CHY2018 Unit 1 Lecture - Phase Equilibria PDF

Physical Chemistry I (CHY2018) Unit 1: Phase Equilibria Prepared by: Dr. A. Redway Modified by: Ms. L. Scarlet 1  Course Information Get course material at utechonline.utech.edu.jm or Scoology.com (access code:...

Physical Chemistry I (CHY2018) Unit 1: Phase Equilibria Prepared by: Dr. A. Redway Modified by: Ms. L. Scarlet 1  Course Information Get course material at utechonline.utech.edu.jm or Scoology.com (access code: 4RDC-F4TD-C9475) Assessment Test 1 Week 6 15% Test 2 Week 12 15% Tutorial quizzes 20% Laboratory 20% Final examination 30% 2 At the end of the unit, students should be able to: Review the colligative Raoult’s Law as applied to properties of solution the vapour pressures of Theory of Ideal Solutions miscible liquids Understand one component Phase diagrams and fractional distillation, systems: vapour pressure azeotropic mixtures and diagrams. eutectic systems. The qualitative relationship Partition coefficients - between boiling point, latent immiscible Solutions heat of Vaporization and intermolecular forces. Two component systems - Recommended text: 3 mixtures of two liquids Elements of Physical Chemistry (miscible). (5th) – by Peter Atkins  What is Phase Equilibria? The study of the equilibrium which exists between or within different states of matter namely solid, liquid and gas. 4  Colligative Properties of solution Colligative properties of solutions are properties that depend upon the concentration of solute molecules or ions, but not upon the identity of the solute. In liquid solutions, the solute molecules displace some solvent molecules and so reduce the concentration of solvent. Colligative properties depend only on the ratio of solute to solvent molecules and not on the properties of the solvent or solute Colligative properties are independent of the nature of the solute. 5  Colligative Properties of solution ‘Colligative’ denotes ‘depending on the collection’. The properties are associated with changes in the entropy or disorder of the solvent. The increase in disorder is independent of the identity of the species used to bring it about the change. It is however dependent on the number of solute particles present and not their chemical identity. These properties are called colligative properties. A 0.01 mol kg−1 aqueous solution of any nonelectrolyte is expected to have the same boiling point, freezing point, and osmotic pressure. Molality (m) is defined as the number of moles of solute per kilogram of solvent 6  Activity Molality = moles of solute/1 kg of solvent The unit is m. Calculate the molality of the following solution: 20.0 g of Br2 in 40.0 g of CH2Cl2 7  Colligative Properties of solution An ideal solute has no effect on the enthalpy (H) of a solution. That is ∆Hmix = 0 An ideal solute impacts the entropy (S) by introducing a degree of disorder that is not present in the pure solvent. ΔS > 0 when two components mix to give an ideal solution. A solute has the ability to modify the physical properties of the solution. 8  Colligative Properties of solution The colligative properties of solutions are: vapor pressure depression boiling point elevation freezing point depression osmotic pressure 9 Colligative Properties of solution 10  Vapour Pressure Depression When a nonvolatile solute is added to a solvent, the vapor pressure of the solvent above the solution is lower than the vapor pressure above the pure solvent. This occurs because the presence of the solute molecules at the surface of the solution reduces the surface area available for the solvent to escape the solution into the gas phase. So, the reduction in vapor pressure of the solvent is proportional to the number of solute particles (molecules or ions) in solution. 11  Vapour Vapour pressures of pressures of pure water sugar solution 12  Vapor Pressure Depression This relationship is described by Raoult’s law, which states that the vapor pressure of the solvent (Psolv) is directly proportional to the mole fraction of solvent (χsolv) in the solution; Psolv = χ solv Po solv where Posolv is the vapour pressure of the pure solvent. So according to Raoult’s law; when χsolv = 1, Psolv = Po solv 13 when χsolv < 1, Psolv < o  Vapour Pressure Depression Remember that although the chemical nature of the solute does not affect the vapor pressure depression, the number of solute species does. The mole fraction of the solvent must include all the species in solution. For sucrose, χ = nsolv/(nsolv+nsucrose) For NaCl, χ = nsolv/(nsolv+ 2nNaCl). 14  Boiling Point Elevation The normal boiling point of any liquid is the point where its vapor pressure reaches 1 atm. Because of the vapor pressure depression, when the solvent contains a nonvolatile solute, the solution will have a vapor pressure less than 1 atm at the normal boiling temperature. So, in order to reach a vapor pressure of 1 atm, the solution must be raised to a temperature higher than the normal boiling point. The boiling point elevation is calculated from a form of Raoult’s law except that the amount of solute particles is expressed as a molality of solute instead of a mole fraction of solvent. 15 Normal Melting and Boiling Normal melting and boiling points points The normal melting and boiling points are those when the pressure is 1 atmosphere. These can be found from the phase diagram by drawing a line across at 1 atmosphere pressure.  Boiling Point Elevation Molality is used for the concentration of solute instead of molarity because it is not affected by changes in temperature. The increase in boiling point of the solution (ΔTsoln) is directly proportional to the concentration (in molality) of the nonvolatile solute in a solvent; ΔTsoln = Kb m where Kb is the molal boiling point elevation constant of the solvent and msolute is the molal concentration of the solute species. solute The constant Kb is proportional to the heat of vaporization of the solvent, which varies depending on the strength of the intermolecular interactions between the solvent molecules. So, Kb has a specific value depending on the identity of the solvent. Δtsoln is added to the normal boiling point of the solvent. 17  Freezing Point Depression The freezing point of a pure liquid is the temperature at which the molecules begin to cluster to form a crystal lattice. Since the freezing point is also the melting point, at this temperature there is a dynamic equilibrium where the rate of freezing equals the rate of melting. While some of the solvent molecules cluster together to form a pure solvent crystal lattice, the liquid solution becomes more concentrated. According to Le Chatelier’s principle, the dynamic equilibrium will tend to shift in the direction of melting to correct the concentration difference between the pure solid and the solution. 19  Freezing Point Depression So, the rate of freezing proceeds slower than the rate of melting, and in order for the dynamic equilibrium to be reestablished, the freezing must occur at a lower temperature for the solution than for the pure solvent. The freezing point depression of a solution is proportional to the molality of the solute species in the same way as for the boiling point elevation; ΔTsoln = Kf m where Kf is the solute molal freezing point depression constant of the solvent, which depends on the strength of the intermolecular interactions between the solvent molecules and so depends on the identity of the solvent. Δtsoln is subtracted from the normal freezing point of the solvent. 20  Freezing Point Depression Freezing point depression is used in many everyday applications. For example, salting of roadways takes advantage of this effect to lower the freezing point of ice in cold weather so that it will form at lower than normal temperatures. The maximum depression of the freezing point using NaCl is about 18°C (0°F), so if the ambient temperature is expected to drop below this limit calcium chloride can be used instead. Since CaCl2 dissolves to give three ions instead of two, it will result in a maximum freezing point depression of 27°C. 21  Freezing Point Depression Another everyday practical application of freezing point depression as well as boiling point elevation is the use of ethylene glycol, a nonvolatile alcohol, in automobile cooling systems. Ethylene glycol lowers the freezing point of the water-ethylene glycol solution so that it will not freeze in winter months in most climates. It also raises the boiling point of the coolant mixture to prevent engine overheating in hot weather. 22 Boiling point elevation and freezing point depression 23  Activity What is the boiling point and freezing point for a 0.501 m solution of glucose? Kb = 0.51oC/m; Kf = 1.86 oC/m Recall: ΔTsoln = Kf m solute ΔTsoln = Kb m solute 24  Osmotic Pressure Osmosis is the process in which a liquid passes through a semipermeable membrane whose pores are large enough to permit the passage of solvent molecules, but are too small for the larger solute molecules to pass through. Normally, in an aqueous solution the transport of solvent through a semipermeable membrane obeys Le Chatelier’s principle, flowing from an area of low solute concentration (high solvent concentration) to an area of high solute concentration (lower solvent concentration). 25  Osmotic Pressure Pressure must be applied to the area of higher concentration to prevent the flow of water entering. Osmotic pressure is the minimum pressure which needs to be applied to the solution to prevent the inward flow of water across the semipermeable membrane. It is also defined as the measure of the tendency of a solution to take in water by osmosis. 26  Osmotic Pressure The osmotic pressure (Π) of a solution is calculated as; Π = MRT where M is the molar concentration of the dissolved species, R is the ideal gas constant, and T is the temperature in Kelvin. Theoretically, since all the colligative properties are related to the concentration of solute in solution, the molar mass of the solute can be obtained by measuring one of the colligative properties of the solution, the mass of the solute, and the mass or volume of the solvent. 27  Osmotic Pressure But, measurements of vapor pressure depression and boiling point elevation are not very sensitive to changes in the solute concentration and are not usually used for molar mass determinations. The colligative properties more commonly used are measurements of freezing point depression for solvents with a large Kf and osmotic pressure. Osmotic pressure is the most sensitive to changes in solution concentration and can be used to determine the molar mass of molecules with a low water solubility such as large biomolecules. 28  Activity URL: joinmyquiz.com Game code: Lecturer will provide Click start. 29  Phase Diagram Substances can also transition from a solid directly to a gas without passing through the liquid state, called sublimation. The transition from a gas to a solid directly without passing through the liquid state is called deposition. The formation of a plasma by super heating a gas is known as ionization and the reverse transition from a plasma back to the classical gas state is known as recombination. Superfluids can be formed by super cooling any of the three classical states of matter (e.g., solids, liquids, or gases) known as coalescence. The phase changes of pure substances as a function of temperature and pressure are commonly presented as a phase diagram. 30  Phase Diagrams One Component system The red curve is the phase boundary between the solid and liquid phase and the temperature and pressure conditions where melting and freezing occur. The blue curve is the phase boundary between the liquid and gas phase and the temperatures and pressures where vaporization and condensation occur. The green curve is the phase boundary between the solid and gas phase and the temperature and pressure conditions where sublimation and deposition occur. 31  Phase Diagram The point where all three boundaries join is known as the triple point (tp) of the pure substance. The temperature and pressure of the triple point are the conditions where all three classical phases of matter can coexist simultaneously. The phase boundary between the liquid and gas phases ends at a point called the critical point (cp). The temperature at this point is known as the critical temperature (Tcr) and the pressure at this point is the critical pressure (Pcr). 32  Phase Diagram Above the critical point, the liquid and gas phases become indistinguishable. The substance becomes a supercritical fluid with properties of both gas and liquid phases. Supercritical fluids are compressible and diffuse rapidly like gases, but with densities similar to liquids. Near the critical point, a small change in pressure or temperature results in a large change in the density of the supercritical fluid. In addition, since there is no liquid-gas phase boundary above the critical point, there is no surface tension. The most common supercritical fluid is carbon dioxide, which is used for the decaffeination of coffee beans and as a replacement for organic solvents in “greener” dry cleaning procedures. 33 Phase Diagram H2 O CO2  Phase Rule F = C - P +2 Degrees of freedom (f) is the number of external variables that can be changed independently without disturbing the number of phases in equilibrium e.g. pressure, temperature and composition Components is a chemically independent constituent of a system. Number of component (c) is the minimum number of independent species necessary to define the composition of all the phase present in the system. Phase (p) is the state of matter that is uniformed throughout in chemical composition and physical state. 35  Phase Rule For a one-component system (eg: pure water):  C = 1, therefore phase rule simplifies to F = 3 - P  When only one phase present, F = 2 (which implies p and T can be varied independently)  When two phases are in equilibrium F = 1 (p is not freely variable with a set T)  When three phases are in equilibrium F = 0 (invariable) – Triple point For two-component systems (binary mixtures):  C=2, therefore F = 4 – P  If p is kept constant, then F’ = 3 – P (F’ is the number of degrees of freedom remaining) 36  Raoult’s law The partial vapour pressure of a substance in a liquid mixture is proportional to its mole fraction in the mixture and its vapour pressure when pure: pJ = xJ pJ* pJ* is the vapour pressure of the pure substance. 37  Raoult’s law The molecular origin of Raoult’s law is the effect of the solute on the entropy of the solution. The molecules have a certain disorder and a corresponding entropy in a pure solvent. When a solute is present, the solution has a greater disorder than the pure solvent. The entropy of the solution is therefore higher than that of the pure solvent. The solution has a lower tendency to acquire an even higher entropy by the solvent vaporizing. The vapour pressure of the solvent in the solution is lower than that of the pure solvent, since the vapour pressure then represents the tendency of the system and its surroundings to reach a higher entropy. 38  Ideal Solutions An ideal solution is a hypothetical solution of a solute B in a solvent A that obeys Raoult’s law throughout the composition range from pure A to pure B. The law is most reliable when the components of a mixture have similar molecular shapes and are held together in the liquid by similar types and strengths of intermolecular forces. A mixture of benzene and toluene is a good approximation to an ideal solution. The partial vapour pressure of each component satisfies Raoult’s law reasonably well throughout the composition range from pure benzene to pure toluene. 39  Limitation of Raoult’s law Raoult's Law only works for: Ideal solutions – a solution which obeys Raoult's Law.  Only very dilute solution obeys this laws.  The forces of attraction between solvent and solute are exactly the same as between the original solvent molecules  Ideal Solutions Mixture are not perfectly ideal and all real mixtures show deviations from Raoult’s law. However, the deviations are small for the component of the mixture that is in large excess (the solvent) and become smaller as the concentration of solute decreases. In a dilute solution, each solute molecule is surrounded by nearly pure solvent. The environment is quite unlike that in the pure solute and it is very unlikely that its vapour pressure will be related in a simple manner to that of the pure solute, except when solute and solvent are very similar (such as benzene and methylbenzene). 41  Ideal Solutions However, it is found experimentally that in dilute solutions the vapour pressure of the solute is in fact proportional to its mole fraction, just as for the solvent. Unlike the solvent, though, the constant of proportionality is not in general the vapour pressure of the pure solute. Raoult’s law provides a good description of the vapour pressure of the solvent in a very dilute solution, when the solvent A is almost pure. However, we cannot in general expect it to be a good description of the vapour pressure of the solute B because a solute in dilute solution is very far from being pure. 42  Examples of ideal mixtures There is actually no such thing as an ideal mixture! However, some liquid mixtures get fairly close to being ideal. These are mixtures of two very closely similar substances. Commonly quoted examples include:  hexane and heptane  benzene and methylbenzene  propan-1-ol and propan-2-ol 43  Vapour Pressure / Composition Diagrams Suppose you have an ideal mixture of two liquids A and B. Each of A and B is making its own contribution to the overall vapour pressure of the mixture. Ptot = PA + PB Suppose you double the mole fraction of A in the mixture (keeping the temperature constant). According to Raoult's Law, you will double its partial vapour pressure. If you triple the mole fraction, its partial vapour pressure will triple - and so on. In other words, the partial vapour pressure of A at a particular temperature is proportional to its mole fraction. If you plot a graph of the partial vapour pressure of A against its mole fraction, you will get a straight line. Vapour Pressure / Composition Diagrams Now we'll do the same thing for B - except that we will plot it on the same set of axes. The mole fraction of B falls as A increases so the line will slope down rather than up. As the mole fraction of B falls, its vapour pressure will fall at the same rate.  Notice that the vapour pressure of pure B is higher than that of pure A. That means that molecules must break away more easily from the surface of B than of A. B is the more volatile liquid. To get the total vapour pressure of the mixture, you need to add the values for A and B together at each composition. The net effect of that is to give you a straight line as shown in the next diagram.  Boiling point / composition diagrams If a liquid has a high vapour pressure at a particular temperature, it means that its molecules are escaping easily from the surface. If, at the same temperature, a second liquid has a low vapour pressure, it means that its molecules aren't escaping so easily. What does that imply about the boiling points of the two liquids? There are two ways of looking at this: EITHER If the molecules are escaping easily from the surface, it must mean that the intermolecular forces are relatively weak. That means that you won't have to supply so much heat to break them completely and boil the liquid. The liquid with the higher vapour pressure at a particular temperature is the one with the lower boiling point. 49 OR Liquids boil when their vapour pressure becomes equal to the external pressure. If a liquid has a high vapour pressure at some temperature, you won't have to increase the temperature very much until the vapour pressure reaches the external pressure. On the other hand if the vapour pressure is low, you will have to heat it up a lot more to reach the external pressure. The liquid with the higher vapour pressure at a particular temperature is the one with the lower boiling point. 50 Constructing a boiling point / Composition diagram Constructing a boiling point / Composition diagram To make this diagram really useful (and finally get to the phase diagram we've been heading towards), we are going to add another line. This second line will show the composition of the vapour over the top of any particular boiling liquid. If you boil a liquid mixture, you would expect to find that the more volatile substance escapes to form a vapour more easily than the less volatile one. That means that in the case we've been talking about, you would expect to find a higher proportion of B (the more volatile component) in the vapour than in the liquid. You can discover this composition by condensing the vapour and analysing it. That would give you a point on the diagram.  Using the phase diagram If you boil a liquid mixture C1, it will boil at a temperature T1 and the vapour over the top of the boiling liquid will have the composition C2. All you have to do is to use the liquid composition curve to find the boiling point of the liquid, and then look at what the vapour composition would be at that temperature. Notice again that the vapour is much richer in the more volatile component B than the original liquid mixture was.  Suppose that you collected and condensed the vapour over the top of the boiling liquid and reboiled it. You would now be boiling a new liquid which had a composition C2. That would boil at a new temperature T2, and the vapour over the top of it would have a composition C3. You can see that we now have a vapour which is getting quite close to being pure B. If you keep on doing this (condensing the vapour, and then reboiling the liquid produced) you will eventually get pure B.  Fractional distillation of ideal mixtures of liquids  Fractional distillation of ideal mixtures of liquids azeotro Phase diagram may look different for pe a number of important cases. Maximum/minimum in boiling point curve In the case of a maximum, there is favourable interactions between the molecules which reduce the vapour pressure of the mixture (less volatile) below the ideal value. Eg: chloroform/water In the case of a minimum, there is unfavourable interactions which result in a more volatile mixture. Eg: dioxane/water 57  Problem An ideal mixture of two liquids A and B contained 1 mole of A and 4 moles of B. The vapour pressure of pure A at the temperature of the mixture was 10 kPa, and that of pure B was 12.5 kPa. (i) Calculate the partial vapour pressure of A in the mixture. (ii) Calculate the partial vapour pressure of B in the mixture. (iii) Calculate the total vapour pressure of the liquid. 58  Definitions Colligative properties of a solution depend upon the concentration of solute molecules or ions, but not upon the identity of the solute. Phase diagram is a graphical representation of the phase changes of pure substances as a function of temperature and pressure Plasma an ionized gas occurring typically at low pressures or at very high temperatures. Supercritical fluid is a substance at a temperature and pressure above its critical point where distinct liquid and gas phases do not exist. Superfluid is a state of matter which behaves like a fluid with zero viscosity 59  Definitions Triple point (tp) is the temperature and pressure where all three classical phases, solid, liquid, and gas, can coexist simultaneously Molarity (M) is defined as the number of moles of solute per liter of solution. Molality (m) is defined as the number of moles of solute per kilogram of solvent Raoult’s law is the vapor pressure of the solvent is directly proportional to the mole fraction of solvent in the solution Azeotrope is a mixture of two liquids that has a constant boiling point and composition throughout. 60  Immiscible Mixtures Mixtures in which the components do not dissolve in each other is referred to as immiscible. When liquids are immiscible, they cannot be separated by distillation, as previously discussed. Separation of immiscible liquids can be accomplished by: Solvent-solvent extraction Solid phase extraction 61  Immiscible Mixtures The distribution of a solute between two phases is an equilibrium condition described by partition theory. This is based on exactly how the analyte move from the water into an organic layer. 62  Partition Coefficient At a certain temperature, the ratio of the concentrations of a solute in each solvent is always constant. KD = Corg / Caq o KD = Partition or distribution coefficient o Corg = Concentration in organic phase o Caq = Concentration in the aqueous phase 63  Problem In extracting Compound X from a solution, the organic phase was isolated and allowed to evaporate, leaving behind 1.235 g of the solute (compound X) with a molar mass of 117.3 g/mol which was then dissolved in 10.00 mL of water. After extracting with 5.00 mL of toluene, 0.889 g of the solute is recovered in the organic phase. What is the partition coefficient of this mixture? Recall, KD = Corg / Caq 64