amorphous but are not so because the fine crystals are randomly oriented. Thus even though each individual crystal is anisotropic the polycrystalline materials as a whole appear to be isotropic. Metal powders are polycrystalline in nature.

Crystalline Solids

Crystalline substances have a definite rigid shape. The shape and size of crystals (even of the same materials) differs depending upon the conditions under which they are grown. Crystals of a given substance are bound by plane surfaces called faces. The angle between any two faces is called interfacial angle. But the angles between the faces of a given form always remains same. This important characteristic feature of a given crystalline substance is known as law of constancy of interfacial angles. Types of Crystalline Solids Crystalline solids may be classified into four types depending upon the nature of bonds present in them. Molecular crystals In molecular crystals, the constituent particles are molecules. These molecules are held together by weak forces known as Van der Waal's forces. Common examples are dry ice, wax, iodine, sulphur, etc.

 Characteristic features of molecular crystals are: 

 Molecular crystals are soft, compressible and can be distorted very easily. 

 They have low melting and boiling points. 

 These are bad conductors of electricity and are regarded as electrical insulators. 

 They are volatile and have low heats of vaporization and low enthalpy of fusion. Ionic crystals The ionic crystals consist of positively and negatively charged ions arranged in a regular fashion throughout the crystal. They form a network of positive and nagative ions in three dimension in such a way that cations and anions occupy alternate sites. These are held together by strong electrostatic forces. The main characteristics of ionic crystals are: 

 Ionic crystals are very hard and brittle. 

 They have very high melting and boiling points. 

 They are poor conductors of electricity and therefore are insulators in the solid state. 

They have high heat of vaporization and so have low vapour pressure. 

 Have high enthalpy of fusion. 

 When melted or dissolved in polar solvents, they conduct elecricity. Common examples of ionic crystals are, salts like NaCl, KNO3, LiF etc. Covalent crystals In covalent crystals, the constituent particles are atoms of the same or different kind, which are bonded to one another by a network of covalent bonds. The important characteristics of covalent crystals are: 

 The covalent crystals are incompressible and hard. 

 They are extremely non-volatile and have very high melting points. 

 They are poor conductors of electricity at all temperatures. 

 They have high heat of fusion and high enthalpy of atomization. The common examples of covalent crystals are diamond, carborundum (silicon carbide), quartz (SiO2,) etc. Metallic crystals In metallic crystals the constituent particles are positive kernels i.e., nuclei where

inner electrons are dispersed in a sea of mobile valence electrons. The forces present between the constituents are metallic bonds. The main characteristics of metallic crystals are: 

 Metallic crystals may be hard as well as soft. 

 They are good conductors of heat and electricity. 

 They have metallic luster and high reflectivity. 

 They are highly ductile and malleable i.e, they can be beaten into sheets and drawn into wires. 

 They have moderate heat of fusion. 

 The properties of metallic crystals vary from metal to metal. The examples of metallic crystals are common metals such as nickel, copper and alloys. Problem 12. The melting point is a rough measure of the attractive forces in solids. Arrange the following solids in the order of increasing strength of attractive forces. 

 Solution The order of increasing strength of attractive forces is: Water   phosphorus   naphthalene  zinc iodide   sodium fluoride.