UNIT IV SOLUTIONS-converted

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III B.SC CHEMISTRY -PHYSICAL CHEMISTRY-I NOTES FOR FOURTH UNIT

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UNIT -V Dr.V.Sangu/Ap/Chemistry CCW-trichy Dr.V.SANGU UNIT-IV SOLUTIONS UNIT IV SOLUTIONS Liquid- liquid mixtures are also called by name solution of liquid in liquid. Solution as we know consist of a solute and a solvent. In liquid- liquid mixture solute and solvent both are in liquid phase and are volatile in nature. The properties of these mixtures depend upon the vapour pressure viscosity refractive index surface tension etc Depending upon the Miscibility of two liquids these mixtures are classified into three types: Immiscible liquid- liquid mixture: Example benzene in water kerosene in water oil in water. Partially miscible mixture: nicotine- water system phenol- water system triethylaminewater system Completely miscible mixture: Ethanol- water system benzene- acetone system RAOULT’S LAW: Raoult’s law is applicable for a solution of a liquid in a liquid Raoult’s law: At any temperature the partial pressure of a component volatile liquid of a solution is equal to the vapour pressure of the pure component multiplied by the mole fraction of that component present in the mixture. Consider a binary mixture containing two volatile liquid A and B. Let xA and xB are the mole fraction of two liquid A and B while PA and PB are the partial pressure of two liquid A and B. Hence according to When the constituent of a mixture affect the intermolecular forces or when there is a formation of a compound by the interaction of the components Raoult’s law is not applicable. HENRY’S LAW: Henry’s law is applicable for a solution of a gas in a liquid. Henry’s law: At a particular temperature the mass of a gas m dissolved in definite amount of a solvent is directly proportional to the pressure of the gas P which is in equilibrium with the solution. m k P Where k is proportionality constant or Henry’s law constant. The value of k depends upon the nature of the gas and the solvent Henry’s law is not applicable under the conditions: 1. When the solubility of a gas in a particular solvent is low. 2. When a gas undergoes association or dissociation in the solvent 3. When pressure is very large 4. When temperature is very low or very high. IDEAL LIQUID MIXTURES A solution is said to be ideal if all the constituent of a mixture obeys Raoult’s law at all temperature and concentration. Raoult’s law: And

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UNIT -V Dr.V.Sangu/Ap/Chemistry CCW-trichy Dr.V.SANGU UNIT-IV SOLUTIONS For an ideal solution enthalpy of mixing is zero ∆ 0 and volume of mixing is also zero ∆ 0. It means that final volume of the solution is equal to the sum of volume of two liquid being mixed. In ideal solution the interaction between A-B is same as the interaction between A-A and B-B which are the constituent. The partial molar volume of a constituent in an ideal solution is equal to the molar volume of the constituent when present in the pure form. For example n-hexane and n-heptane benzene and toluene carbon tetrachloride and chloroform n-butyl chloride and n- butyl bromide. Where o and are the vapour pressure of the pure liquid A and B respectively. A solution is said to be ideal if all the constituent of a mixture obeys Raoult’s law at all temperature and concentration. NON- IDEAL SOLUTION OR REAL SOLUTIONS If a solution don not obey Raoult’s law over the entire range of concentration and temperature the solution is said to be non- ideal solution. The vapour pressures of these solutions are higher or lower than the pressure obtained by using Raoult’s law. Here the enthalpy of mixing and volume of mixing is not equal to zero. In these solutions the force between A-B is different from A-A and B-B individual components. Non- ideal solutions are classified into two types: 1. Non- ideal solution showing positive deviation vapour pressure obtained is higher than calculated using Raoult’s law In the solution of component A and B the interaction between A-B is weaker than A-A and B-B interaction. Hence the vapour pressure of the solution is higher than the pressure predicted by Raoult. The enthalpy of mixing is positive. For example ethanol and hexane acetone and carbon disulphide carbon tetrachloride and benzene carbon tetrachloride and toluene 2. Non- ideal solution showing negative deviation vapour pressure obtained is lower than calculated using Raoult’s law. In the solution of component A and B the interaction between A-B is stronger than A-A and B-B interaction. Here the vapour pressure of a solution is lower than the pressure predicted by Raoult. The enthalpy of mixing is negative. For example acetone and water phenol and aniline

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UNIT -V Dr.V.Sangu/Ap/Chemistry CCW-trichy Dr.V.SANGU UNIT-IV SOLUTIONS chloroform and benzene acetic acid and pyridine. Figure represents the curve showing negative deviation. Ideal solutions Non-ideal solutions Positive deviation from Raoult’s law Negative deviation from Raoult’s law Obey Raoult’s law at every range of concentration. Do not obey Raoult’s law. Do not obey Raoult’s law ΔHmix 0 neither is evolved nor absorbed during dissolution. ΔHmix0. Endothermic dissolution heat is absorbed. ΔHmix0. Exothermic dissolution heat is evolved. ΔVmix 0 total volume of solution is equal to sum of volumes of the components. ΔVmix 0. Volume is increased after dissolution. ΔVmix 0. Volume is decreased during dissolution. P pA + pB pA 0 XA + pB 0 XB pA pA 0 XA pB pB 0 XB ∴ pA + pB pA 0 XA + pB 0 XB pA pA 0 XA pB pB 0 XB ∴ pA + pB pA 0 XA + pB 0 XB A—A A—B B—B interactions should be same i.e. ‘A’ and ‘B’ are identical in shape size and character. A—B attractive force should be weaker than A—A and B—B attractive forces. ‘A’ and ‘B’ have different shape size and character. A—B attractive force should be greater than A—A and B— B attractive forces. ‘A’ and ‘B’ have different shape size and character. Escaping tendency of ‘A’ and ‘B’ should be same in pure liquids and in the solution. ‘A’ and B’ escape easily showing higher vapour pressure than the expected value. Escaping tendency of both components ‘A’ and ‘B’ is lowered showing lower vapour pressure than expected ideally. Duhem-Margules equation Let us considered a binary solution of component A and B where and are mole fraction of component A and B in the solution. Then according to the Gibb’s Duhem equation + 0 Where and are chemical potential of component A and B respectively. Divide throught the equation by +

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UNIT -V Dr.V.Sangu/Ap/Chemistry CCW-trichy Dr.V.SANGU UNIT-IV SOLUTIONS + + + 0 + 0 We know that chemical potential 0 + Since 0 is constant Hence we can write the equation + 0 as + 0 Divide this equation by d + 0 We know that + 1 + 0 Hence − ∴ − 0 Fugacity f is replaced by pressure p is a thermodynamic statement of the relationship between the two components of a single liquid where the vapour mixture is regarded as an ideal gas: where P A and P B are the partial vapour pressures of the two constituents and x A and x B are the mole fractions of the liquid. AZEOTROPES: Azeotropes are constant boiling mixtures of solution which have same composition both in solution phase as well as in vapour phase It is difficult to separate the components of these mixtures by fractional distillation. Azeotropes have a characteristic boiling point which is either lower negative deviation or higher positive deviation than any of its constituents. Azeotropes having positive deviation are called maximum boiling point: Example azeotropes – Ethanol –water system nitric acid and water.

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UNIT -V Dr.V.Sangu/Ap/Chemistry CCW-trichy Dr.V.SANGU UNIT-IV SOLUTIONS Azeotropes having negative deviation are called minimum boiling point: Example azeotropes – HCl-H2O. HCl-H2O MAXIMUM BOILING AZEOTROPES HCl- H2O system is a two-component Azeotrope mixture. In the solution of component A and B the interaction between A-B is stronger than A-A and B-B Interaction. Here the vapour pressure of a solution is lower than the pressure predicted by Raoult. The enthalpy of mixing is negative. This system has low volatility. It possess maximum boiling point. Figure represents the boiling temperature versus composition curve of HCl- H2O system. We know that pure water boils at 100 o C and the boiling point of HCl is –85oC. Their azeotrope mixture that constitutes 20.24 of HCl and 79.76 of H2O boils at 108.5 o C and at 1atm pressure. If a solution contains less than 20.24 is distillated. HCl present in distillate the water constitute residual solution. In this case we are unable to recover the pure HCl as the residue left contain a mixture of the same composition. If a solution contains more than 20.24 is distillated HCl undergoes distillation as shown by BD the pure HCl constitute the filtrate. In this case we are able to recover the pure HCl as the residue having the same composition. ETHANOL-WATER SYSTEM MINIMUM BOILING AZEOTROPES Ethanol-H2O system is a two component Azeotrope mixture. In the solution of component A and B the interaction between A-B is weaker than A-A and B-B Interaction. Here the vapour pressure of a solution is higher than the pressure predicted by Raoult. The enthalpy of mixing is positive. This system has high volatility. It possess minimum boiling point. Figure represents the boiling temperature versus composition curve of C2H5OH- H2O system.

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UNIT -V Dr.V.Sangu/Ap/Chemistry CCW-trichy Dr.V.SANGU UNIT-IV SOLUTIONS The azeotropic mixture of ethanol and water boils at 78.13 o C and at one atmospheric pressure shown by point C. The mixture contains 95.6 of ethanolic solution in water. If a solution having composition between pure water and 95.6 ethanol undergoes distillation as shown in Figure 10 by AC ethanol 95.6 constitute the distillate while the pure water constitute the residue. If the solution having composition between water and 95.6 ethanol undergoes distillation as shown in Figure 10 by BC ethanol 95.6 and pure ethanol get separated. PARTIALLY MISCIBLE LIQUIDS The liquid mixture forming two layers which are soluble in each other to some extent are called as partially miscible liquids. The miscibility of these liquid mixtures depends on temperature. For example phenol- water system triethylamine- water system and nicotine-water system. Consolute Temperature CST: The miscibility of these liquid mixtures depends on temperature. At a particular temperature two partially miscible liquid mixtures become completely miscible. This temperature is known as critical solution temperature or consolute temperature. LOWER AND UPPER CONSOLUTE TEMPERATUTE: Consolute or critical solution temperature defined as a temperature at which two partially miscible liquid becomes completely miscible. There are two consolute temperatures: 1. Lower consolute temperature: The two liquids are completely soluble below the critical temperature. Example trimethylamine- water system 2. Upper consolute temperature: The two liquids are completely soluble above the critical temperature. Example phenol- water system. EFFECT OF IMPURITY ON CONSOLUTE TEMPERATURE We know that consolute temperature is one of the characteristic properties of a system and is affected by the presence of small amount of impurities. If impurity is soluble in any one of the liquid it will affect the miscibility decreases thereby raising the upper consolute temperature and decreasing the lower consolute temperature.

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UNIT -V Dr.V.Sangu/Ap/Chemistry CCW-trichy Dr.V.SANGU UNIT-IV SOLUTIONS The presence of sodium chloride as impurity in phenol- water system raises the upper consolute temperature. If the impurity is soluble in both the liquid the miscibility of two liquid increases thereby decreasing the upper consolute temperature and increasing the lower consolute temperature. Presence of sodium salt soap in phenol- water system lowers the upper consolute temperature. Phenol –water system: Phenol-water system is partially miscible liquid system. When phenol mixed with water they form two layers. Figure shows the variation on miscibility of two liquid with respect to temperature and composition of the two components. It is clear that with increase in temperature the miscibility of two liquid increases. At 65.8 ₀ C two liquids phenol and water get completely miscible and the corresponding temperature is known as critical solution temperature. Critical solution temperature is a characteristic property of a particular system. This system possesses upper critical solution temperature. This system possesses upper critical solution temperature. Sodium chloride is soluble in water but not in phenol. The presence of sodium chloride as impurity in phenol- water system raises the upper consolute temperature. If the impurity is soluble in both the liquid the miscibility of two liquid increases thereby decreasing the upper consolute temperature and increasing the lower consolute temperature. Presence of sodium salt soap in phenol- water system lowers the upper consolute temperature. Triethylamine-water system: In this system two liquids which are taken are trimethylamine and water. Both the liquids are allowed to mix resulting in the formation of two layers. The critical solution temperature is below 18.5⁰C and above this temperature these two liquids becomes partially miscible as shown in Figure. These systems possess lower critical solution temperature.

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UNIT -V Dr.V.Sangu/Ap/Chemistry CCW-trichy Dr.V.SANGU UNIT-IV SOLUTIONS Nicotine- water system: Nicotine and water which are partially soluble. Both the liquids are allowed to mix resulting in the formation of two layers. These liquid mixtures get completely miscible at two temperatures. These two temperatures are 60.8 ₀ C lower critical temperature and 208 o C upper critical temperature. It is Clear that when temperature range is between 60.8 o C to 208 o C the two liquids become partially Miscible as shown in Figure. IMMISCIBLE LIQUIDS STEAM DISTILLATION Principle of Steam distillation: When two partially miscible liquids one of the liquid must be water are heated to the vapour phase each constitute independently exert its vapour pressure as the function of temperature. Consequently vapour pressure of the whole system increases. The liquid starts to boil if total vapour pressure just exceed the atmospheric pressure. Distillation is a process that involves evaporation followed by condensation. In steam distillation steam is passed into a round bottom flask containing the impure organic liquid. Through steam distillation we purify the given organic liquid which is immiscible in water based on their volatility. In round bottom flask impure organic liquid containing water having non-volatile impurities is placed. Our aim is to remove the impurity and purify the organic liquid. Allow the steam to pass through the round bottom flask.

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UNIT -V Dr.V.Sangu/Ap/Chemistry CCW-trichy Dr.V.SANGU UNIT-IV SOLUTIONS Now using a burner heat the flask this leads to the formation of vapour. The vapour along with steam passes through the condenser. Condenser converting vapour phase into liquid phase. The distillate liquid produced after the process of distillation is collected in a flat bottom flask. In the flat bottom flask two layers are formed takes place. One layer is of pure organic liquid and another layer is of water. Then by using separating funnel we can separate the two liquid. In this way we purify the organic liquid. The process of steam distillation is used for the purification of phenylamine i.e. aniline and for calculating the approximate weight of an organic liquid. Steam distillation also used. Nernst distribution law – derivation: Nernst gave a generalized governing law for the distribution of a solute between two immiscible solvents. This is called Nernst’s distribution law or Nernst’s partition law or simply distributions law or Partition law. If the solute X distributes itself between two immiscible solvents A and B at constant temperature and X is in the same molecular conditions in both solvents. Then Cx is concentration of solute in solvent A and Cy concentration of solute in solvent B. KD is called distributions coefficient or Partition coefficient. Thermodynamics derivation for Nernst distribution Law: Suppose a solute A is present in two immiscible solvent 1 and 2 in contact with each other. Suppose further that its chemical potential in solvent 1 is 1 and in solvent 2 is 2 . When two phases are in equilibrium. Their chemical potential will be equal to another 1 1 0 + ln 1 for phase I 2 2 0 + ln 2 For phase II For equilibrium reaction 1 0 + ln 1 2 0 + ln 2

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UNIT -V Dr.V.Sangu/Ap/Chemistry CCW-trichy Dr.V.SANGU UNIT-IV SOLUTIONS Now at constant temperature the standard chemical potential 1 and 2 are constant. Since R a constant then a 1 a 2 constant Since solution is dilute Hendry’s law can be applicable. Hence a 1 a 2 K 1 x 1 K 2 x 2 constant 1 and 2 are the mole fraction of solute in the two phases and 1 and 2 are the Hendry’s law constant for the solute in two phases x 1 x 2 c 1 c 2 constant 1. Association of solute in one phase: Example distribution of benzoic acid in water and benzene Let us considered a solute X remain as such in solvent -1. It concentration C1 . In solvent -2 it is associated to give a molecule Xn Applying the law of chemical equilibrium we get √ If the solution is very dilute then concentration of associated molecule may be equal to C2 √ 2 C 1 √ 2 2. Dissociation of solute in one of the solvent Let us considered a solute X remain as such in solvent -1. It concentration C1 . In solvent -2 α moles of solute dissociated. Then concentration of various species are given as below X A + B C 2 1- C 2 C 2 According to the distribution law C 1 C 2 1 − α 3. Solute entre into chemical contribution with one of the solvent Let us considered a solute X remain as such in solvent -1. In solvent -2 it entre in the form of complex with solvent. x 1 x 2 c 1 c 2 This is Nernst’s distribution Law

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UNIT -V Dr.V.Sangu/Ap/Chemistry CCW-trichy Dr.V.SANGU UNIT-IV SOLUTIONS X + nS X.nS Concentration of on complexes solute is C 21-α Concentration of complex molecule is C 2α Applying the law of chemical equilibrium we get K αC 2 solvent n 1−αC 2 Colligative Properties Colligative properties are those properties which depends only upon the number of solute particles in a solution irrespective of their nature. Relative Lowering of Vapour Pressure It is the ratio of lowering in vapour pressure to vapour pressure of pure solvent. The relative lowering in vapour pressure of solution containing a nonvolatile solute is equal to the mole fraction of solute in the solution.

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UNIT -V Dr.V.Sangu/Ap/Chemistry CCW-trichy Dr.V.SANGU UNIT-IV SOLUTIONS Above expression is used to find the molecular weight of an unknown solute issolved in a given solvent. Where WB and WA mass of Solute and solvent respectively. MB and MA molecular weight of solute and solvent respectively. Ostwald and Walker method is used to determine the relative lowering of vapour pressure. Elevation in Boiling Point ΔTb Boiling point of a liquid is the temperature at which its vapour pressure becomes qual to the atmospheric pressure. As the vapour pressure of a solution containing a nonvolatile solute is lower than that of the pure solvent it boiling point will be higher than that of the pure solvent as shown in figure. The increase in boiling point is known as elevation in boiling point ΔTb ΔTb Tb – T°b ΔTb Kb m where m molality Kb is molal elevation constant or ebullioscopic constant. Molecular mass of solute can be calculated as where WB and WA mass of solute and solvent respectively. Kb has units of K / m or K kg mol -1 for water Kb 0.52 K kg mol -1 The boiling point elevation of a solution is determined by i Landsberger ‟s method ii Cottrell ’s method Depression in Freezing Point ΔTf Freezing point of a liquid is the temperature at which vapour pressure of the solvent in its liquid and solid phase become equal. As we know that vapour pressure of solution

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UNIT -V Dr.V.Sangu/Ap/Chemistry CCW-trichy Dr.V.SANGU UNIT-IV SOLUTIONS containing non-volatile solute is lower than that of pure solvent solid form gets separated out at a lower temperature as shown in the figure. This decrease in freezing point of a liquid is known as depression in freezing point. Depression in freezing point ΔTf T°f – Tf To find molecular mass of solute where Kf is molal depression constant or cryoscopic constant. Kf has units of K /m orK kg mol -1 . Ethylene glycol is usually added to water in the radiator to lower its freezing point. It is called antifreeze solution. Common salt NaCI and anhydrous CaC12 are used to clear snow on the roads because they depress the freezing point of water. The freezing point depression is determined by Beckmann method or Rast method. Calculations of molal elevation constant Kb and molal depression constant Kf Osmotic Pressure π

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UNIT -V Dr.V.Sangu/Ap/Chemistry CCW-trichy Dr.V.SANGU UNIT-IV SOLUTIONS Osmosis is the phenomenon of spontaneous flow of the solvent molecules through a semipermeable membrane from pure solvent to solution or from a dilute solution to concentrated solution. Some natural semipermeable membranes are animal bladder cell membrane etc. CU2FeCN6is an artificial semipermeable membrane which does not work in non- aqueous solutions as it dissolves in them. Osmosis may be i Exosmosis It is outward flow of water or solvent from a cell through semipermeable membrane. ii Endosmosis It is inward flow of water or solvent from a cell through a semipermeable membrane. The hydrostatic pressure developed on the solution which just prevents the osmosis of pure solvent into the solution through a semipermeable membrane is called osmotic pressure. where d density R solution constant T temperature MB molar mass of solute Osmotic pressure can be determined by anyone of the method listed below i Pfeffer ‟s method ii Berkeley and Hartley ‟s method very good method iii Morse and Frazer ‟s method On the basis of osmotic pressure -the solution can be i Hypertonic solution A solution is called hypertonic if its osmotic pressure is higher than that of the solution from which it is separated by a semipermeable membrane. When a plant cell is placed in a hypertonic solution the fluid from the plant cell comes out and cell shrinks this phenomenon is called plasmolysis. ii Hypotonic solution A solution is called hypotonic if its osmotic pressure is lower than that of the solution from which it is separated by a semipermeable membrane.

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UNIT -V Dr.V.Sangu/Ap/Chemistry CCW-trichy Dr.V.SANGU UNIT-IV SOLUTIONS iii Isotonic solution Two solutions are called isotonic if they exert the same osmotic pressure. These solutions have same molar concentration. 0.91 solution of pure NaCl is isotonic with human RBC ‟s. Two solutions are isotonic if they have the same molar concentration e.g. if x solution of X is isotonic with y solution of Y this means molar concentration of X Molar concentration of Y Osmotic pressure method is the best method for determining the molecular masses of polymers. since observed value of any other colligative property is too small to be measured with reasonable accuracy. Reverse osmosis When the external pressure applied on the solution is more than osmotic pressure the solvent flows from the solution to the pure solvent I which is called reverse osmosis. Desalination of sea water is done by reverse Osmosis. Abnormal Molecular Masses In some cases observed colligative properties deviate from their normal calculated values due to association or dissociation of molecules. As we know Colligative property ∝ 1 / MB lienee higher and lower values of molar mass is observed in case of association and dissociation respectively e.g. in benzene acetic acid gets associated so its observed molecular mass is 120. Similarly KCI undergoes dissociation in aqueous solution so its observed molecular mass is 37.25. These observed values are corrected by multiplying with van ‟t Hoff factor i. van’t Hoff Factor i It is the ratio of observed value of colligative property to the calculated value of colligative property. i observed value of colligative property / calculated value of colligative property or i normal molecular mass / observed molecular mass or i number of particles after association or dissociation / number of particles initially So to correct the observed value of molar mass van ‟t Hoff factor i must be included in different expressions for colligative properties.

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UNIT -V Dr.V.Sangu/Ap/Chemistry CCW-trichy Dr.V.SANGU UNIT-IV SOLUTIONS Degree of Dissociation α and van’t Hoff Factor i i If one molecule of a substance gets dissociated into n particles or molecules and α is the degree of dissociation then Degree of Association α and van’t Hoff Factor i If n molecules of a substance A associate to form An and α is the degree of association then

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UNIT -V Dr.V.Sangu/Ap/Chemistry CCW-trichy Dr.V.SANGU UNIT-IV SOLUTIONS van ‟t Hoff factor i 1 for solutes undergoing dissociation and it is 1 for solutes undergoing association.

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UNIT -V Dr.V.Sangu/Ap/Chemistry CCW-trichy Dr.V.SANGU UNIT-IV SOLUTIONS Phase diagram of Bismuth-Cadmium Bi-Cd system This is an example of a two component system which forms a simple eutectic. The various phases that may be present are I solid bismuth ii Solid cadmium iii Solution of bismuth in cadmium orvice versa in the molten stale ivVapour.

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