UNIT 5 ( PAGE 2)
Equation of State for Real Gases
van der Waal's Equation.
To account for the behaviour of real gases it is necessary to apply suitable corrections to the ideal gas equation, P V = n R T, so as to make it applicable to real gases. The ideal gas equation was modified by van der Waal who incorporated the idea of finite molecular volume and intermolecular forces. The modified equation of the state which explains the deviations of real gases from ideality is known as van der Waal’s Equation of state. He applied the following corrections to the ideal gas equation.
1. Volume correction
The volume occupied by the molecules cannot be neglected in comparison to total volume. This means that the molecules are not free to move in the whole volume V, but the free volume is less than the observed volume. In other words, the ideal volume of the gas is less than the observed volume. It was therefore suggested by van der Waal that a suitable correction term may be subtracted from the observed volume. The correction term for one mole of gas is ‘b’ where ‘b’ is constant depending upon the nature of the gas and is known as ‘excluded volume’ or co-volume. The excluded volume is the volume within which the molecules cannot move. The co-volume has found to be four times the actual volume of the molecules. Thus, if V be the volume occupied by 1 mole of the gas, then the volume available to the molecules for the movement i.e. the corrected volume is :
Vcorrected = ( V - b ) for one mole.
For ‘n’ moles of the gas :
Vcorrected = ( V - n b ) for n mole.
Pressure Correction - Correction due to inter-molecular forces
Some attractive forces do exist between the molecules of real gases . Consider a molecule of a gas in the middle of the container
The molecule being attracted uniformly by neighbouring molecules. The attractive forces neutralise one another and there is no resultant pull on the molecule. On the other hand , when a molecule approaches the wall of the container, it experiences an inward pull as a result of attractive forces exerted by the neighbouring molecules inside the vessel. Thus, the molecule strikes the wall with lesser force than it would have done if there were no attractive forces. Therefore, the observed pressure is less than the ideal pressure. Consequently, some correction term should be added to the observed pressure in order to calculate ideal pressure. Hence, corrected pressure, Pcorrected is given by :
Pcorrected = P + p
where P is the observed pressure and p is the correction term.
The inward attractive force on the molecule about to strike the wall of the container will be proportional to the number of molecules, in the bulk of the gas and, therefore, to the density of the gas (n/V) . Also the number of molecules striking the container wall at any given instant will also be proprtional to the density of the gas. Thus :
Force on the gas molecules near the wall
where a is a constant.
Substituting the values of the corrected pressure and volume in an ideal gas equation, P V = n R T we get :
[ P + ( an2 / V2 ) ] ( V n b ) = n R T for ‘n’ moles
[ P + ( a / V2 ) ] ( V b ) = R T for one mole.
The constants ‘a’ and ‘b’ are also called van der Waal’s constants.
Significance and units of ‘a’ and ‘b’
The constants ‘a’ and ‘b’ are called van der Waal’s constants and their values depend upon the nature of the gas. The constant ‘a’ measures the forces of attraction between the molecules of a gas. Greater the value of ‘a’ greater is the strength of van der Waal’s interactions. The value of ‘a’ for the gas with lower molecular mass such as H2 and He is quite low whereas the values of ‘a’ for gases with high molecular mass is relatively high. It may be noted that the greater the value of ‘a’ of a gas also reflects its greater tendency to be liquefied. Therefore, the gases having higher values of ‘a’ will be easily liquefied.
The constant ‘b’ relates to incompressible volume of molecules and measures the effective size of gas molecules. It may be noted that ‘b’ is not equal to actual volume of the molecule but it is four times the actual volume of molecules.
We know:
P = a n2 / V2
or a = P V2 / n2
= (pressure ) (volume )2
( moles) 2
Therefore the units of ‘a’ are atm L2mol2
Similarly, V = n b or b = ( V / n )
Therefore , the units of ‘b’ are L mol 1
Exceptional behaviour of H2 and He
The behaviour of H2 and He is exceptional because the compressibility factor always increases with increase in pressure. This is due to the fact that ‘a’ for hydrogen and helium are very small indicating that forces of attraction in these gases are very weak. Therefore, (an2/ V2) is negligible at all pressures so that Z is always greater than one.
Problems
54. Calculate the pressure exerted by 8.5 g of ammonia contained in 0.5 L vessel at 300 K. For ammonia a = 4 atm L2 mol2 ; b = 0.036 L mol1.
55. Calculate the pressure in atmosphere exerted by 2 moles of chlorobenzene vapours confined to 10 L at 298 K using
(a) the ideal gas equation and
(b) the van der Waal’s equation. a = 25.43 L2 atm mol2 ;
b = 0.1453 L mol1.
LIQUEFACTION OF GASES AND CRITICAL CONSTANTS
All gases can be condensed into liquids at sufficiently low temperatures, however, carbon dioxide condenses even at room temperature under high pressure. Thomas Andrew noted that carbon dioxide can be liquefied below 31.1C by increasing pressure. It could not be liquefied above 31.1C inspite of high pressure. This led him to call 31.1C as the critical temperature, Tc, for carbon dioxide. The Fig shows the isotherms of carbon dioxide gas obtained by plotting Andrew’s data.
Isotherms of CO2 and critical temperature
The minimum pressure necessary to liquefy any gas at its critical temperature is called the critical pressure, Pc, and the corresponding volume occupied by one mole of the gas is called critical volume , Vc.
At 50C, the isotherm for carbon dioxide looks similar to that for an ideal gas. As the temperature is lowered the deviation from the expected theoretical curve becomes more and more pronounced . At at a low temperature say 21C the isotherm ABCD consists of three parts. The volume of the gas decreases along AB as pressure increases. Along the horizontal portion BC there is a considerable change in volume with no change in pressure, indicating the process of liquefaction. At C, when liquefaction is complete the isotherm rises steeply as there is very little change in volume of the liquid as pressure increases. At 31.1C the isotherm has a very small flat portion, virtually reduced to a point F. Above 31.1C under all pressures it remains in gaseous state. Generally gases below their critical temperatures are called vapours. Critical constants for some common substances are given in the Table.
Gas Pc atm Vc mol dm3 Tc , K Z =PCVc/nRTc
He 2.3 57.8 5.3 0.306
H2 12.8 65.0 33.2 0.304
Ne 26.9 41.7 44.4 0.302
N2 33.6 90.1 126.1 0.291
O2 50.3 74.4 154.5 0.302
CO2 72.7 95.0 304.2 0.275
H2O 218.0 55.6 647.3 0.227
NH3 112.0 72.0 405.5 0.243
CH4 45.8 99.0 191.0 0.290
C2H6 48.2 139.0 305.5 0.267
C2H4 50.5 124.0 417.2 0.275
At critical point the densities of a substance in gaseous and liquid states are same. There is no distinction between the gaseous state and no second phase is formed irrespective of the pressure of the system.
Fluids above the critical temperatures are known as critical fluids which dissolve many organic substances. These are used for speedy separation of a mixture into its components. Catbon dioxide above 31.1C and above 600 bar pressure has a density around 1 g cm3 and is used to remove caffeine from coffee beans, instead of using chlorofluorocarbons, which are not environmetal friendly.
LIQUEFACTION OF GASES
Presence of intermolecular forces between gas molecules suggests that all gases can be liquefied if subjected to high pressure and low temperatures. Discovery of critical phenomenon by Andrews in 1861 showed that gases cannot be liquefied by the application of pressure alone ; they must be first cooled below critical temperature and then subjected to adequate pressures to cause liquefaction. The principles involved in liquefaction are :
(i) A gas must be at or below its critical temperature. Lower the temperature below the critical value, easier will be the liquefaction and less would be the pressure for liquefaction : and
(ii) The gas is cooled either by doing external work or by expanding against the internal forces of molecular attractions.
The low temperature for liquefaction of gases may be attained by following techniques.
(a) Use of freezing mixtures.
(b) Cooling by Joule-Thomson effect.
(c) Cooling by adiabatic expansion involving mechanical work.
(d) Cooling by adiabatic demagnetisation.
1. LINDE’S METHOD
This method makes use of Joule-Thomson effect and is used for the liquefaction of air. The apparatus used is shown in Figure.
Linde’s method for liquefaction of air
The pure and dry air is introduced into a compressor , where it is compressed to about 200 atmospheres. It is then passed through a pipe cooled by a refrigerating liquid such as liquid ammonia which removes the heat of compression. The compressed air is then passed through a spiral pipe having a jet at its end and fitted with an insulated chamber. As compressed air passes through the jet, it suffers Joule-Thomson expansion resulting in a considerable decrease in its temperature. The expanded air moves up the chamber and cools the fresh air coming through the spiral tube. It is then collected through a pipe and again sent to the compressor. The process is repeated over and again when air gets sufficiently cooled and gets liquefied.
2. CLAUDE’S METHOD
This method makes use of both Joule-Thomson effect and adiabatic expansion of the gas involving mechanical work and is more efficient as compared to Linde’s method.
The apparatus used in the method is shown in Figure.
Claude’s method for liquefaction of air
Pure and dry air is admitted in the compressor where it is compressed to about 200 atmospheres. It is then cooled by refrigerating liquid to remove the heat of compression. The compressed gas is taken to an insulated chamber through a tube. Here, it is bifurcated into two parts. One part is passed through a spiral tube having a jet at the end, where it suffers Joule-Thomson expansion and records a fall in temperature. The other part is taken to the cylinder of an engine, where it does mechanical work by pushing back the piston and gets cooled. It then enters the insulated chamber and mixes with the air coming out of the jet. It then cools the pipe carrying the incoming air. The cooled air is collected and taken into the compressor again. The entire process is repeated over and over again when the air gets sufficiently cooled and gets liquefied.
Relationship between critical constants and van der Waal’s constants
The critical constants of gases are related to their van der Waal’s constants as follows. These relations are derived from the calculations based on van der Waal’s equations.
If van der Waal’s equation is obeyed by gases at critical points, then the compressibility factor Zc,
should be equal to 3/8 or 0.375.
Problems
56. The van der Waal’s constant for HCl are a = 0.367 N m4 mol2 and b = 0.0408 x 103m3mol1. Calculate critical constants of the gas.
57. The critical temperature and critical pressure of a gas are 393 K and 50 atmospheres respectively. Calculate the van der Waal’s constants.
58. Critical temperatures of ammonia and carbon dioxide are 405.5 K and 304.10 K respectively. Which of these gases will liquefy first when you start cooling from 500 K to their critical temperature.
LIQUID STATE
The liquid state is intermediate state between gaseous state and solid state. In this state particles are close together and have quite strong inter-particle forces. Compared to solids, molecules in liquids do not occupy fixed positions showing regular patterns. Thus liquids are neither completely disordered (as gases are ) nor completely ordered (as solids are). This intermediate situation is characterized by partial order and partial disorder complicates the study of liquids. In terms of kinetic model, the nature of liquid state is described as follows:
i) There are appreciable attractive forces between the molecules.
ii) The molecules are relatively close together.
iii) The molecules are in constant random motion.
iv) The average kinetic energy of molecules in a given sample is proportional to the absolute temperature.
Properties of Liquids
1.Volume
Liquids unlike gases, have definite volume. Their volume does not depend upon the size or shape of the container. In liquids the molecules are quite close and forces of attraction between them are strong. Hence they are not quite free to occupy the whole space available to them. If the container is of larger size, the liquid remains confined to the lower part of the container, however, it can fill it because the molecules in the liquid state are still free to move around.
2. Density
The closer approach of molecules in the liquid state provides an explanation for the fact that densities of the liquids are about thousand times greater than the densities of gases under comparable conditions.
3. Compressibilty
Liquids are much less compressible than gases. This is due to the fact that very little free space is available in liquids.
4. Diffusion
Diffusion involves movement of molecules from one place to another. Like gases , liquids also diffuse, but they do so rather slowly. In liquid state molecules undergo a number of collisions with neighbouring molecules. In gases, there is little obstruction to the moving molecules because of large empty space available for movement. Thus slower diffusion of a liquid is thus easily understandable.
5. Evaporation
When a liquid is placed in an open vessel it gradually disappears because the liquid is converted into its vapours. This process is called evaporation. Molecules in the liquid phase escapes from the surface of the liquid into the space above the liquid.
Distribution of kinetic energy
Although there are strong intermolecular attractive forces which hold the molecules of the liquid together, the molecules having sufficient kinetic energy can escape to the gas phase if such molecules happen to come near the surface. In a sample, of liquid all the molecules do not have the same kinetic energy. There is a small fraction of molecules which have enough kinetic energy to overcome the attractive forces and escape into the gas phase. The Fig shows typical energy distribution for molecules of a liquid. If E corresponds to the minimum kinetic energy required to overcome attractive forces and escape, then the shaded area in the graph represents the molecules which have enough energy to overcome the attractive forces and undergo evaporation.
Evaporation causes Cooling
This is due to the reason that the molecules which undergo evaporation are high energy molecules, therefore the kinetic energy of the molecules , which are left behind is less. Since the remaining molecules have lower average kinetic energy , then the temperature must be lower. If the temperature is kept constant, the remaining liquid will have the same distribution of molecular kinetic energies and the high energy molecules will keep on escaping from the liquid into the gas phase. If the liquid is taken in an open vessel, evaporation will continue until whole of the liquid evaporates.
Factors that affect Rate of Evaporation
The factors that change the speed at which liquid evaporates are :
1. Nature of liquid
The weaker the intermolecular attractive forces in the liquid, the more rapidly evaporation occurs .For example, dimethyl ether evaporates at much faster than ethyl alcohol. A liquid which evaporate more readily is described as being the more volatile.
2. Temperature
The rate of evaporation increases with increase in temperature. At higher temperature the fraction of molecules having sufficient kinetic energy to escape from the surface increases. This results in the in increase in the rate of evaporation. The figure provides the graphic explanation for this behaviour.
3. Surface area of the liquid
Evaporation is a surface phenomenon. The high energy molecules from the liquid can go into gas phase only through surface. Therefore, greater the surface area of the liquid, the greater is the rate of evaporation.
4. Heat of evaporation
The quantity of heat required to evaporate a given liquid at constant temperature is defined as the heat of evaporation or vaporisation . The quantity of heat depends upon the strength of the forces of attraction between the molecules in the liquid. Water has a relatively high heat of vaporisation because of the presence of strong attractive forces. When one mole of water is completely vaporised at 25C , it absorbs 44,180 Joules of energy from its surroundings.
H2O(ℓ) + 44,180 Joules H2O(g)
The molar heat of vaporisation of water at 25C is thus 44.180 kJ.
VAPOUR PRESSURE
A liquid placed in an open vessel evaporates completely. If however the liquid is allowed to evaporate in a closed system, such as a stoppered bottle, evaporation starts and after some time, the level of the liquid does not change further and remains constant. This is explained as follows :
Fig 14. Attainment of Equilibrium in evaporation
of a liquid.
Molecules which evaporate from the liquid surface are confined to a limited space. These molecules may collide among themselves or with the molecules of air. In the process they are pushed back to the surface of the liquid, a process referred as condensation. At start, the rate of evaporation is much greater than the rate of condensation. But as molecules accumulate in the space above the liquid, the rate of condensation increases. Eventually , a condition is reached when rate of condensation becomes equal to the rate of evaporation. When the two opposing processes proceed at extremely the same rate, the system is said to be in a state of dynamic equilibrium ( Fig ). In such a state, there is no observable change in the system. The amount of liquid in the bottle remains constant. The molecules in the vapour phase exert pressure. The pressure of a liquid has a characteristic value at a given temperature. The number of molecules escaping from the surface of liquid increases with temperature resulting in an increase in the vapour pressure. The Figure shows the temperature dependence of vapour pressure of some liquids.
Fig. 15. Temperature dependence of
Vapour Pressure of liquids.
BOILING
When a liquid is gradually heated, the temperature of the liquid rises and its vapour pressure increases. At lower temperatures the equilibrium vapour pressure is much less than the pressure of the atmosphere acting on the liquid surface. If the temperature is increased until the vapour pressure becomes equal to the atmospheric pressure, the vapour formed with in the liquid can be freely rise through the liquid in the form of bubbles and escapes into the air. When this happens, we say the liquid is boiling. Although boiling and evaporation are similar processes, they differ in some respects. While evaporation occurs spontaneously at all temperatures boiling takes place only at a particular temperature at which the vapour pressure is equal to the pressure of the atmosphere. Another point of difference between evaporation and boiling is that evaporation takes place only at the surface of the liquid whereas boiling involves the formation of bubbles of vapour below the surface of liquid.
The temperature at which boiling occurs is called boiling point of a liquid. At this temperature, the vapour pressure of the liquid is equal to the atmospheric pressure. The boiling point therefore depends upon the atmospheric pressure. The normal boiling point is defined as the temperature at which the vapour pressure of the liquid is equal to one atmospheric pressure. Its value can be determined from the vapour pressure - temperature curve ( Fig 15 ).
A liquid may be made to boil at any desired temperature by altering the external pressure. It may be made to boil at lower temperature by decreasing the pressure. Substances which decompose at their normal boiling points are usually made to boil under reduced pressure. This principle is used in purifying less stable liquids by distillation under reduced pressure.
At high altitudes atmospheric pressure is low. Therefore liquids at high altitudes boil at lower temperatures in comparison to that at sea level. Since water boils at low temperature on hills, the pressure cooker is used for cooking food. In hospitals surgical instruments are sterilized in autoclaves in which boiling point of water is increased by increasing the pressure above the atmospheric pressure by using a weight covering the vent.
Boiling does not occur when liquid is heated in a closed vessel. On heating continuously vapour pressure increases. At first a clear boundary is visible between liquid and vapour phase because liquid is more dense than vapour. As the temperature increases more and more molecules go to vapour phase and density of vapours rises. At the same time liquid becomes less dense. It expands because molecules move apart. When density of the liquid and vapours become the same ; the clear boundary between liquid and vapours disappears. This temperature is called critical temperature.
SURFACE TENSION
Surface tension of a liquid is related to intermolecular forces. A molecule well with in the body of the liquid is attracted equally in all directions by surrounding molecules.
Fig. 16. Forces acting on a molecule
in the bulk of a liquid and at the surface.
However, a molecule, on the surface of the liquid is attracted only by molecules below and beside it (Fig 16). This creates an imbalance of forces at the surface. Consequently, molecules at the surface are pulled inward and the surface area of the liquid tends to be minimum. As a result of tendency to contract, a liquid surface behave as if it were in a state of tension. This effect is called Surface Tension, which is defined as the force in newtons acting at right angles along the surface of a liquid one meter in length. It is generally represented by and is expressed in dynes cm1 in CGS system and in J m2 or N m1 in SI system.
Surface tension accounts for the spherical shapes of liquid drops or bubbles of a gas in a liquid. It is also responsible for rise or fall of liquids in capillary tubes. For example water , rises in a capillary tube while mercury falls in a capillary. The concave meniscus we observe (while handling burettes and pipettes) also arises from the surface tension of liquids.
Surface Energy
As a result of the inward pull, surface of the liquid always tend to contract to the smallest possible surface area. In order to increase the surface area it is necessary to do work to bring molecules from bulk of the liquid on the surface against the inward attractive forces. The work required to increase the surface area by unity is called the surface energy. It is expressed in Jm-2 or Nm-1.
The surface tension is defined as the work required to enlarge the surface area by unity and is therefore frequently referred to the surface energy per unit area. The surface tension (N m1) is numerically equal to the rate of increase of surface energy with area (Jm2)
The surface tension is a characteristic property of each liquid and differs largely in different liquids. The Table lists the values of surface tension of a few liquids.
Surface Tensions of Liquids at 293 K
Liquid
Dynes cm1 N m1 x 102
Methanol 22.20 2.260
Ethanol 22.75 2.275
Acetone 23.70 2.370
Ethyl acetate 23.90 2.390
Carbon tetrachloride 26.95 2.695
Toluene 28.50 2.850
Benzene 28.85 2.850
Nitrobenzene 41.80 4.180
Water 72.80 7.280
Angle of Contact
The rise and fall of liquid levels in a container depends on the interaction between liquid surface and walls of the container. If the intermolecular forces between liquid molecules are weaker than the forces between the liquid and the solid surface, the liquid will rise and wet the solid surface. If the solid- liquid interactions are weaker than the intermolecular forces in the liquid its level will fall and the liquid will not wet the solid surface. The angle between the tangent to the liquid surface at the point of contact and the solid surface inside the liquid is known as the contact angle() for the pair of liquid and solid surface Fig 16 .
Fig 16 Contact angle for a liquid
(a) that wets the glass
(b) that does not wet the glass
The contact angle can have any value between 0 and 180. For liquids that wet the solid surface, is less than 90, while those which do not wet the solid surface, is more than 90.
Variation of Surface Tension with temperature
Surface tension decreases with increase of temperature and vanishes at critical temperature. Increase in temperature of the liquid is accompanied by an increase in the energy of the molecules ; the intermolecular forces decreases with rise of temperature. The environment of the molecules in the bulk tend to become similar to that on the surface of higher temperatures. Consequently , less work would be required to bring molecules from the bulk of the liquid on to the surface.
An equation which relates the surface tension with temperature is given by Eotvos and is known as Eotvos equation
= surface tension of the liquid
M = molecular mass of the liquid
d = density of the liquid
Tc = the critical temperature
T = temperature
K = a constant
As T approaches critical temperature, the surface tension becomes zero. At this stage the meniscus between liquid and vapour disappear.
APPLICATIONS OF SURFACE TENSION
(i) Soaps and detergents are used as cleaning agents and their cleansing actions are due to their property of lower interfacial tension between water and oily and greasy substances. It thus becomes possible to detach oil or grease from a soiled surface and bring it into finely divided state, dispersed throughout water , with surface of each globule protected by a layer of detergent ion.
(ii) Synthetic detergents on account of their strong effect of decreasing surface tension of water, are being incorporated in preparations like tooth paste, toilet creams, etc.,
(iii) Surface tension measurements may be used for elucidating molecular structure.
VISCOSITY
It is a common experience of our daily life that different liquids flow with different speeds. For example, water flows with greater speed than glycerol. Obiously some sort of internal friction is operating which checks the flow of liquids and which varies from liquid to liquid. This internal friction in the case of liquids is primarily due to forces of attraction between the molecules. If we have laminar flow of a liquid in a tube, then the
velocity of the layer just in touch with the side of the tube is zero and it increases as we proceeds towards the centre of the tube (Fig ). Thus there exists a velocity gradient between different layers of the liquid.
Parallel layers of area A in a liquid
Due to greater intermolecular attractions amongst the molecules of a liquid , the molecule moving in any one layer will tend to impede the movement of molecules in the adjacent faster moving layer. As a result, the velocity of the molecules in the faster layer decreases. Unless this decrease is prevented by applying a force along the layer in the forward direction, the velocity of the faster moving layer will go on decreasing and will ultimately become zero. At this stage the liquid will stop flowing. The internal friction which resists the flow of a liquid can be measured in terms of the tangential force which is needed to keep the speeds of different layers constant. The force ( F ) depends on the following factors:
i) It is directly proportional to A, the area of contact of two
adjacent layers.
ii) It is directly proportional to dv the velocity difference between the adjacent layers.
iii) It is inversely proportional to dx, the distance between the two adjacent layers.
The constant is known as the coefficient of viscosity or simply the viscosity of a liquid. It may be defined as the force per unit area required to maintain a velocity difference of unity between two parallel layers of liquid unit distance apart.
The unit of viscosity
The SI unit of viscosity is 1 newton second per square metre ( N s m2) = Pascal second (Pa s = 1 kg m1 s1 ).
In CGS system the unit of coefficient of viscosity is poise.
1 poise = 1 g cm1 s1 = 101 kg m1 s1 .
Poise is one tenth of the SI unit. The viscosity of most liquids are small in magnitude. These are therefore expressed in units of centipoise (102 poise) and millipoise ( 10-3 poise ). Polyhydric alcohols like glycerol have high viscosities because of the formation of a network of hydrogen bonds between molecules. The net work which extends through out the liquids makes the flow difficult. The viscosity values of some liquids are given below.
Coefficients of viscosity in centipoises (20C)
Liquid Liquid
Water 1.008 Benzene 0.647
Chloroform 0.563 Acetone 0.329
Ethyl alcohol 1.216 Acetic acid 1.229
Methyl alcohol 0.593 Nitrobenzene 2.010
Ethyl ether 0.233 Carbon tetrachloride
The viscosity is related to intermolecular forces ; stronger the forces ; higher the viscosity. Greater the viscosity, the more slowly the liquid flows. Hydrogen bonding and van der Waal’s forces are strong enough to cause high viscosity> Glass is an extremely viscous liquid> It is so viscous that many of its properties resemble solids. However, property of flow of glass can be experienced by measuring the thickness of windowpanes of old buildings. These become thicker at the bottom than at the top.
When temperature is raised , the viscosity of liquids decreases. This is because , increase in temperature increases the average kinetic energy of molecules which overcomes the attractive forces between them.
Problems
59. Which of the liquids in each of the following pairs has higher vapour pressure :
a) alcohol, glycerine b) petrol, kerosene
c) mercury , water.
60. Which one in each of the following pairs is more viscous :
a) coconut oil , castor oil
b) glycerine , kerosene
c ) soft drink, aerated water.
61. Separate portions of chloroform and water at the same temperature are poured on your hands. The chloroform feels colder. Account for this in terms of attractive forces.
62. What is the effect of temperature on :
a) density b) surface tension
c) viscosity d) vapour pressure of a liquid.
63. Explain the following :
i) The boiling point of a liquid rises on increasing pressure.
ii) Drops of liquids assume a spherical shape.
iii) The boiling point of water (373 K ) is abnormally high when compared to that of H2S ( 211.2 K ).
iv) The level of mercury in a capillary tube is lower than the level outside , when a capillary tube is inserted in mercury.
v) Liquids like ether and acetone are kept in cool places.
vi) Tea or coffee is sipped from a saucer, when it is quite hot.
64. Arrange the following solids in the order of increasing strength of attractive forces.
Naphthalene 353 K
Sodium fluoride 1272 K
Water (ice) 273 K
Phosphorus 317 K
Zinc iodide 719 K
Questions
1. What is the nature and composition of matter ?
2. State Boyle's law.
3. State Charle's law.
4. Derive the expression P V = n R T for general gas equation.
5. What is S.T.P ?
6. State Gay-Lussac's law of gaseous volumes.
7. State Avogadro's law.
8. What do you under stand by Avogado's number ?
9. Explain what is meant by 'Molar volume of a gas'.
10. State Dalton's law of partial pressures.
11. What is meant by an ideal gas ?
12. What are elastic collisions ?
13. Write a note on kinetic equation for an ideal gas.
14. Explain the term 'root mean square velocity' of gaseous molecules.
15. Deduce from kinetic theory:
i) Boyle's law ii) Charle's law
iii) Dalton's law iv) Avogadro's hypothesis.
16. Explain the term absolute zero.
17. How is centigrade temperature is related to Kelvin temperature ? What is absolute zero ?
18. What is meant by the term molefraction of a gas in gaseous mixture ?
19. Deduce the relationship between partial pressures and number of moles in a gaseous mixture.
20. What are the applications of Dalton's law of partial pressures ?
21. State and explain Graham's law of diffusion.
22. Write a note on distribution of velocities of gas molecules.
23. Deduce the relationship between various velocities of gas molecules.
24. How can you calculate the root mean square velocity of gas molecules ?
25. Which gas will diffuse faster ammonia or carbon dioxide ? What are their relative rates of diffusion ?
26. Explain the following :
i) Aerated water bottles are kept under water during summer.
ii) Liquid ammonia bottle is cooled before opening the seal.
iii) The tyre of an automobile is inflated to lesser pressure in summer than in winter.
iv) The size of a weather balloon becomes larger as it ascends into higher altitudes.
27. How does a real gas differ from ideal gas ?
28. What are the causes of deviation of real gases from ideal behaviour ?
29. Write van der Waal's equation for 1 mole of a gas.
30. How can you explain the behaviour of real gases on the basis of van der Waal's equation ?
31. What are the general characteristics of a gaseous state of matter ?
32. Give the characteristics of liquid state of matter.
33. Explain the terms evaporation and vapour pressure of a liquid.
34. Explain the term 'boiling point' of a liquid.
35. What is surface tension of a liquid ?
36. Explain the term viscosity of a liquid.
37. What is heat of vaporisation of a liquid ?
38. Why do liquids evaporate at all temperatures ?
39. Which of the liquids in each of the following pairs has higher vapour pressure ?
i) alcohol , glycerine
ii) petrol, kerosene
iii) mercury , water.
40. Which of the following pairs is more viscous :
a) coconut oil, caster oil b) glycerine, kerosene
c) soft drink , aerated drink.
41. What is the effect of temperature on :
a) density b) Surface tension c) viscosity
d) vapour pressure of a liquid.
42. Explain the following:
(a) The boiling point of a liquid rises on increasing pressure.
(b) Drops of liquid assume a spherical shape.
(c) The boiling point of water (373 K) is abnormally high , when compared to that of hydrogen sulphide (211.2 K).
(d) The level of mercury in a capillary tube is lower than the level outside, when the capillary tube is inserted in mercury.
(e) Liquids like ether and acetone are kept in cool places.
(f) Tea and coffee is sipped from a saucer, when it is quite hot.
43. What is meant by liquefaction of gases ? How can it be brought about ?
44. How do amorphous solids differ from crystalline solids ?
45. What are the different types of bonding in solids ?
46. Account for the fact that diamond is the hardest substance known ; while graphite is very soft ?
47. Account for the fact that diamond is a bad conductor of electricity ; white graphite is a good conductor.
48. Explain the following statements:
(a) Sodium chloride pieces are harder than sodium metal.
(b) Copper is ductile and malleable, but brass is not.
(c) The latent heat of fusion of solid carbon dioxide is much less than that of silicon dioxide.
(d) Water has a maximum density at 277 K.
(e) Ice floats on the surface of water near its melting point.
49. Using the equation of state PV = n R T ; show that at a given temperature density of a gas is proportional to gas pressure P.
50. Explain the physical significance of van der Waal’s parameters.
51. What is the SI unit of :
(a) Viscosity (b) surface tension (c) the quantity PV2T2 / n
52. Critical temperature for CO2 and methane are 31.1C and 81.9C respectively. Which of these have stronger intermolecular forces and why ?