32 CHEMISRY UNI 5 SAES OF MAER After studying this unit you will be able to exlain the existence of different states of matter in terms of balance between intermolecular forces and thermal energy of articles; exlain the laws governing behaviour of ideal gases; aly gas laws in various real life situations; exlain the behaviour of real gases; describe the conditions required for liquifaction of gases; realise that there is continuity in gaseous and liquid state; differentiate between gaseous state and vaours; exlain roerties of liquids in terms of intermolecular attractions. he snowflake falls, yet lays not long Its feath ry gras on Mother Earth Ere Sun returns it to the vaors Whence it came, Or to waters tumbling down the rocky sloe. INRODUCION Rod O Connor In revious units we have learnt about the roerties related to single article of matter, such as atomic size, ionization enthaly, electronic charge density, molecular shae and olarity, etc. Most of the observable characteristics of chemical systems with which we are familiar reresent bulk roerties of matter, i.e., the roerties associated with a collection of a large number of atoms, ions or molecules. For examle, an individual molecule of a liquid does not boil but the bulk boils. Collection of water molecules have wetting roerties; individual molecules do not wet. Water can exist as ice, which is a solid; it can exist as liquid; or it can exist in the gaseous state as water vaour or steam. Physical roerties of ice, water and steam are very different. In all the three states of water chemical comosition of water remains the same i.e., H 2 O. Characteristics of the three states of water deend on the energies of molecules and on the manner in which water molecules aggregate. Same is true for other substances also. Chemical roerties of a substance do not change with the change of its hysical state; but rate of chemical reactions do deend uon the hysical state. Many times in calculations while dealing with data of exeriments we require knowledge of the state of matter. herefore, it becomes necessary for a chemist to know the hysical 32 C:\ChemistryXI\Unit-5\Unit-5(4)-Lay-2.md 4..6 (Final), 7..6, 24..6
SAES OF MAER 33 laws which govern the behaviour of matter in different states. In this unit, we will learn more about these three hysical states of matter articularly liquid and gaseous states. o begin with, it is necessary to understand the nature of intermolecular forces, molecular interactions and effect of thermal energy on the motion of articles because a balance between these determines the state of a substance. 5. INERMOLECULAR FORCES Intermolecular forces are the forces of attraction and reulsion between interacting articles (atoms and molecules). his term does not include the electrostatic forces that exist between the two oositely charged ions and the forces that hold atoms of a molecule together i.e., covalent bonds. Attractive intermolecular forces are known as van der Waals forces, in honour of Dutch scientist Johannes van der Waals (837-923), who exlained the deviation of real gases from the ideal behaviour through these forces. We will learn about this later in this unit. van der Waals forces vary considerably in magnitude and include disersion forces or London forces, diole-diole forces, and diole-induced diole forces. A articularly strong tye of diole-diole interaction is hydrogen bonding. Only a few elements can articiate in hydrogen bond formation, therefore it is treated as a searate category. We have already learnt about this interaction in Unit 4. At this oint, it is imortant to note that attractive forces between an ion and a diole are known as ion-diole forces and these are not van der Waals forces. We will now learn about different tyes of van der Waals forces. 5.. Disersion Forces or London Forces Atoms and nonolar molecules are electrically symmetrical and have no diole moment because their electronic charge cloud is symmetrically distributed. But a diole may develo momentarily even in such atoms and molecules. his can be understood as follows. Suose we have two atoms A and B in the close vicinity of each other (Fig. 5.a). It may so haen that momentarily electronic charge distribution in one of the atoms, say A, becomes unsymmetrical i.e., the charge cloud is more on one side than the other (Fig. 5. b and c). his results in the develoment of instantaneous diole on the atom A for a very short time. his instantaneous or transient diole distorts the electron density of the other atom B, which is close to it and as a consequence a diole is induced in the atom B. he temorary dioles of atom A and B attract each other. Similarly temorary dioles are induced in molecules also. his force of attraction was first roosed by the German hysicist Fritz London, and for this reason force of attraction between two temorary Fig. 5. Disersion forces or London forces between atoms. 33 C:\ChemistryXI\Unit-5\Unit-5 (4)-Lay-2.md 4..6 (Final), 7..6, 24..6
34 CHEMISRY dioles is known as London force. Another name for this force is disersion force. hese forces are always attractive and interaction energy is inversely roortional to the sixth ower of the distance between two interacting articles (i.e., /r 6 where r is the distance between two articles). hese forces are imortant only at short distances (~500 m) and their magnitude deends on the olarisability of the article. 5..2 Diole - Diole Forces Diole-diole forces act between the molecules ossessing ermanent diole. Ends of the dioles ossess artial charges and these charges are shown by Greek letter delta (δ). Partial charges are always less than the unit electronic charge (.60 9 C). he olar molecules interact with neighbouring molecules. Fig 5.2 (a) shows electron cloud distribution in the diole of hydrogen chloride and Fig. 5.2 (b) shows diole-diole interaction between two HCl molecules. his interaction is stronger than the London forces but is weaker than ion-ion interaction because only artial charges are involved. he attractive force decreases with the increase of distance between the dioles. As in the above case here also, the interaction energy is inversely roortional to distance between olar molecules. Diole-diole interaction energy between stationary olar molecules (as in solids) is roortional to /r 3 and that between rotating olar molecules is Fig. 5.2 (a) Distribution of electron cloud in HCl a olar molecule, (b) Diole-diole interaction between two HCl molecules roortional to /r 6, where r is the distance between olar molecules. Besides diolediole interaction, olar molecules can interact by London forces also. hus cumulative effect is that the total of intermolecular forces in olar molecules increase. 5..3 Diole Induced Diole Forces his tye of attractive forces oerate between the olar molecules having ermanent diole and the molecules lacking ermanent diole. Permanent diole of the olar molecule induces diole on the electrically neutral molecule by deforming its electronic cloud (Fig. 5.3). hus an induced diole is develoed in the other molecule. In this case also interaction energy is roortional to /r 6 where r is the distance between two molecules. Induced diole moment deends uon the diole moment resent in the ermanent diole and the olarisability of the electrically neutral molecule. We have already learnt in Unit 4 that molecules of larger size can be easily olarized. High olarisability increases the strength of attractive interactions. Fig. 5.3 Diole - induced diole interaction between ermanent diole and induced diole In this case also cumulative effect of disersion forces and diole-induced diole interactions exists. 5..4 Hydrogen bond As already mentioned in section (5.); this is secial case of diole-diole interaction. We have already learnt about this in Unit 4. his 34 C:\ChemistryXI\Unit-5\Unit-5(4)-Lay-2.md 4..6 (Final), 7..6, 24..6
SAES OF MAER 35 is found in the molecules in which highly olar N H, O H or H F bonds are resent. Although hydrogen bonding is regarded as being limited to N, O and F; but secies such as Cl may also articiate in hydrogen bonding. Energy of hydrogen bond varies between 0 to 00 kj mol. his is quite a significant amount of energy; therefore, hydrogen bonds are owerful force in determining the structure and roerties of many comounds, for examle roteins and nucleic acids. Strength of the hydrogen bond is determined by the coulombic interaction between the lone-air electrons of the electronegative atom of one molecule and the hydrogen atom of other molecule. Following diagram shows the formation of hydrogen bond. δ+ δ δ+ δ H F H F Intermolecular forces discussed so far are all attractive. Molecules also exert reulsive forces on one another. When two molecules are brought into close contact with each other, the reulsion between the electron clouds and that between the nuclei of two molecules comes into lay. Magnitude of the reulsion rises very raidly as the distance searating the molecules decreases. his is the reason that liquids and solids are hard to comress. In these states molecules are already in close contact; therefore they resist further comression; as that would result in the increase of reulsive interactions. 5.2 HERMAL ENERGY hermal energy is the energy of a body arising from motion of its atoms or molecules. It is directly roortional to the temerature of the substance. It is the measure of average kinetic energy of the articles of the matter and is thus resonsible for movement of articles. his movement of articles is called thermal motion. 5.3 INERMOLECULAR FORCES vs HERMAL INERACIONS We have already learnt that intermolecular forces tend to kee the molecules together but thermal energy of the molecules tends to kee them aart. hree states of matter are the result of balance between intermolecular forces and the thermal energy of the molecules. When molecular interactions are very weak, molecules do not cling together to make liquid or solid unless thermal energy is reduced by lowering the temerature. Gases do not liquify on comression only, although molecules come very close to each other and intermolecular forces oerate to the maximum. However, when thermal energy of molecules is reduced by lowering the temerature; the gases can be very easily liquified. Predominance of thermal energy and the molecular interaction energy of a substance in three states is deicted as follows : We have already learnt the cause for the existence of the three states of matter. Now we will learn more about gaseous and liquid states and the laws which govern the behaviour of matter in these states. We shall deal with the solid state in class XII. 5.4 HE GASEOUS SAE his is the simlest state of matter. hroughout our life we remain immersed in the ocean of air which is a mixture of gases. We send our life in the lowermost layer of the atmoshere called trooshere, which is held to the surface of the earth by gravitational force. he thin layer of atmoshere is vital to our life. It shields us from harmful radiations and contains substances like dioxygen, dinitrogen, carbon dioxide, water vaour, etc. Let us now focus our attention on the behaviour of substances which exist in the gaseous state under normal conditions of temerature and ressure. A look at the eriodic table shows that only eleven elements 35 C:\ChemistryXI\Unit-5\Unit-5 (4)-Lay-2.md 4..6 (Final), 7..6, 24..6
36 CHEMISRY Fig. 5.4 Eleven elements that exist as gases exist as gases under normal conditions (Fig 5.4). he gaseous state is characterized by the following hysical roerties. Gases are highly comressible. Gases exert ressure equally in all directions. Gases have much lower density than the solids and liquids. he volume and the shae of gases are not fixed. hese assume volume and shae of the container. Gases mix evenly and comletely in all roortions without any mechanical aid. Simlicity of gases is due to the fact that the forces of interaction between their molecules are negligible. heir behaviour is governed by same general laws, which were discovered as a result of their exerimental studies. hese laws are relationshis between measurable roerties of gases. Some of these roerties like ressure, volume, temerature and mass are very imortant because relationshis between these variables describe state of the gas. Interdeendence of these variables leads to the formulation of gas laws. In the next section we will learn about gas laws. 5.5 HE GAS LAWS he gas laws which we will study now are the result of research carried on for several centuries on the hysical roerties of gases. he first reliable measurement on roerties of gases was made by Anglo-Irish scientist Robert Boyle in 662. he law which he formulated is known as Boyle s Law. Later on attemts to fly in air with the hel of hot air balloons motivated Jaccques Charles and Joseh Lewis Gay Lussac to discover additional gas laws. Contribution from Avogadro and others rovided lot of information about gaseous state. 5.5. Boyle s Law (Pressure - olume Relationshi) On the basis of his exeriments, Robert Boyle reached to the conclusion that at constant temerature, the ressure of a fixed amount (i.e., number of moles n) of gas varies inversely with its volume. his is known as Boyle s law. Mathematically, it can be written as ( at constant and n) (5.) =k (5.2) where k is the roortionality constant. he value of constant k deends uon the amount of the gas, temerature of the gas and the units in which and are exressed. On rearranging equation (5.2) we obtain = k (5.3) It means that at constant temerature, roduct of ressure and volume of a fixed amount of gas is constant. If a fixed amount of gas at constant temerature occuying volume at ressure undergoes exansion, so that volume becomes 2 and ressure becomes 2, then according to Boyle s law : = 2 2 = constant (5.4) = 2 2 (5.5) 36 C:\ChemistryXI\Unit-5\Unit-5(4)-Lay-2.md 4..6 (Final), 7..6, 24..6
SAES OF MAER 37 Figure 5.5 shows two conventional ways of grahically resenting Boyle s law. Fig. 5.5 (a) is the grah of equation (5.3) at different temeratures. he value of k for each curve is different because for a given mass of gas, it varies only with temerature. Each curve corresonds to a different constant temerature and is known as an isotherm (constant temerature lot). Higher curves corresond to higher temerature. It should be noted that volume of the gas doubles if ressure is halved. able 5. gives effect of ressure on volume of 0.09 mol of CO 2 at 300 K. Fig 5.5 (b) reresents the grah between Fig. 5.5(a) Grah of ressure, vs. olume, of and. It is a straight line assing through a gas at different temeratures. origin. However at high ressures, gases deviate from Boyle s law and under such conditions a straight line is not obtained in the grah. Exeriments of Boyle, in a quantitative manner rove that gases are highly comressible because when a given mass of a gas is comressed, the same number of molecules occuy a smaller sace. his means that gases become denser at high ressure. A relationshi can be obtained between density and ressure of a gas by using Boyle s law : By definition, density d is related to the mass m and the volume by the relation m d =. If we ut value of in this equation Fig. 5.5 (b) Grah of ressure of a gas, vs. able 5. Effect of Pressure on the olume of 0.09 mol CO 2 Gas at 300 K. Pressure/0 4 Pa olume/0 3 m 3 (/ )/m 3 /0 2 Pa m 3 2.0 2.0 8.90 22.40 2.5 89.2.2 22.30 3.5 64.2 5.6 22.47 4.0 56.3 7.7 22.50 6.0 37.4 26.7 22.44 8.0 28. 35.6 22.48 0.0 22.4 44.6 22.40 37 C:\ChemistryXI\Unit-5\Unit-5 (4)-Lay-2.md 4..6 (Final), 7..6, 24..6
38 CHEMISRY from Boyle s law equation, we obtain the relationshi. m d = k = k his shows that at a constant temerature, ressure is directly roortional to the density of a fixed mass of the gas. Problem 5. A balloon is filled with hydrogen at room temerature. It will burst if ressure exceeds 0.2 bar. If at bar ressure the gas occuies 2.27 L volume, uto what volume can the balloon be exanded? Solution According to Boyle s Law = 2 2 If is bar, will be 2.27 L If 2 = 0.2 bar, then 2 = bar 2.27L 2 = =.35 L 0.2 bar Since balloon bursts at 0.2 bar ressure, the volume of balloon should be less than.35 L. 5.5.2 Charles Law (emerature - olume Relationshi) Charles and Gay Lussac erformed several exeriments on gases indeendently to imrove uon hot air balloon technology. heir investigations showed that for a fixed mass of a gas at constant ressure, volume of a gas increases on increasing temerature and decreases on cooling. hey found that for each degree rise in temerature, volume of a gas increases by of the original 273.5 volume of the gas at 0 C. hus if volumes of the gas at 0 C and at t C are 0 and t resectively, then t t = 0 + 0 273.5 t t = 0 + 273.5 2 273.5+ t (5.6) 273.5 t = 0 At this stage, we define a new scale of temerature such that t C on new scale is given by = 273.5 + t and 0 C will be given by 0 = 273.5. his new temerature scale is called the Kelvin temerature scale or Absolute temerature scale. hus 0 C on the celsius scale is equal to 273.5 K at the absolute scale. Note that degree sign is not used while writing the temerature in absolute temerature scale, i.e., Kelvin scale. Kelvin scale of temerature is also called hermodynamic scale of temerature and is used in all scientific works. hus we add 273 (more recisely 273.5) to the celsius temerature to obtain temerature at Kelvin scale. If we write t = 273.5 + t and 0 = 273.5 in the equation (5.6) we obtain the relationshi = t 0 t 0 t t = (5.7) 0 0 hus we can write a general equation as follows. = 2 2 = 2 2 (5.8) =constant= k 2 (5.9) hus = k 2 (5.0) he value of constant k 2 is determined by the ressure of the gas, its amount and the units in which volume is exressed. Equation (5.0) is the mathematical exression for Charles law, which states that ressure remaining constant, the volume 38 C:\ChemistryXI\Unit-5\Unit-5(4)-Lay-2.md 4..6 (Final), 7..6, 24..6
SAES OF MAER 39 of a fixed mass of a gas is directly roortional to its absolute temerature. Charles found that for all gases, at any given ressure, grah of volume vs temerature (in celsius) is a straight line and on extending to zero volume, each line intercets the temerature axis at 273.5 C. Sloes of lines obtained at different ressure are different but at zero volume all the lines meet the temerature axis at 273.5 C (Fig. 5.6). Fig. 5.6 olume vs emerature ( C) grah Each line of the volume vs temerature grah is called isobar. Observations of Charles can be interreted if we ut the value of t in equation (5.6) as 273.5 C. We can see that the volume of the gas at 273.5 C will be zero. his means that gas will not exist. In fact all the gases get liquified before this temerature is reached. he lowest hyothetical or imaginary temerature at which gases are suosed to occuy zero volume is called Absolute zero. All gases obey Charles law at very low ressures and high temeratures. Problem 5.2 On a shi sailing in acific ocean where temerature is 23.4 C, a balloon is filled with 2 L air. What will be the volume of the balloon when the shi reaches Indian ocean, where temerature is 26. C? Solution = 2 L 2 = 26. + 273 = (23.4 + 273) K = 299. K = 296.4 K From Charles law = 2 2 2 = 2 2L 299.K 2 = 296.4 K = 2L.009 =2.08L 5.5.3 Gay Lussac s Law (Pressure- emerature Relationshi) Pressure in well inflated tyres of automobiles is almost constant, but on a hot summer day this increases considerably and tyre may burst if ressure is not adjusted roerly. During winters, on a cold morning one may find the ressure in the tyres of a vehicle decreased considerably. he mathematical relationshi between ressure and temerature was given by Joseh Gay Lussac and is known as Gay Lussac s law. It states that at constant volume, ressure of a fixed amount of a gas varies directly with the temerature. Mathematically, = constant = k 3 his relationshi can be derived from Boyle s law and Charles Law. Pressure vs temerature (Kelvin) grah at constant molar volume is shown in Fig. 5.7. Each line of this grah is called isochore. 39 C:\ChemistryXI\Unit-5\Unit-5 (4)-Lay-2.md 4..6 (Final), 7..6, 24..6
40 CHEMISRY Fig. 5.7 Pressure vs temerature (K) grah (Isochores) of a gas. 5.5.4 Avogadro Law (olume - Amount Relationshi) In 8 Italian scientist Amedeo Avogadro tried to combine conclusions of Dalton s atomic theory and Gay Lussac s law of combining volumes (Unit ) which is now known as Avogadro law. It states that equal volumes of all gases under the same conditions of temerature and ressure contain equal number of molecules. his means that as long as the temerature and ressure remain constant, the volume deends uon number of molecules of the gas or in other words amount of the gas. Mathematically we can write n where n is the number of moles of the gas. = n (5.) k 4 he number of molecules in one mole of a gas has been determined to be 6.022 0 23 and is known as Avogadro constant. You * will find that this is the same number which we came across while discussing definition of a mole (Unit ). Since volume of a gas is directly roortional to the number of moles; one mole of each gas at standard temerature and ressure (SP)* will have same volume. Standard temerature and ressure means 273.5 K (0 C) temerature and bar (i.e., exactly 0 5 ascal) ressure. hese values aroximate freezing temerature of water and atmosheric ressure at sea level. At SP molar volume of an ideal gas or a combination of ideal gases is 22.7098 L mol. Molar volume of some gases is given in (able 5.2). able 5.2 Molar volume in litres er mole of some gases at 273.5 K and bar (SP). Argon 22.37 Carbon dioxide 22.54 Dinitrogen 22.69 Dioxygen 22.69 Dihydrogen 22.72 Ideal gas 22.7 Number of moles of a gas can be calculated as follows n = M m (5.2) Where m = mass of the gas under investigation and M = molar mass hus, m = k 4 (5.3) M Equation (5.3) can be rearranged as follows : M = k 4 m = k 4 d (5.4) he revious standard is still often used, and alies to all chemistry data more than decade old. In this definition SP denotes the same temerature of 0 C (273.5 K), but a slightly higher ressure of atm (0.325 kpa). One mole of any gas of a combination of gases occuies 22.43996 L of volume at SP. Standard ambient temerature and ressure (SAP), conditions are also used in some scientific works. SAP conditions means 298.5 K and bar (i.e., exactly 0 5 Pa). At SAP ( bar and 298.5 K), the molar volume of an ideal gas is 24.789 L mol. 40 C:\ChemistryXI\Unit-5\Unit-5(4)-Lay-2.md 4..6 (Final), 7..6, 24..6
SAES OF MAER 4 Here d is the density of the gas. We can conclude from equation (5.4) that the density of a gas is directly roortional to its molar mass. A gas that follows Boyle s law, Charles law and Avogadro law strictly is called an ideal gas. Such a gas is hyothetical. It is assumed that intermolecular forces are not resent between the molecules of an ideal gas. Real gases follow these laws only under certain secific conditions when forces of interaction are ractically negligible. In all other situations these deviate from ideal behaviour. You will learn about the deviations later in this unit. 5.6 IDEAL GAS EQUAION he three laws which we have learnt till now can be combined together in a single equation which is known as ideal gas equation. At constant and n; Boyle s Law At constant and n; Charles Law At constant and ; n Avogadro Law hus, n (5.5) n =R (5.6) where R is roortionality constant. On rearranging the equation (5.6) we obtain = n R (5.7) R= (5.8) n R is called gas constant. It is same for all gases. herefore it is also called Universal Gas Constant. Equation (5.7) is called ideal gas equation. Equation (5.8) shows that the value of R deends uon units in which, and are measured. If three variables in this equation are known, fourth can be calculated. From this equation we can see that at constant temerature and ressure n moles of any gas R will have the same volume because = n and n,r, and are constant. his equation will be alicable to any gas, under those conditions when behaviour of the gas aroaches ideal behaviour. olume of one mole of an ideal gas under SP conditions (273.5 K and bar ressure) is 22.7098 L mol. alue of R for one mole of an ideal gas can be calculated under these conditions as follows : R= 5 3 3 ( 0 Pa)( 22.7 0 m ) ( mol)( 273.5 K ) = 8.34 Pa m 3 K mol = 8.34 0 2 bar L K mol = 8.34 J K mol At SP conditions used earlier (0 C and atm ressure), value of R is 8.20578 0 2 L atm K mol. Ideal gas equation is a relation between four variables and it describes the state of any gas, therefore, it is also called equation of state. Let us now go back to the ideal gas equation. his is the relationshi for the simultaneous variation of the variables. If temerature, volume and ressure of a fixed amount of gas vary from, and to 2, 2 and 2 then we can write = nr and = nr 2 2 2 2 2 = (5.9) 2 Equation (5.9) is a very useful equation. If out of six, values of five variables are known, the value of unknown variable can be calculated from the equation (5.9). his equation is also known as Combined gas law. 4 C:\ChemistryXI\Unit-5\Unit-5 (4)-Lay-2.md 4..6 (Final), 7..6, 24..6
42 CHEMISRY Problem 5.3 At 25 C and 760 mm of Hg ressure a gas occuies 600 ml volume. What will be its ressure at a height where temerature is 0 C and volume of the gas is 640 ml. Solution = 760 mm Hg, = 600 ml = 25 + 273 = 298 K 2 = 640 ml and 2 = 0 + 273 = 283 K According to Combined gas law 22 = 2 2 = 2 = 2 2 ( 760 mm Hg) ( 600 ml) ( 283 K ) ( 640 ml ) ( 298K ) = 676.6 mm Hg 5.6. Density and Molar Mass of a Gaseous Substance Ideal gas equation can be rearranged as follows: n = R Relacing n by M m, we get m M = R (5.20) d = (where d is the density) (5.2) M R On rearranging equation (5.2) we get the relationshi for calculating molar mass of a gas. R M = d (5.22) 5.6.2 Dalton s Law of Partial Pressures he law was formulated by John Dalton in 80. It states that the total ressure exerted by the mixture of non-reactive gases is equal to the sum of the artial ressures of individual gases i.e., the ressures which these gases would exert if they were enclosed searately in the same volume and under the same conditions of temerature. In a mixture of gases, the ressure exerted by the individual gas is called artial ressure. Mathematically, otal = + 2 + 3 +...(at constant, ) (5.23) where otal is the total ressure exerted by the mixture of gases and, 2, 3 etc. are artial ressures of gases. Gases are generally collected over water and therefore are moist. Pressure of dry gas can be calculated by subtracting vaour ressure of water from the total ressure of the moist gas which contains water vaours also. Pressure exerted by saturated water vaour is called aqueous tension. Aqueous tension of water at different temeratures is given in able 5.3. Dry gas = otal Aqueous tension (5.24) able 5.3 Aqueous ension of Water (aour Pressure) as a Function of emerature Partial ressure in terms of mole fraction Suose at the temerature, three gases, enclosed in the volume, exert artial ressure, 2 and 3 resectively. then, R = n (5.25) 42 C:\ChemistryXI\Unit-5\Unit-5(4)-Lay-2.md 4..6 (Final), 7..6, 24..6
SAES OF MAER 43 2 2R = n (5.26) 70.6 g = 32 g mol 3R 3 = n (5.27) where n n 2 and n 3 are number of moles of these gases. hus, exression for total ressure will be otal = + 2 + 3 R R R = n + n2 + n3 = (n + n 2 + n 3 ) R On dividing by total we get n R = total n+ n2+ n3 R n n n + n + n n = = = 2 3 where n = n +n 2 +n 3 x is called mole fraction of first gas. x (5.28) hus, = x total Similarly for other two gases we can write 2 = x 2 total and 3 = x 3 total hus a general equation can be written as i = x i total (5.29) where i and x i are artial ressure and mole fraction of i th gas resectively. If total ressure of a mixture of gases is known, the equation (5.29) can be used to find out ressure exerted by individual gases. Problem 5.4 A neon-dioxygen mixture contains 70.6 g dioxygen and 67.5 g neon. If ressure of the mixture of gases in the cylinder is 25 bar. What is the artial ressure of dioxygen and neon in the mixture? Number of moles of dioxygen = 2.2 mol Number of moles of neon 67.5 g = 20 g mol = 8.375 mol Mole fraction of dioxygen 2.2 = 2.2 + 8.375 2.2 = 0.585 = 0.2 8.375 Mole fraction of neon = 2.2 + 8.375 = 0.79 Alternatively, mole fraction of neon = 0.2 = 0.79 Partial ressure = mole fraction of a gas total ressure Partial ressure = 0.2 (25 bar) of oxygen = 5.25 bar Partial ressure of neon = 0.79 (25 bar) = 9.75 bar 5.7 KINEIC MOLECULAR HEORY OF GASES So far we have learnt the laws (e.g., Boyle s law, Charles law etc.) which are concise statements of exerimental facts observed in the laboratory by the scientists. Conducting careful exeriments is an imortant asect of scientific method and it tells us how the articular system is behaving under different conditions. However, once the exerimental facts are established, a scientist is curious to know why the system is behaving in that way. For examle, gas laws hel us to redict that ressure increases when we comress gases 43 C:\ChemistryXI\Unit-5\Unit-5 (4)-Lay-2.md 4..6 (Final), 7..6, 24..6
44 CHEMISRY but we would like to know what haens at molecular level when a gas is comressed? A theory is constructed to answer such questions. A theory is a model (i.e., a mental icture) that enables us to better understand our observations. he theory that attemts to elucidate the behaviour of gases is known as kinetic molecular theory. Assumtions or ostulates of the kineticmolecular theory of gases are given below. hese ostulates are related to atoms and molecules which cannot be seen, hence it is said to rovide a microscoic model of gases. Gases consist of large number of identical articles (atoms or molecules) that are so small and so far aart on the average that the actual volume of the molecules is negligible in comarison to the emty sace between them. hey are considered as oint masses. his assumtion exlains the great comressibility of gases. here is no force of attraction between the articles of a gas at ordinary temerature and ressure. he suort for this assumtion comes from the fact that gases exand and occuy all the sace available to them. Particles of a gas are always in constant and random motion. If the articles were at rest and occuied fixed ositions, then a gas would have had a fixed shae which is not observed. Particles of a gas move in all ossible directions in straight lines. During their random motion, they collide with each other and with the walls of the container. Pressure is exerted by the gas as a result of collision of the articles with the walls of the container. Collisions of gas molecules are erfectly elastic. his means that total energy of molecules before and after the collision remains same. here may be exchange of energy between colliding molecules, their individual energies may change, but the sum of their energies remains constant. If there were loss of kinetic energy, the motion of molecules will sto and gases will settle down. his is contrary to what is actually observed. At any articular time, different articles in the gas have different seeds and hence different kinetic energies. his assumtion is reasonable because as the articles collide, we exect their seed to change. Even if initial seed of all the articles was same, the molecular collisions will disrut this uniformity. Consequently the articles must have different seeds, which go on changing constantly. It is ossible to show that though the individual seeds are changing, the distribution of seeds remains constant at a articular temerature. If a molecule has variable seed, then it must have a variable kinetic energy. Under these circumstances, we can talk only about average kinetic energy. In kinetic theory it is assumed that average kinetic energy of the gas molecules is directly roortional to the absolute temerature. It is seen that on heating a gas at constant volume, the ressure increases. On heating the gas, kinetic energy of the articles increases and these strike the walls of the container more frequently thus exerting more ressure. Kinetic theory of gases allows us to derive theoretically, all the gas laws studied in the revious sections. Calculations and redictions based on kinetic theory of gases agree very well with the exerimental observations and thus establish the correctness of this model. 5.8 BEHAIOUR OF REAL GASES: DEIAION FROM IDEAL GAS BEHAIOUR Our theoritical model of gases corresonds very well with the exerimental observations. Difficulty arises when we try to test how far the relation = nr reroduce actual ressure-volume-temerature relationshi of gases. o test this oint we lot vs lot 44 C:\ChemistryXI\Unit-5\Unit-5(4)-Lay-2.md 4..6 (Final), 7..6, 24..6
SAES OF MAER 45 of gases because at constant temerature, will be constant (Boyle s law) and vs grah at all ressures will be a straight line arallel to x-axis. Fig. 5.8 shows such a lot constructed from actual data for several gases at 273 K. Fig. 5.8 Plot of vs for real gas and ideal gas It can be seen easily that at constant temerature vs lot for real gases is not a straight line. here is a significant deviation from ideal behaviour. wo tyes of curves are seen.in the curves for dihydrogen and helium, as the ressure increases the value of also increases. he second tye of lot is seen in the case of other gases like carbon monoxide and methane. In these lots first there is a negative deviation from ideal behaviour, the value decreases with increase in ressure and reaches to a minimum value characteristic of a gas. After that value starts increasing. he curve then crosses the line for ideal gas and after that shows ositive deviation continuously. It is thus, found that real gases do not follow ideal gas equation erfectly under all conditions. Deviation from ideal behaviour also becomes aarent when ressure vs volume lot is drawn. he ressure vs volume lot of exerimental data (real gas) and that theoretically calculated from Boyle s law (ideal gas) should coincide. Fig 5.9 shows these lots. It is aarent that at very high ressure the measured volume is more than the calculated volume. At low ressures, measured and calculated volumes aroach each other. Fig. 5.9 Plot of ressure vs volume for real gas and ideal gas It is found that real gases do not follow, Boyle s law, Charles law and Avogadro law erfectly under all conditions. Now two questions arise. (i) Why do gases deviate from the ideal behaviour? (ii) What are the conditions under which gases deviate from ideality? We get the answer of the first question if we look into ostulates of kinetic theory once again. We find that two assumtions of the kinetic theory do not hold good. hese are (a) here is no force of attraction between the molecules of a gas. (b) olume of the molecules of a gas is negligibly small in comarison to the sace occuied by the gas. If assumtion (a) is correct, the gas will never liquify. However, we know that gases do liquify when cooled and comressed. Also, liquids formed are very difficult to comress. 45 C:\ChemistryXI\Unit-5\Unit-5 (4)-Lay-2.md 4..6 (Final), 7..6, 24..6
46 CHEMISRY his means that forces of reulsion are owerful enough and revent squashing of molecules in tiny volume. If assumtion (b) is correct, the ressure vs volume grah of exerimental data (real gas) and that theoritically calculated from Boyles law (ideal gas) should coincide. Real gases show deviations from ideal gas law because molecules interact with each other. At high ressures molecules of gases are very close to each other. Molecular interactions start oerating. At high ressure, molecules do not strike the walls of the container with full imact because these are dragged back by other molecules due to molecular attractive forces. his affects the ressure exerted by the molecules on the walls of the container. hus, the ressure exerted by the gas is lower than the ressure exerted by the ideal gas. 2 an ideal = real + 2 (5.30) observed correction ressure term Here, a is a constant. Reulsive forces also become significant. Reulsive interactions are short-range interactions and are significant when molecules are almost in contact. his is the situation at high ressure. he reulsive forces cause the molecules to behave as small but imenetrable sheres. he volume occuied by the molecules also becomes significant because instead of moving in volume, these are now restricted to volume ( nb) where nb is aroximately the total volume occuied by the molecules themselves. Here, b is a constant. Having taken into account the corrections for ressure and volume, we can rewrite equation (5.7) as 2 an + 2 ( nb) = nr (5.3) Equation (5.3) is known as van der Waals equation. In this equation n is number of moles of the gas. Constants a and b are called van der Waals constants and their value deends on the characteristic of a gas. alue of a is measure of magnitude of intermolecular attractive forces within the gas and is indeendent of temerature and ressure. Also, at very low temerature, intermolecular forces become significant. As the molecules travel with low average seed, these can be catured by one another due to attractive forces. Real gases show ideal behaviour when conditions of temerature and ressure are such that the intermolecular forces are ractically negligible. he real gases show ideal behaviour when ressure aroaches zero. he deviation from ideal behaviour can be measured in terms of comressibility factor Z, which is the ratio of roduct and nr. Mathematically Z = n R (5.32) For ideal gas Z = at all temeratures and ressures because = n R. he grah of Z vs will be a straight line arallel to ressure axis (Fig. 5.0). For gases which deviate from ideality, value of Z deviates from unity. At very low ressures all gases shown Fig. 5.0 ariation of comressibility factor for some gases 46 C:\ChemistryXI\Unit-5\Unit-5(4)-Lay-2.md 4..6 (Final), 7..6, 24..6
SAES OF MAER 47 have Z and behave as ideal gas. At high ressure all the gases have Z >. hese are more difficult to comress. At intermediate ressures, most gases have Z <. hus gases show ideal behaviour when the volume occuied is large so that the volume of the molecules can be neglected in comarison to it. In other words, the behaviour of the gas becomes more ideal when ressure is very low. Uto what ressure a gas will follow the ideal gas law, deends uon nature of the gas and its temerature. he temerature at which a real gas obeys ideal gas law over an areciable range of ressure is called Boyle temerature or Boyle oint. Boyle oint of a gas deends uon its nature. Above their Boyle oint, real gases show ositive deviations from ideality and Z values are greater than one. he forces of attraction between the molecules are very feeble. Below Boyle temerature real gases first show decrease in Z value with increasing ressure, which reaches a minimum value. On further increase in ressure, the value of Z increases continuously. Above exlanation shows that at low ressure and high temerature gases show ideal behaviour. hese conditions are different for different gases. More insight is obtained in the significance of Z if we note the following derivation real Z = (5.33) nr If the gas shows ideal behaviour then R ideal = n. On utting this value of nr in equation (5.33) we have real Z = (5.34) ideal From equation (5.34) we can see that comressibility factor is the ratio of actual molar volume of a gas to the molar volume of it, if it were an ideal gas at that temerature and ressure. In the following sections we will see that it is not ossible to distinguish between gaseous state and liquid state and that liquids may be considered as continuation of gas hase into a region of small volumes and very high molecular attraction. We will also see how we can use isotherms of gases for redicting the conditions for liquifaction of gases. 5.9 LIQUIFACION OF GASES First comlete data on ressure - volume - temerature relations of a substance in both gaseous and liquid state was obtained by homas Andrews on carbon dioxide. He lotted isotherms of carbon dioxide at various temeratures (Fig. 5.). Later on it was found that real gases behave in the same manner as carbon dioxide. Andrews noticed that at high temeratures isotherms look like that of an ideal gas and the gas cannot be liquified even at very high ressure. As the temerature is lowered, shae of the curve changes and data shows considerable deviation from ideal behaviour. At 30.98 C Fig. 5. Isotherms of carbon dioxide at various temeratures 47 C:\ChemistryXI\Unit-5\Unit-5 (4)-Lay-2.md 4..6 (Final), 7..6, 24..6
48 CHEMISRY carbon dioxide remains gas uto 73 atmosheric ressure. (Point E in Fig. 5.). At 73 atmosheric ressure, liquid carbon dioxide aears for the first time. he temerature 30.98 C is called critical temerature ( C ) of carbon dioxide. his is the highest temerature at which liquid carbon dioxide is observed. Above this temerature it is gas. olume of one mole of the gas at critical temerature is called critical volume ( C ) and ressure at this temerature is called critical ressure ( C ). he critical temerature, ressure and volume are called critical constants. Further increase in ressure simly comresses the liquid carbon dioxide and the curve reresents the comressibility of the liquid. he stee line reresents the isotherm of liquid. Even a slight comression results in stee rise in ressure indicating very low comressibility of the liquid. Below 30.98 C, the behaviour of the gas on comression is quite different. At 2.5 C, carbon dioxide remains as a gas only uto oint B. At oint B, liquid of a articular volume aears. Further comression does not change the ressure. Liquid and gaseous carbon dioxide coexist and further alication of ressure results in the condensation of more gas until the oint C is reached. At oint C, all the gas has been condensed and further alication of ressure merely comresses the liquid as shown by stee line. A slight comression from volume 2 to 3 results in stee rise in ressure from 2 to 3 (Fig. 5.). Below 30.98 C (critical temerature) each curve shows the similar trend. Only length of the horizontal line increases at lower temeratures. At critical oint horizontal ortion of the isotherm merges into one oint. hus we see that a oint like A in the Fig. 5. reresents gaseous state. A oint like D reresents liquid state and a oint under the dome shaed area reresents existence of liquid and gaseous carbon dioxide in equilibrium. All the gases uon comression at constant temerature (isothermal comression) show the same behaviour as shown by carbon dioxide. Also above discussion shows that gases should be cooled below their critical temerature for liquification. Critical temerature of a gas is highest temerature at which liquifaction of the gas first occurs. Liquifaction of so called ermanent gases (i.e., gases which show continuous ositive deviation in Z value) requires cooling as well as considerable comression. Comression brings the molecules in close vicinity and cooling slows down the movement of molecules therefore, intermolecular interactions may hold the closely and slowly moving molecules together and the gas liquifies. It is ossible to change a gas into liquid or a liquid into gas by a rocess in which always a single hase is resent. For examle in Fig. 5. we can move from oint A to F vertically by increasing the temerature, then we can reach the oint G by comressing the gas at the constant temerature along this isotherm (isotherm at 3. C). he ressure will increase. Now we can move vertically down towards D by lowering the temerature. As soon as we cross the oint H on the critical isotherm we get liquid. We end u with liquid but in this series of changes we do not ass through two-hase region. If rocess is carried out at the critical temerature, substance always remains in one hase. hus there is continuity between the gaseous and liquid state. he term fluid is used for either a liquid or a gas to recognise this continuity. hus a liquid can be viewed as a very dense gas. Liquid and gas can be distinguished only when the fluid is below its critical temerature and its ressure and volume lie under the dome, since in that situation liquid and gas are in equilibrium and a surface searating the two hases is visible. In the absence of this surface there is no fundamental way of distinguishing between two states. At critical temerature, liquid asses into gaseous state imercetibly and continuously; the surface searating two hases disaears (Section 5.0.). A gas below the critical temerature can be liquified by alying ressure, and is called vaour of the substance. Carbon dioxide gas below its 48 C:\ChemistryXI\Unit-5\Unit-5(4)-Lay-2.md 4..6 (Final), 7..6, 24..6
SAES OF MAER 49 critical temerature is called carbon dioxide vaour. Critical constants for some common substances are given in able 5.4. able 5.4 Critical Constants for Some Substances Problem 5.5 Gases ossess characteristic critical temerature which deends uon the magnitude of intermolecular forces between the gas articles. Critical temeratures of ammonia and carbon dioxide are 405.5 K and 304.0 K resectively. Which of these gases will liquify first when you start cooling from 500 K to their critical temerature? Solution Ammonia will liquify first because its critical temerature will be reached first. Liquifaction of CO 2 will require more cooling. 5.0 LIQUID SAE Intermolecular forces are stronger in liquid state than in gaseous state. Molecules in liquids are so close that there is very little emty sace between them and under normal conditions liquids are denser than gases. Molecules of liquids are held together by attractive intermolecular forces. Liquids have definite volume because molecules do not searate from each other. However, molecules of liquids can move ast one another freely, therefore, liquids can flow, can be oured and can assume the shae of the container in which these are stored. In the following sections we will look into some of the hysical roerties of the liquids such as vaour ressure, surface tension and viscosity. 5.0. aour Pressure If an evacuated container is artially filled with a liquid, a ortion of liquid evaorates to fill the remaining volume of the container with vaour. Initially the liquid evaorates and ressure exerted by vaours on the walls of the container (vaour ressure) increases. After some time it becomes constant, an equilibrium is established between liquid hase and vaour hase. aour ressure at this stage is known as equilibrium vaour ressure or saturated vaour ressure.. Since rocess of vaourisation is temerature deendent; the temerature must be mentioned while reorting the vaour ressure of a liquid. When a liquid is heated in an oen vessel, the liquid vaourises from the surface. At the temerature at which vaour ressure of the liquid becomes equal to the external ressure, vaourisation can occur throughout the bulk of the liquid and vaours exand freely into the surroundings. he condition of free vaourisation throughout the liquid is called boiling. he temerature at which vaour ressure of liquid is equal to the external ressure is called boiling temerature at that ressure. aour ressure of some common liquids at various temeratures is given in (Fig. 5.2). At atm ressure boiling temerature is called normal boiling oint. If ressure is bar then the boiling oint is called standard boiling oint of the liquid. Standard boiling oint of the liquid is slightly lower than the normal boiling oint because bar ressure is slightly less than atm ressure. he normal boiling oint of water is 00 C (373 K), its standard boiling oint is 99.6 C (372.6 K). At high altitudes atmosheric ressure is low. herefore liquids at high altitudes boil at lower temeratures in comarison to that at sea level. Since water boils at low temerature on hills, the ressure cooker is used for cooking food. In hositals surgical 49 C:\ChemistryXI\Unit-5\Unit-5 (4)-Lay-2.md 4..6 (Final), 7..6, 24..6
50 CHEMISRY Fig. 5.2 aour ressure vs temerature curve of some common liquids. instruments are sterilized in autoclaves in which boiling oint of water is increased by increasing the ressure above the atmosheric ressure by using a weight covering the vent. Boiling does not occur when liquid is heated in a closed vessel. On heating continuously vaour ressure increases. At first a clear boundary is visible between liquid and vaour hase because liquid is more dense than vaour. As the temerature increases more and more molecules go to vaour hase and density of vaours rises. At the same time liquid becomes less dense. It exands because molecules move aart. When density of liquid and vaours becomes the same; the clear boundary between liquid and vaours disaears. his temerature is called critical temerature about which we have already discussed in section 5.9. 5.0.2 Surface ension It is well known fact that liquids assume the shae of the container. Why is it then small dros of mercury form sherical bead instead of sreading on the surface. Why do articles of soil at the bottom of river remain searated but they stick together when taken out? Why does a liquid rise (or fall) in a thin caillary as soon as the caillary touches the surface of the liquid? All these henomena are caused due to the characteristic roerty of liquids, called surface tension. A molecule in the bulk of liquid exeriences equal intermolecular forces from all sides. he molecule, therefore does not exerience any net force. But for the molecule on the surface of liquid, net attractive force is towards the interior of the liquid (Fig. 5.3), due to the molecules below it. Since there are no molecules above it. Liquids tend to minimize their surface area. he molecules on the surface exerience a net downward force and have more energy than the molecules in the bulk, which do not exerience any net force. herefore, liquids tend to have minimum number of molecules at their surface. If surface of the liquid is increased by ulling a molecule from the bulk, attractive forces will have to be overcome. his will require exenditure of energy. he energy required to increase the surface area of the liquid by one unit is defined as surface energy. Fig. 5.3 Forces acting on a molecule on liquid surface and on a molecule inside the liquid 50 C:\ChemistryXI\Unit-5\Unit-5(4)-Lay-2.md 4..6 (Final), 7..6, 24..6